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JRS TUTORIALS, Durgakund, Varanasi – 221 005 (U.P.) Ph. No. (0542) 2311922, 2311777

JRS TUTORIALS Mathematics Problem Sheet

Inverse Trigonometric Functions 3

1. If ,coscoscos 111 π=++ −−− zyx where 1,,1 ≤≤− zyx then find the value of x2 + y2 + z2 + 2xyz. 2. Find the value of the following:

+

−+

+

−−−−

8

19cotcot

8

13tantan

7

46coscos

7

33sinsin 1111 ππππ

.

3. Prove that: (i) 2 tan-1 (cosec tan–1x – tan cot–1x) = tan–1x (ii) tan (tan–1x + tan–1y + tan–1z) = cot (cot–1x + cot–1y + cot–1z) 4. Solve the following equations:

(i) xx

x

x

x

+=

+−−

+−−−

1

1sin

1

1sin

1sin 111

(ii) Solve for x, if (tan–1x)2 + (cot–1x)2 = 8

5 2π

5. Prove that the value of expression,

( ) ( )AAA 3111 cottancottan2tan2

1tan −−− ++

for 0 < A < (π/4) is independent of A.

6. If

+−=

−+= −−

2

211

1

1sin&

1

1tan2

x

x

x

x βα for 0 < x < 1, then prove that α + β = π.

What the value of α + β will be if x > 1? 7. If X = cosec tan–1 cos cot–1 sec sin–1 a & Y = sec cot–1 sin tan–1 cosec cos–1 a; where

.10 ≤≤ a Find the relation between X & Y. Express them in terms of ‘a’. 8. Solve the following inequalities:

(i) cos–1x > cos–1x2 (iii) tan–1x > cot–1x (iv) sin–1(sin 5) > x2 – 4x (vi) arc cot2x – 5 arc cot x + 6 > 0 9. Find the sum of each of the following series:

(i) 137

1tan

75

1tan

33

1tan

1

1tan

21

21

21

21

+++

+++

+++

++−−−−

xxxxxxxx

to n terms

(ii) ∞++

+++ −

−−−− ...

21

2tan...

9

2tan

3

1tan

12

1111

n

n

(iii) ( ) ∞++

−−++−+ −−− ...

1

1sin...

6

12sin

2

1sin 111

nn

nn


10. Prove that the equation, (sin-1x)3 + (cos–1x)3 = α π3 has no roots for .32

1<α

11. (i) Find all positive integral solutions of the equation, tan–1x + cot–1y = tan–13. (ii) If ‘ k’ be a positive integer, then show that the equation: tan–1x + tan–1y = tan–1k has no non-zero integral solution. 12. Find the number of values of x satisfying the equation sin2 (2 cos–1(tan x)) = 1. 13. Find the number of real solutions of (x, y) where, |y| = sin x, y = cos–1(cos x), –2π ≤ x ≤ 2π.

14. If ( )

−++= −− 211 33

2

1

2coscos x

xxxf then find the value of

(i)

3

2f (ii)

3

1f

15. Solve the following equations:

(i) 42

1tan

2

1tan 11 π=

+++

−− −−

x

x

x

x (ii)

3

22sinsin 11 π=+ −− xx

(iii) .,1;1secsecsecsec 1111 babaabb

x

a

x ≠≥≥−=− −−−−

ANSWERS

1. 1 2. 28

45π 4. (i) 0≥x (ii) 1−=x

6. –π 7. 23 aYX −==

8. (i) [ )0,1 (iii) x > 1 (iv) ππ 292292 −+<<−− x

(vi) ( ) ( )∞∞− ,2cot3cot, ∪

9. (i) tan–1(x + n) – tan–1x (ii) 4

π (iii)

2

π

11. Two solutions (1, 2) (2, 7) 12. 2 13. 3

14. (i) 3

π (ii)

33

1cos2 1 π−− 15. (i)

2

1± (ii)2

1=x (iii) x = ab

JRS Tutorials, Durgakund, Varanasi-221005, Ph No. (0542) 2311777, 2311922, 9794757100, 317347706

JRS TUTORIALS

CHEMISTRY-20-21 MOLE CONCEPT –DPP-2(XI-IIT and PMT)

List of Anion :

H– Hydride ion ClO3 Chlorate

OH– Hydroxide ion ClO4 Perchlorate

22O Peroxide I Iodide

O 2 Superoxide IO3

Iodate

2HO Biperoxide (hydroperoxide) IO4

Periodate or meta per iodate

O Oxide Br Bromide

HCO3 (Hydrogen Carbonate) bicarbonate BrO Hypobromite

CO3 Carbonate BrO2

Bromite

C4 Methanide BrO3

Bromate

22C Acetylide BrO4

Per bromate

43C Propynide BO2

Metaborate

N3 Nitride BF4 Fluoro borate

NO2 Nitrite SiO3

2- Meta silicate

NO3 Nitrate 3

3BO Borate or orthoborate

N3 Azide 2

74OB Tetraborate

CNS Thio cyanate 26SiF

Fluoro Silicate (Silico fluoride)

CN Cyanide SnO3

Meta stanate

NC Isocyanide H2AsO4 Dihydrogen Arsenate

NH 2 Amide CrO4

Chromate

S Sulphide MnO42 Manganate

HSO3 Bisulphite (Hydrogen sulphite) MnO4

Permanganate

SO3 Sulphite 2

4MoO Molybdate

SO4 Sulphate

2CrO Chromite

HSO4 Bisulphate (Hydrogen sulphate) 2

72OCr Dichromate

S2O3 Thiosulphate Fe(CN) 4

6 Ferocyanide

S4O2

6 Tetrathionate Fe(CN)63 Ferricyanide

SO52 Per sulphate (Carro salt) anion AsO 3

3 Arsenite or ortho arsenite


2 S2O8

2 Per disulphate (Marshall salt anion) AsO43 Arsenate or arsorate

PO 34 ortho phosphate X Halide ion

HPO4 Hydrogen phosphate OX Hypohalite ion

H2PO4 Di hydrogen phosphate XO

2 Halite ion

H2 PO2 Hydrogen phosphite (hypophosphite) XO

3 Halate ion

PO3 Meta phosphate XO

4 Perhalate

P2O4

7 Pyrophosphate HCOO Formate

Cl Chloride CH3COO Acetate

ClO Hypochlorite C2O4 Oxalate

ClO2 Chlorite HC2O

4 Hydrogen oxalate

List of cations :

NH4+ Ammonium Mg2+ Magnesium Hg2+ Mercury (Mercuric)

Na+ Sodium Ca2+ Calcium Pb2+ Lead (Plumbus)

K+ Potassium Sr2+ Strontium Sn2+ Tin (Stannous)

Rb+ Rubidium Ba2+ Barium Fe2+ Iron (Ferrous)

Cs+ Cesium Zn2+ Zinc Fe3+ Iron (Ferric)

Ag+ Silver Cd2+ Cadmium Al3+ Aluminium

Cu+ Copper (Cuprous) Ni2+

Nickel(II) Cr3+ Chromium

Au+ Gold (Aurous) Cu2+ Copper (Cupric) Au3+ Gold (Auric)

22Hg Mercurous Sn4+ Tin (Stanic) Pb4+ Lead (Plumbic)


3 Writing formula of ionic compounds Case I: When cation and anion have equal charges

Na+ Cl-& NaCl

Ca2+ CO32-& CaCO3

Al3+ N3-& AlN

NH4+ NO3

-& NH4NO3

Mg2+ O2-& MgO

Fe3+ PO43-& FePO4

one positive & one negative

two positive & two negative

three positive & three negative

Case II: When cation and anion have unequal charges

Q. Write formula for following salts of sodium, calcium and aluminum

1. Chloride 2. Bromide 3. Nitrate 4. Sulphate 5. Carbonate 6. Phosphate 7. Hydrogen phosphate 8. Dihydrogen phosphate 9. Oxalate 10. Dichromate

Ans 1. NaCl, CaCl2, AlCl3 2. NaBr, CaBr2, AlBr3

3. NaNO3, Ca(NO3)2, Al(NO3)3 4. Na2SO4, CaSO4, Al2(SO4)3 5. Na2CO3, CaCO3, Al2(CO3)3 6. Na3PO4, Ca3(PO4)2, AlPO4 7. Na2HPO4, CaHPO4, Al2(HPO4)3 8. NaH2PO4,Ca(H2PO4)2, Al(H2PO4)3 9. Na2C2O4, CaC2O4, Al2(C2O4)3 10. Na2Cr2O7, CaCr2O7, Al2(Cr2O7)3

Cation Anion An+ Bm

AmBn (n : m is the simplest ratio)


4 Formula of some important compounds

Name of the compound Cation Anion Formula of the compounds Ferric tetrathionate Fe3+ S4O6

2– Fe2(S4O6)3 Aluminium thiosulphate Al3+

S2O

3 Al2(S2O3)3

Ferric sulphate Fe3+ SO 2

4 Fe2(SO4)3

Aluminium hydrogen oxalate Al3+ HC2O

4 Al(HC2O4)3

Calcium dihydrogen phosphate Ca++ H2PO

4 Ca(H2PO4)2

Barium bicarbonate Ba++ HCO 3 Ba(HCO3)2

Ferric hydrogen phosphate Fe3+ HPO 4 Fe2(HPO4)3

Radium phosphate Ra++ PO 3

4 Ra3(PO4)2

Cesium oxalate Cs+ C2O

4 Cs2C2O4

Zinc nitrate Zn++ NO

3 Zn(NO3)2

Silver chromate Ag+ CrO 4 Ag2CrO4

Potassium dichromate K+ Cr2O2

7 K2Cr2O7

Aluminium dichromate Al3+ Cr2O

7 Al2(Cr2O7)3

Lead chlorate Pb2+ ClO

3 Pb(ClO3)2

Magnesium oxalate Mg++ C2O

4 MgC2O4

Cuprous sulphide Cu+ S Cu2S Cupric arsenate Cu++

AsO 34 Cu3(AsO4)2

Ferrous phosphate Fe++ PO 3

4 Fe3(PO4)2

Ferric chromate Fe3+ CrO 2

4 Fe2(CrO4)3

Thallic perchlorate or Thallium(III)perchlorate

Tl3+ ClO

4 Tl(ClO4)3

Thallous sulphate or Thallium(I) sulphate

Tl+ SO 2

4 Tl2SO4

Mercuric nitrate Hg++ NO

3 Hg(NO3)2

Stanic oxide Sn4+ O2- SnO2

Stanic phosphate Sn4+ PO 3

4 Sn3(PO4)4

Stannous nitrate Sn2+ NO

3 Sn(NO3)2

Calcium dihydrogenphosphate Ca++ H2PO

4 Ca(H2PO4)2

Ferric Ferrocyanide Fe3+ [Fe(CN)6]4 Fe4[Fe(CN)6]3

Ferrous Ferrocyanide Fe++ [Fe(CN)6]4– Fe2[Fe(CN)6]

Ferric ferricyanide Fe3+ [Fe(CN)6]3 Fe[Fe(CN)6]

Ferrous ferricyanide Fe2+ [Fe(CN)6]3 Fe3[Fe(CN)6]2


5 Common Name, Chemical Name and Chemical Formula :

Common Name Chemical Name Chemical Formula

Alum Ammonium aluminium sulphate (NH4)2SO4.Al2(SO4)3.24H2O

Potash alum Potassium aluminium sulphate K2SO4.Al2(SO4)3.24H2O

Battery acid or oil of vitriol

Sulphuric acid H2SO4

Blue vitriol Copper sulphate CuSO4.5H2O

Baking soda Sodium bicarbonate NaHCO3

Bleaching powder Calcium chlorohypochlorite CaOCl2

Borax Sodium tetraborate Na2B4O7.10H2O

Butter of tin Stannic chloride SnCl4.5H2O

Caustic soda Sodium hydroxide NaOH

Caustic potash Potassium hydroxide KOH

Carbolic acid Phenol C6H5OH

Chile saltpetre Sodium nitrate NaNO3

Carborundum Silicon carbide SiC

Corrosive sublimate Mercuric chloride HgCl2

Calomel Mercurous chloride Hg2Cl2

Dry ice Carbon dioxide (solid) CO2

Grain alcohol (Spirit) Ethyl alcohol C2H5OH

Green vitriol Ferrous sulphate FeSO4.7H2O

Gypsum Calcium sulphate CaSO4.2H2O

Gammexane (BHC) Benzene hexachloride C6H6Cl6

Hydrolith Calcium hydride CaH2

Hypo (Antichlor) Sodium thiosulphate Na2S2O3.5H2O

Indian nitre Potassium nitrate KNO3

Limestone Calcium carbonate CaCO3

Lunar caustic Silver nitrate AgNO3

Laughing gas Nitrous oxide N2O

Litharge Lead monoxide PbO

Muriatic acid Hydrochloric acid HCl

Mohr’s salt Ferrous ammonium sulphate FeSO4(NH4)2SO4.6H2O

Milk of magnesia Magnesium hydroxide Mg(OH)2

Microcosmic salt Sodium ammonium hydrogen phosphate

Na(NH4)HPO4

Marsh gas (Damp fire) Methane CH4

Oleum Sulphuric acid (Fuming) H2S2O7

Oxone Sodium peroxide Na2O2


6 Plaster of Paris Calcium sulphate hemihydrate

CaSO4 .2

1H2O

Philosopher’s wool Zinc oxide ZnO

Phosgene Carbonyl chloride COCl2

Pearl ash Potassium carbonate K2CO3

Pyrene Carbon tetrachloride CCl4

Quick lime Calcium oxide CaO

Red lead (Minium) Lead tetra oxide Pb3O4

Slaked lime (Milk of lime) Calcium hydroxide Ca(OH)2

Sal ammoniac Ammonium chloride NH4Cl

Sugar of lead Lead acetate (CH3COO)2 Pb

Sand Silicon dioxide SiO2

TEL Tetra-ethyl lead Pb(C2H5)4

Tear gas Chloropicrin CCl3NO2

Washing soda Sodium carbonate Na2CO3.10H2O

Water glass Sodium silicate Na2SiO3

White vitriol Zinc sulphate ZnSO4.7H2O

Concept of mole

A collection of 6.022 × 1023 particles of anything is referred to as one mole e.g.

1 mole balls = 6.022 × 1023 balls

1 mole electrons = 6.022 × 1023 electrons

1 mole water = 6.022 × 1023 molecules of water (H2O)

1 mole carbon dioxide = 6.022 × 1023 molecules of carbon dioxide (CO2)

1 mole methane = 6.022 × 1023 molecules of methane (CH4)

1 mole glucose = 6.022 × 1023 molecules of glucose (C6H12O6)

1 mole oxygen = 6.022 × 1023 molecules of oxygen (O2)

1 mole nitrogen = 6.022 × 1023 molecules of nitrogen (N2)

1 mole chlorine = 6.022 × 1023 molecules of chlorine (Cl2)

1 mole hydrogen = 6.022 × 1023 molecules of hydrogen (H2)

1 mole sodium = 6.022 × 1023 atoms of sodium (Na)

1 mole silver = 6.022 × 1023 atoms of silver (Ag)

Note– All elements do not make well defined molecules e.g. hydrogen (H2), oxygen(O2), nitrogen(N2) form

diatomic molecules but metallic elements e.g. silver (Ag) and sodium (Na) etc. do not form well defined

molecules. This can be explained by using concepts of chemical bonding.

Solved problems

Que 1: Find out number of atoms in following

1. 5 moles of oxygen 2. 5 moles of water

3. 5 moles of glucose 4. 5 moles of CuSO4.5H2O

Ans:

(1) 5 moles of oxygen = 5 × 6.022 × 1023 molecules of oxygen (O2)

= 2 × 5 × 6.022 × 1023 atoms


7 = 6.022 × 1024 atoms

(2) 5 moles of water = 5 × 6.022 × 1023 molecules of water (H2O)

= 3 × 5 × 6.022 × 1023 atoms

= 90.33 × 1023 atoms

= 9.033 × 1024 atoms

(3) 5 moles of glucose = 5 × 6.022 × 1023 molecules of glucose (C6H12O6)

= 24 × 5 × 6.022 × 1023 atoms

= 722.64 × 1023 atoms

= 7.2264 × 1025 atoms

(4) 5 moles of CuSO4.5H2O = 5 × 6.022 × 1023 units of CuSO4.5H2O

= 21 × 5 × 6.022 × 1023 atoms

= 6.323 × 1025 atoms

Que 2: Find out number of carbon atoms in

1. Two thousand molecules of glucose (C6H12O6)

2. Two lakh molecules of glucose (C6H12O6)

3. Two mole molecules of glucose (C6H12O6)

Ans: Each glucose molecule contain 6 carbon atom therefore,

1. Number of carbon atoms in two thousand molecules of glucose = 6 × 2 thousands = 12 thousands

2. Number of carbon atoms in two lakh molecules of glucose = 6 × 2 lakh = 12 lakh

3. Number of carbon atoms in two mole molecules of glucose = 6 × 2 moles = 12 moles

Que 3: Find out number of electrons in 20 moles of water

Ans: Number of electron in one molecule of water

= Number of electron in two hydrogen atoms + Number of electron in one oxygen atom

= 2 + 8 = 10

20 mole of water = 20 6.022 1023 molecule

= 10 20 6.022 1023 electrons


8 Practice problems

1. Find out number of atoms in following

A. 25 moles of nitrogen B. 0.24 moles of methane

C. 1.2 moles of glucose D. 200 milimoles of water

Hint: 1 mole = 1000 millimoles

2. Convert following into moles

A. 3.011 × 1023 molecules of water B. 1.2044 × 1025 molecules of water

C. 3.011 × 1020 molecules of oxygen D. 2.4088 × 1022 molecules of nitrogen

3. Find out number of electrons in following

A. 6.022 × 103 molecules of water B. 10 moles of water

C. 0.0024 moles of carbon dioxide D. 400 milimoles of oxygen

Answers

1. A. 25 2 NA B. 0.24 5 NA C. 1.2 24 NA D. 200 10–3 3 NA

2. A. 0.5 B. 20 C. 5 × 10–4 D. 0.04

3. A. 6.022 × 104 B. 10 ×10 × 6.022 × 1023

C. 3.17 × 1022 D. 3.85 × 1024 ]

Atomic masses of common elements

Element Mass Element Mass

H 1 S 32

C 12 Cl 35.5

N 14 Ca 40

O 16 Mn 55

Na 23 Fe 56

Mg 24 Cu 63.5

Al 27 Ag 108

P 31 S 32

Unit of the atomic mass The above atomic masses can be expressed in two units (1). amu per atom and (2). gram per mole

Ex1. Atomic mass of carbon = 12 amu for one atom = 12 gram for one mole atoms

Ex2. Atomic mass of sodium = 23 amu for one atom = 23 gram for one mole atoms


9 Relation between amu and gram

1 gram = 6.022 × 1023 amu

1 amu = 2310022.6

1

gram = 1.66 × 10-24 gram

Definition of amu (Atomic Mass Unit): 1 amu is defined as 1/12th of mass of carbon atom i.e.

12

atomcarbononeofmassamu1

Solved problems

Que 1: What is mass of five sodium atoms in amu

Ans: Mass of one sodium atom = 23 amu

Mass of five sodium atoms = 5 × 23 amu = 115 amu

Que 2: Find out number of atoms of magnesium in 1800 amu magnesium.

Ans: Mass of one Mg atom = 24 amu

Number of Mg atoms in 1800 amu = 1800/24 = 75 atoms

Que 3: Find out mass of one Mg atom in gram

Ans: Mass of one Mg atom = 24 amu = 24 × (1.66 × 10-24 gram) = 39.84 × 10-24 gram

Molecular mass and formula mass

Since we know the atomic masses of the elements, we can find out molecular mass of a compound can be

obtained by adding the mass of atoms present in its formula

Ex 1: Molecular mass of water (H2O)

= mass of two hydrogen atoms + mass of one oxygen atom

= 2 × 1 + 16 × 1

= 2 + 16

= 18

Ex 2: Molecular mass of glucose (C6H12O6)

mass of six carbon atom + mass of twelve hydrogen atoms + mass of six oxygen atoms

= 6 × 12 + 12 × 1 + 6 × 16

= 72 + 12 + 96

= 180

Ex 3: Formula mass of sodium carbonate (Na2CO3)

= mass of two sodium atom + mass of one carbon atom + mass of three oxygen atoms

= 2 × 23 + 12 + 3 × 16

= 106

Ex 4: Formula mass of sodium carbonate deca–hydrate (Na2CO3. 10 H2O) = mass of Na2CO3 + mass of 10 H2O molecules = 106 + 10 × 18 = 286

Unit of molecular mass?

Unit of molecular mass of molecule will be same as that of atomic mass thus when we calculate that

molecular mass of water is 18 it means

Mass of one molecule of water (H2O) = 18 amu


10 Mass of one mole molecules of water (H2O) = 18 gram

Solved problems Que 1: Find out mass of 120 molecules of water in amu Ans: Mass of one molecule of water (H2O) = 18 amu

Mass of 120 molecule of water (H2O) = 120 ×18 amu = 2160 amu Que 2: What should be mass of one molecule of water in gram Ans: Mass of one molecule of water (H2O) = 18 amu = 18 × (1.66 × 10-24 gram) = 29.88 × 10-24 gram

Que 3: Find out number of electrons in 90 amu of water

Ans: 90 amu of water = (90/18) molecules of water

= 5 molecules

= 5 × 10 electrons [Each molecule of water contains 10 electrons]

= 50 electrons

Inter conversion of mass and mole

Molar mass: It is defined as mass of one mole substance. Since molar atomic masses of elements are known

in literature we can find out the molar mass of a substance by using its chemical formula.

Relation between number of moles and molar mass

Solved problems

Que 1: Find out number of moles in 0.0036 gram of water?

Ans:

Que 2: Find out number of moles in 0.072 gram of glucose?

Ans:

Number of moles of waterMass of water

Molar mass of water=

0.0036 g

18 g mole-1= = 0.0002 mole

Number of moles of glucoseMass of glucose

Molar mass of glucose=

0.072 g

180 g mole-1= = 0.0004 mole


11 Que 3: Find mass of 0.14 mole of glucose?

Ans: Number of moles of glucose = Mass of glucose / molar mass of glucose

Mass of glucose = Number of moles of glucose × Molar mass of glucose

= 0.14 mole × 180 gram mole-1

= 25.2 gram

Inter conversion of volume and mole

Molar volume: It can be defined as volume of one mole substance. For ideally behaving gases molar

volume is 22.4 L at STP. Here STP stand for standard temperature (273.15 K) and pressure (1 atm). But

roughly in calculations we use 273 K as the standard temperature. For example if we take 1 mole of CO2 and

1 mole of CH4, both will will occupy nearly 22.4 L at STP.

Relation between number of moles and molar volume

Solved problems

Que 1: Find out number of moles of CH4 in 5.6 L of CH4 at STP.

Ans:

Que 2: Find out total number of moles of atoms in 2.8 L of CH4 at STP.

Ans:

Que 3: Find out volume of 10 moles methane at STP.

Ans: Volume of 1 mole methane at STP = 22.4 L

Volume of 10 mole methane at STP = 10 × 22.4 L = 224 L

Moles of CH4Volume of CH4 at STP

Molar volume of CH4 at STP=

2.8 L

22.4 L mole-1= = 0.125 mole

= 5 × 0.125 moles

Since each CH4 molecule contains f ive atoms, we can write that

Moles of atoms in 0.125 mole of CH4

= 0.625 moles

Moles of CH4Volume of CH4 at STP

Molar volume of CH4 at STP=

5.6 L

22.4 L mole-1= = 0.25 mole


12

Only one option is correct 1. An organic compound contains C, H and S. The minimum molecular weight of the

compound containing 8% sulphur is : (atomic weight of S=32 amu) 1. 200 g mol−1 2. 400 g mol−1 3. 600 g mol−1 4. 300 g mol−1

2. The hydrated salt Na2SO4.nH2O undergoes 55.9 % loss in mass on heating and becomes

anhydrous. The value of ‘n’ will be 1. 5 2. 3 3. 7 4. 10 3. Equal mass of Fe2O3 and FeO has mass of oxygen in the ratio 1. 1.35 2. 0.74 3. 0.37 4. 2.7 4. A certain compound has molecular formula X4O6. If 10.0 g of the compound contains 5.62

g of x. The atomic mass of x is 1. 62.0 amu 2. 48.0 amu 3. 32.0 amu 4. 30.8 amu 5. A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of

hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is: (atomic mass, Ba =137 amu, Cl = 35.5 amu) 1. BaCl2.H2O 2. BaCl2.2H2O 3. BaCl2.3H2O 4. BaCl2.4H2O

6. 0.5 g of sample of an alloy gave 0.30 g of Mg2P2O7 (molar mass of Mg and P are 24 and

31 g mol–1 respectively). The percentage of Mg in the alloy would be 1. 10.5% 2. 12.97% 3. 15.23% 4. 18.31% 7. The combustion of 4.24 mg of an organic compound produces 8.45 mg of CO2 and 3.46 mg

of water. The mass percentages of C and H in the compound respectively are 1. 54.4, 9.1 2. 9.1, 54.4 3. 27.2, 18.2 4. 18.2, 27.2 8. Lithium occurs in two isotopes, namely, 7Li (atomic mass 7.00 a.m.u) and 6Li (atomic mass

6.00 a.m.u). If there exists 7.4% of 6Li in naturally occurring Lithium, then it atomic mass will be

1. 6.2 a.m.u 2. 6.5 amu 3. 6.94 amu 4. 7.2 amu 9. The simplest formula of the compound which contains 85.6% C and 14.4% H by mass is 1. CH 2. CH2 3. C2H3 4. CH3 10. A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO2. The

empirical formula of the hydrocarbon is 1. C6H5 2. C7H8 3. C2H4 4. C3H4 11. An insecticide contains 47.5%C, 2.54% H and 50% chlorine by mass. It’s empirical formula

is 1. C13H8Cl5 2. C14H9Cl5 3. C12H10Cl5 4. C15H12Cl6 12. An organic compound contains 20.0% C, 6.66%, H 47.33% N and the rest was oxygen. Its

molar mass is 60 g mol–1. The molecular formula of the compound is 1. CH4N2O 2. CH2NO2 3. C2H6NO 4. CH18NO


13 13. The simplest formula of the compound containing 32.5% K, 0.839% H, 26.7% S and

39.9% O by mass is 1. KHSO2 2. KHSO3 3. KHSO4 4. K2H2S2O7 14. The simplest formula of a compound containing 21.9% Mg, 27.8 % P and 50.3% O by mass

is 1. Mg2P3O5 2. MgP2O4 3. Mg2P2O7 4. Mg3PO4 15. Iron has a density of 7.86 g cm–3 and atomic mass of 55.85 amu. The volume occupied by

one mole of Fe is 1. 0.141 cm3mol–1 2. 7.11 cm3mol–1 3. 4.28 1024 cm3mol–1 4. 22.8 cm3mol–1 16. A metal (M) forms of a compound M2HPO4. The formula of the metal sulphate is 1. M2SO4 2. MSO4 3. M(SO4)2 4. M2(SO4)3 17. A partially dried clay mineral contains 8% water. The original sample contained 12% water

and 45% silica. The % of silica in the partially dried sample is nearly. 1. 50% 2. 49% 3. 55% 4. 47% 18. If 1 g each of the following is taken, which will have maximum amount of charge? 1. PO4

3– 2. SO42– 3. Al3+ 4. NH4

+

19. Haemoglobin contains 0.25% iron by weight. The molecular weight of Haemoglobin is 89600. Calculate the no. of iron atom per molecule of Haemoglobin.

1. 2 2. 8 3. 4 4. 5

20. If formula of metallic Pyrophosphate is M(P2O7)2 . The formula of metallic nitride is

1. M8N3 2. M3N4 3. MN8 4. M3N8

21. What amount of charge is present on 17.4 gram of pyrophosphate ion. 1. 4298.65 coulomb 2. 38600 coulomb 3. 9650 coulomb 4. 22183.9 coulomb

22. Which of the following pairs have the same number of atoms? I. 16g of O2 and 4 g of H2 II. 16g of O2 and 44 g of CO2 III. 28g of N2 and 32 g of O2 IV. 12g of C and 23 g of Na 1. Both I and II 2. II, III and IV

3. Both III and IV 4. I, III and IV

23. How many of the following are compound. Milk, hydrochloric acid, acetic acid, fog, cloud, silica, allumina, ozone, heavy water 1. 3 2. 4 3. 5 4. 6

24. Mass of 821ml of X2(g) at 270C and 380 mmHg pressure is 1 gram. Mass of one atom of X is

1. 100/NA g 2. 30/NA g 3. 78.94/NA g 4. 86.2/NA g

25. Carbohydrates are represented by the general formula Cm(H2O)n. On heating, in absence of air, they decompose into steam (H2O) and carbon. 3.1 g of a carbohydrate, on complete decomposition by heating in absence of air, leave a residue of 1.24 g of carbon. If the molecular mass of the carbohydrate be 180, find the value of (m + n)

1. 6 2. 12 3. 18 4. 4


14

26. An oxybromo compound, KBrOx, where x is unknown, is analysed and found to contain 47.90% Br. What is the value of x?

1. 1 2. 2 3. 3 4. 4

27. A molecule contains 30 C-atoms, 50 H-atoms, 2 O-atom, 2 S-atom and 4.98 10–22 g other

atoms. What is molecular mass of compound? 1. 874 2. 894 3. 806 4. 774

28. Number of electrons in 18 ml H2O measured at 4C and one atm pressure 1. 6.022 × 1022 2. 6.022 × 1023 3. 6.022 × 1024 4. 6.022 × 1025 29. A trivalent cation is isoelectronic with NH3 and has (Z + 1) neutrons. Mass number for

cation is 1. 21 2. 23 3. 25 4. 27

30. If 1 g each of the following were taken which will show minimum radioactivity (at. wt Ra = 226)

1. Radium nitrate 2. Radium chloride 3. Radium phosphate 4. Radium sulphate 31. If 1g each of the following are taken, which will contain maximum number of electrons 1. CO3

2 – 2. PO43– 3. Na+ 4. Mg2+

32. X and Y are two elements which form X2Y3 and X3Y4. If 0.20 mol of X2Y3 weighs 32.0 g

and 0.4 mol X3Y4 weighs 92 g, the atomic weights of X and Y are respectively 1. 16.0 and 56.0 2. 8.0 and 28.0 2. 56.0 and 16.0 4. 50 and 20 33. A hydrated salt of Na2SO3 loses 22.22% of its mass on strong heating. The hydrated salt is 1. Na2SO3.4H2O 2. Na2SO3.6H2O 3. Na2SO3.H2O 4. Na2SO3.2H2O 34. Find empirical formula of the compound. If M = 68% (atomic mass = 34) and remaining

32% oxygen. 1. MO 2. M2O 3. MO2 4. M2O3 35. The vapour density of a gas is 11.2. The volume occupied by one gram of the gas at STP is 1. 1.0 L 2. 11.2 L 3. 22.4 L 4. 0.1L 36. 60 g of a compound on analysis produced 24 g carbon, 4g hydrogen and 32 g oxygen. The

empirical formula of the compound is 1. CH2O2 2. CH2O 3. CH4O 4. C2H4O2 37. One atom of an element weighs 1.8 × 10–23 g. Its atomic mass is 1. 29.9 2. 154 3. 10.83 4. 18 38. 25 g of MCl4 contains 0.5 mole chlorine then its molecular weight is 1. 100 g mol–1 2. 200 g mol–1 3. 150 g mol–1 4. 400 g mol–1


15 39. The mass of 112 cm3 of CH4 gas at STP is 1. 0.16 g 2. 0.8 g 3. 0.08 g 4. 1.6 g 40. How many moles of magnesium phosphate, Mg3(PO4)2 will contain 0.25 mole of oxygen

atom ? 1. 0.02 2. 3.125 × 10–2 3. 1.25 × 10–2 4. 2.5 × 10–2

Answers

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 2 4 1 4 2 2 1 3 2 2 Q. No. 11 12 13 14 15 16 17 18 19 20 Answer 2 1 2 3 2 1 3 3 3 4 Q. No. 21 22 23 24 25 26 27 28 29 30 Answer 2 3 2 2 2 3 3 3 4 1 Q. No. 31 32 33 34 35 36 37 38 39 40 Answer 1 4 4 1 1 2 3 2 3 2

JRS Tutorials, Durgakund, Varanasi-221005, Ph No. (0542) 2311922, 2311777, Mob. 9794757100, 7317347706

Page No. - 1

JRS TUTORIALS

Chemistry Problem Sheet' 2020-21 Coordination compound XII-IIT

A– Introduction, Important Terms and Werner’s theory

1. Consider the following statements: According the Werner's theory. (1) Ligands are connected to the metal ions by covalent bonds. (2) Secondary valencies have directional properties (3) Secondary valencies are non-ionisable Among these statements: 1. 1, 2 and 3 are correct 2. 2 and 3 are correct 3. 1 and 3 are correct 4. 1 and 2 are correct 2. In which of the following complexes the nickel metal is in highest oxidation state: 1. Ni(CO)4 2. K2 [NiF6] 3. [Ni(NH3)6](BF4)2 4. K4[Ni(CN)6] 3. A complex of platinum, ammonia and chloride produces four ions per molecule in the

solution. The structure consistent with the observation is: 1. [Pt(NH3)4]Cl4 2. [Pt(NH3)2Cl4] 3. [Pt(NH3)5Cl]Cl3 4. [Pt(NH3)4Cl2]Cl2 4. The oxidation state of Mo in its oxo-complex species [Mo2O4(H2O)2(C2H4)2]2– is: 1. +2 2. +3 3. +4 4. +5 5. In which complex is the transition metal in zero oxidation state: 1. [Co(NH3)6]Cl2 2. [Fe(H2O)6]SO4

3. [Ni(CO)4] 4. [Pt(NH3)3Cl2] 6. Which one is the most likely structure of CrCl3·6H2O if 1/3 of total chlorine of the

compound is precipitate by adding AgNO3 to its aqueous solution: 1. CrCl3·6H2O 2. [Cr(H2O)3Cl3]·(H2O)3 3. [Cr(H2O)4Cl2]·Cl·2H2O 4. [CrCl(H2O)5]Cl2·H2O 7. The complex [Co(NH3)5Br]SO4 will give white ppt. with: 1. PbCl2 2. AgNO3 3. KI 4. All of these

8. Diethylene triamine is: 1. Chelating agent 2. Neutral ligand

3. Tridentate ligand 4. All of these 9. How many maximum moles of AgCl would be obtained, when 100 ml of 0.1 M

Co(NH3)5Cl3 is treated with excess of AgNO3? (Coordination no. of Co = 6) 1. 0.01 2. 0.02 3. 0.03 4. AgCl is not formed 10. 0.001 mol of Co(NH3)5(NO3)(SO4) was passed through a cation exchanger and the acid

coming out of it required 20 ml of 0.1 M NaOH for neutralisation. Hence, the complex can be 1. [Co(NH3)5SO4]NO3 2. [Co(NH3)5NO3]SO4 3. [Co(NH3)5](SO3)(NO3) 4. Both (1) and (2)


Page No. - 2

11. Cu2+ mostly shows coordination number of 1. 2 only 2. 2 or 4 3. 4 only 4. 4 or 6 12. Which of the following is not chelating agent? 1. thiosulphato 2. oxalato 3. glycinato 4. ethylenediamine 13. Which of the following has five donor (coordinating) sites? 1. Triethylenetetramine 2. Ethylenediaminetetracetate ion 3. Ethylenediaminetriacetate ion 4. Diethylenetriamine 14. A compound contains 1.08 mol of Na, 0.54 mol of Cu and 2.16 mol of F. Its aqueous

solution shows osmotic pressure which is three times that of urea having same molar concentration. The formula of the compound is

1. Na4[CuF6] 2. Na[CuF4] 3. Na2[CuF4] 4. Na2[CuF3] 15. The molar ionic conductances of the octahedral complexes. (I) PtCl4·5NH3 (II) PtCl4·4NH3 (III) PtCl4·3NH3 (IV) PtCl4·2NH3 1. I < II < III < IV 2. IV < III <II < I 3. III < IV < II < I 4. IV < III < I < II 16. On treatment of 10 ml of 1M solution of the complex CrCl3·6H2O with excess of AgNO3,

4.305 g of AgCl was obtained. The complex is : (AgCl = 143.5) 1. [Cr(H2O)3Cl3]·3H2O 2. [Cr(H2O)4Cl2]Cl·2H2O 3. [Cr(H2O)5Cl]Cl2·H2O 4. [Cr(H2O)6] Cl3 17. Which of the following species is not expected to be a ligand 1. NO+ 2. NH4

+ 3. NH2– NH3+ 4. CO

18. The number of donor sites in dimethylglyoxime, glycinato, diethylenetriamine and EDTA

are respectively: 1. 2, 2, 3 and 4 2. 2, 2, 3 and 6 3. 2, 2, 2 and 6 4. 2, 3, 3 and 6 19. The complex ion which has no 'd' electrons in the central metal atom is: 1. [Co(NH3)6]3+ 2. [Fe(CN)6]3–

3. [Cr(H2O)6]3+ 4. [MnO4]– 20. Oxidation number of Fe in violet coloured complex Na4[Fe(CN)5(NOS)] is: 1. 0 2. +2 3. +3 4. +4 21. Complexes [Co(NH3)5SO4]Br and [Co(NH3)5Br]SO4 can be distinguished by 1. conductance measurement 2. using BaCl2 3. using AgNO3 4. all 22. 50 ml of 0.2 M solution of a compound with empirical formula CoCl3.4NH3 on treatment

with excess of AgNO3(aq) yields 1.435 g of AgCl. Ammonia is not removed by treatment with concentrated H2SO4. The formula of the compound is:

1. [Co(NH3)4Cl]Cl2 2. [Co(NH3)4Cl2]Cl 3. [Co(NH3)4]Cl3 4. [CoCl3(NH3)3]NH3


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23. Which of the following is non–conducting complex ? 1. CoCl3.6NH3 2. CoCl3.5NH3 3. CoCl3.4NH3 4. CoCl3.3NH3

24. The oxidation number of Co in the complex ion 1. +2 2. +3 3. +4 4. +6 25. Oxidation state of Ag in Na3[Ag(S2O3)2] is 1. + 2 2. – 2 3. 0 4. +1 26. Which gives only 25% mole of cloride as AgCl, when reacts with excess AgNO3 1. PtCl2.4NH3 2. PtCl4.5NH3 3. PtCl4.4NH3 4. PtCl4.3NH3 27. A complex Kn [MnF6] has magnetic moment 4.9 BM what will be the oxidation state of Mn and the value of n ? 1. Mn(II), n = 4 2. Mn(III) ; n = 3 3. Mn(IV) ; n = 2 4. Mn(V) ; n = 1 28. A coordination complex compound of cobalt has the molecular formula containing five

ammonia molecules, one nitro group and two chloride ions for one cobalt atom. One mole of this compound produces three mole ions in an aqueous solution. On reacting this solution with excess of AgNO3 solution, we get two moles of AgCl precipitate. The formula for this complex would be

1. [Co(NH3)5(NO2)]Cl2 2. [Co(NH3)5Cl2](NO2) 3. [Co(NH3)4(NO2)Cl](NH3)Cl 4. [Co(NH3)5] (NO2)2Cl2 29. How many EDTA (ethylenediaminetetraacetic acid) molecules are required to make an

octahedral complex with a Ca2+ ion? 1. Six 2. Three 3. One 4. Two 30. Mixture X = 0.02 mole of [Co(NH3)5SO4]Br and 0.02 mole of [Co(NH3)5Br]SO4 was

prepared in 2 litre of solution 1 litre of mixture X + excess AgNO3 ⎯→ Y ↓(pale yellow) 1 litre of mixture X + excess BaCl2 ⎯→ Z ↓ (white) No. of moles of Y and Z are 1. 0.01, 0.01 2. 0.02, 0.01 3. 0.01, 0.02 4. 0.02, 0.02 31. Which of the following complexes exhibits highest molar conductivity ? 1. [Co(NH3)6]Cl3 2. [Co(NH3)5Cl]Cl2 3. [Co(NH3)4Cl2]Cl 4. [Co(NH3)3Cl3]

32. The oxidation number of Pt in [Pt(C2H4)Cl3]− is 1. + 1 2. + 2 3. + 3 4. + 4 33. When 0.1 mol CoCl3 (NH3)5 is treated with excess of AgNO3, 0.2 mol of AgCl are obtained. The conductivity of solution will correspond to : 1. 1 : 3 electrolyte 2. 1 : 2 electrolyte 3. 1 : 1 electrolyte 4. 3 : 1 electrolyte

2 4+


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34. The oxidation number of iron in the complex Na2 [Fe(CN)5NO] is 1. 0 2. +1 3. +2 4. +3 35. Which will give a white precipitate with AgNO3 in aqueous solution? 1. [Co(NH3)5Cl](NO2)2 2. [Pt(NH3)6]Cl4 3. [Pt(en)Cl]Br 4. [Cu(NH3)4]SO4 36. Among the following ion which one has the highest paramagnetism ? 1. [Cu(H2O)6]3+ 2. [Fe (H2O)6]2+ 3. [Cu(H2O)6]2+ 4. [Zn(H2O)6]2+ 37. The oxidation number of M in the complex K[M(CO)4] is 1. +3 2. +1 3. −3 4. −1 38. In tris(ethane1,2-diamine)cobalt (III) chloride the co-ordination number of cobalt is 1. 3 2. 4 3. 6 4. 7 39. Which of the following forms with an excess of CN− a complex having co-ordination

number two? 1. Ag+ 2. Fe2+ 3. Ni2+ 4. Cu2+ 40. The co-ordination number and oxidation number of X in the compound [X(NH3)5(SO4)]Cl

will be 1. 2 and 6 2. 6 and 4 3. 6 and 2 4. 6 and 3 41. Number of electrons gained by Pd in [PdCl4]−2 due to coordinate bond formation is : 1. 4 2. 8 3. 10 4. 0 42. The primary valency of Fe in K3[Fe(CN)6] is 1. 3 2. 2 3. 1 4. 0 43. One mole of Co(NH3)5Cl3 gives 3 moles of ions on dissolution in water. One mole of this

reacts with two moles of AgNO3 to give two moles of AgCl. The complex is 1. [Co(NH3)4Cl2]Cl⋅NH3 2. [Co(NH3)4Cl]Cl2⋅NH3 3. [Co(NH3)5Cl]Cl2 4. [Co(NH3)3Cl3].2NH3 44. Coordination number of Ni in [Ni(C2O4)3]4- is 1. 3 2. 6 3. 4 4. 2 45. Which of the following will exhibit maximum ionic conductivity ? 1. K4[Fe(CN)6] 2. [Co(NH3)6]Cl3

3. [Cu(NH3)4]Cl2 4. [Ni(CO)4]


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46. A solution containing 0.319 g of complex CrCl3.6H2O was passed through cation exchanger and the solution given out was neutralized by 28.5 mL of 0.125 M NaOH. What is the correct formula of the complex? [At. wt. of Cr = 52 , Cl = 35.5]

1. [Cr(H2O)6]Cl3 2. [Cr(H2O)5Cl]Cl2 3. [Cr(H2O)4Cl2 4. [Cr(H2O)3Cl3] 47. Identify the complexes which are expected to be coloured 1. [Ti(NO3)4] 2. [Cu(NCCH3)4]+ BF4

− 3. [Cr(NH3)6]Cl3 4. All of the above 48. The correct order of the stoichiometries of AgCl formed when AgNO3 in excess is treated

with one mole each of the complexes : CoCl3.6NH3, CoCl3.5NH3, CoCl3.4NH3 respectively is :- 1. 3 AgCl, 1 AgCl, 2 AgCl 2. 3 AgCl, 2 AgCl, 1 AgCl 3. 2 AgCl, 3 AgCl, 1 AgCl 4. 1 AgCl, 3 AgCl, 2 AgCl

49. Match the compound given in Column I with the oxidation state of central metal present in

it (given in Column II) and assign the correct code :

Column I (Compound)

Column II (Oxidation state of central metal)

(i) [Co (NH3)5 (NCS)]SO3 (A) + 4

(ii) [Pt(NH2OH)(NH3)4Cl]Cl3 (B) 0

(iii) Na4[Co(S2O3)3] (C) + 1

(iv) [Co2 (CO)8] (D) + 2

(E) + 3

Code : 1. i (A) ii (B) iii (D) iv (E) 2. i (D) ii (C) iii (B) iv (A) 3. i (E) ii (A) iii (D) iv (B) 4. i (D) ii (A) iii (B) iv (C) B – Nomenclature

1. IUPAC name of complex K3[Al(C2O4)3] is : 1. Potassium tris-oxalatoaluminate (III)

2. Potassium trioxalatoaluminate (III) 3. Potassium aluminium (III) oxalate

4. Potassium trioxalatoaluminate (IV)


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CoCl2 is:

2. Trioxalato aluminate (III) ion and tetrafluoro-borate (III) ion are: 1. [Al(C2O4)3] , [BF4]3– 2. [Al(C2O4)3]3+ , [BF4]3+ 3. [Al(C2O4)3]3– , [BF4]– 4. [Al(C2O4)3]2– , [BF4]2–

3. The correct IUPAC name of the complex:

1. Dichlorodimethylglyoximatecobalt (II)

2. Bis(dimethyglyoxime)dichlorocobalt(II) 3. Dimethylglyoximecobalt(II)chloride

4. Dichlorodimethylglyoximecobalt(II) 4. The IUPAC name of the red coloured complex [Fe(C4H7O2N2)2] obtained from the

reaction of Fe2+ and dimethyl glyoxime 1. bis (dimethyl glyoxime) ferrate (II)

2. bis (dimethyl glyoximato) iron (II) 3. bis (2, 3-butanediol dioximato) iron (II)

4. bis (2, 3-butenedione dioximato) iron (III) 5. The IUPAC name for the coordination compound Ba[BrF4]2 is 1. Barium tetrafluorobromate (V)

2. Barium tetrafluorobromate (III) 3. Barium bis (tetrafluorobromate) (III)

4. Barium ditetrafluorobromate (III) 6. The formula of the complex hydridotrimethoxoborate (III) ion is: 1. [BH(OCH3)3]2- 2. [BH2(OCH3)3]2-

3. [BH(OCH3)3]– 4. [BH(OCH3)3]+ 7. IUPAC name of [Pt(NH3)3 (Br) (NO3) Cl] Cl is 1. triamminebromochloronitratoplatinum (IV) chloride 2. triamminebromonitrochloroplatium (IV) chloride 3. triamminechlorobromonitroplatinum (IV) chloride 4. triamminenitrochlorobromoplatium (IV) chloride 8. The formula of dichlorobis (urea) copper (II) is : 1. [Cu(O = C(NH2)2]Cl2 2. [CuCl2{O = C(NH2)2}2] 3. [Cu{O = C(NH2)2}Cl]Cl 4. [CuCl2][O = C(NH2)2]H2 9. The IUPAC name of [Pt(NH3)4NO2Cl]SO4 is 1. Chloronitroplatinum(IV) sulphate 2. TetramminechloroN-nitritoplatinum(IV) sulphate 3. Chloronitrotetraammineplatinum(IV) sulphate 4. Platinum(IV)tetraamminenitrochloro sulphate


Page No. - 7

10. The complex chlorodiaquatriamminecobalt(III) chloride can be represented as 1. [CoCl(NH3)3(H2O)2]Cl2 2. [Co(NH3)3(H2O)Cl3] 3. [Co(NH3)3(H2O)2Cl] 4. [Co(NH3)3(H2O)3]Cl3 C– Bonding VBT and CFT

1. Which ion has tetrahedral geometry: 1. [Fe(CO)5] 2. [PtCl4]2– 3. [NiCl4]2– 4. Ni(CN)4]2– 2. The hydridisation and unpaired electrons in [Fe(H2O)6]2+ ion are : 1. sp3d2 ; 4 2. d2sp3 ; 3 3. sp3d ; 4 4. sp3 d2 ; 2 3. The hybrisation involved in [CoF6]3– is: 1. d2sp3 2. d3sp2 3. dsp3 4. sp3d2 4. The structure of iron pentacarbonyl is: 1. Square planar 2. Trigonal bipyramid

3. Triangular 4. Tetrahedral 5. Point out the correct statements amongst the following 1. [Cu(CN)4]3– has tetrahedral geometry and dsp2 hybridization 2. [Ni(CN)6]4– is octahedral and Ni has d2sp3 hybridization 3. [ZnBr4]2– is tetrahedral and diamagnetic 4. [Cr(NH3)6]3+ has octahedral geometry and sp3d2 hybridization 6. Among the following ions which one has the highest paramagnetism 1. [Cr(H2O)6]3+ 2. [Fe(H2O)6]2+

3. [Cu(H2O)6]2+ 4. [Zn((H2O)6]2+ 7. The geometry of Ni(CO)4 and [Ni(PPh3)2Cl2] are 1. both square planar 2. tetrahedral and square planar 3. both tetrahedral 4. square planar and tetrahedral 8. Of the following which is diamagnetic in nature? 1. [CoF6]3– 2. [NiCl4]2– 3. [CuCl4]2– 4. [Ni(CN)4]2– 9. The [Fe(CN)6]3– complex ion 1. exhibits planar geometry 2. is diamagnetic 3. should be very stable 4. has 2 unpaired electrons 10. [Cu(NH3)4]2+ has hybridisation and magnetic moment 1. sp3, 1.73 B.M. 2. sp3d, 1.73 B.M. 3. dsp2, 2.83 B.M. 4. dsp2, 1.73 B.M. 11. [FeF6]3– has Fe atom ---hybridised with unpaired ----electrons 1. d2sp3, 4 2. d2sp3, 5 3. sp3d2, 5 4. sp3d2, 3


Page No. - 8

12. Which of the following statements is not true? 1. −2

4MnCl ion has tetrahedral geometry and is paramagnetic 2. [Mn(CN)6]2– ion has octahedral geometry and is paramagnetic 3. [CuCl4]2– has square planar geometry and is paramagnetic 4. [Ni(Ph3P)2Br3] has trigonal bipyramidal geometry and three unpaired electron 13. The increasing order of magnetism of (I) MnSO4.4H2O (II) FeSO4.7H2O (III) NiSO4.6H2O (IV) CuSO4.5H2O 1. I < II < III < IV 2. IV < III < II < I

3. III < IV < II < I 4. III < IV < I < II 14. Octahedral complex of Ni(II) must be 1. inner orbital

2. outer orbital 3. inner or outer orbital depending upon the strong or weak field ligand 4. diamagnetic 15. For the correct assignment of electronic configuration of a complex, the valence bond

theory often requires the measurement of 1. molar conductance 2. optical activity

3. magnetic moment 4. dipole moment 16. Mn2+ forms a complex with Br– ion. The magnetic moment of the complex is 5.92 B.M.

What could not be the probable formula and geometry of the complex? 1. [MnBr6]4–, octahedral 2. [MnBr4]2–, square planar 3. [MnBr4]2–, tetrahedral 4. [MnBr5]3–, trigonal bipyramidal 17. A complex of certain metal has the magnetic moment of 4.91 BM whereas another

complex of the same metal with same oxidation state has zero magnetic moment. The metal ion could be

1. Co2+ 2. Mn2+ 3. Fe2+ 4. Fe3+ 18. The tetrahedral [CoI4]2– and square planar [PdBr4]2– complex ions are respectively 1. low spin, high spin 2. high spin, low spin

3. low spin, low spin 4. high spin, high spin 19. The species having tetrahedral shape is 1. [PdCl4]2– 2. [Ni(CN)4]2– 3. [Pd(CN)4]2– 4. [NiCl4]2– 20. [Cu(H2O)4]2+ absorbs orange light and the transmitted complementary colour will be 1. Green 2. Yellow 3. Blue 4. Violet 21. Hexafluorocobaltate(III) ion is found to be high spin complex, the probable hybrid state of

cobalt in it, is 1. dsp2 2. d2sp3 3. sp3d2 4. sp3d


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22. Which of the following system has maximum number of unpaired electrones 1. d5 (Octahedral, low spin) 2. d8 (Tetrahedral) 3. d6 (Octahedral, low spin) 4. d3 (Octahedral) 23. Which of the following pair of molecule have identical shape 1. [NiCl4]–2 and XeF4 2. [Zn(H2O)4]+2 and SiCl4 3. [Fe(CO)5] and XeOF4 4. [Ag(NH3)2]+ and SF2 24. Which one of the following is an inner orbital complex as well as diamagnetic in

behaviour? (At no : Zn = 30, Cr = 24, Co = 27, Ni = 28) 1. [Zn(NH3)6]2+ 2. [Cr(NH3)6]3+ 3. [Co(NH3)6]3+ 4. [Ni (NH3)6]2+ 25. Which of the following coordination compounds would exhibit optical isomerism ? 1. Pentaamminenitrocobalt(III) Iodide 2. Diamminedichloroplatinum(II) 3. trans-dicyanobis(ethylenediamine)chromium(III) chloride 4. Tris-(ethylenediamine)cobalt(III) bromide 26. Considering H2O as a weak field ligand, the number of unpaired electrons in [Mn(H2O)6]2+

will be (At no of Mn = 25) :− 1. 3 2. 5 3. 2 4. 4 27. A square planar complex is formed by hybridization of which atomic orbitals? 1. s, px, py, dyz 2. s, px, py, dx

2 –y

2 3. s, px, py, dz

2 4. s, px, py, dxy

28. The CFSE for octahedral [CoCl6]4 – is 18,000 cm-1. The CFSE for tetrahedral [CoCl4]2-

will be : 1. 18,000 cm-1 2. 16,000 cm-1 3. 8,000 cm-1 4. 20,000 cm-1

29. Atomic number of Mn, Fe and Co are 25, 26 and 27 respectively. Which of the following inner orbital octahedral complex ions are diamagnetic ? a. [Co (NH3)6]3+ b. [Mn (CN)6]3- c. [Fe (CN)6]4- d. [Fe (CN)6]3-

Codes : 1. a, b, c, d 2. a, c 3. a, c, d 4. a, b, c

30. Which of the following options are correct for [Fe (CN)6]3- complex ? a. d2sp3 hybridisation b. sp3d2 hybridisation c. Paramagnetic d. Diamagnetic 1. a, d 2. a, c 3. b, d 4. b, c 31. Which of the following is correctly matched about Ni(CO)4, [Ni(CN)4]2− and NiCl −2

4 Ni(CO)4 [Ni(CN)4]2− NiCl −2

4 1. diamagnetic paramagnetic paramagnetic 2. diamagnetic diamagnetic paramagnetic 3. paramagnetic diamagnetic diamagnetic

4. diamagnetic paramagnetic diamagnetic


Page No. - 10

32. In the complex ion [Pd NH3BrCl2] palladium uses d orbital for its formation is 1. 4dxy 2. 4dZ

2 3. 4dx2 − y2 4. 4dyz 33. The d orbitals used by iron in [FeF6]3− for forming hybrid orbitals is 1. 3dz2 and 3dx2 − y2 2. 4dZ

2 and 4dyz 3. 4dz2 and 4dx2 − y2 4. 4dxy and 4dx2 − y2 34. The species with metal ion having d5 configuration is 1. K4[Fe(CN)6] 2. [Co(NH3)6]PO4

3. K4[Mn(CN)6] 4. [Co(NH3)5(SO4)]NO3 35. The energy for low spin d4 octahedral complex is : 1. –1.2 Δ0 2. –0.6 Δ0 3. –1.8 Δ0 4. –1.6 Δ0 + P 36. The number of unpaired electrons in the complex ion [CoF6]3- is

(At no Co = 27) 1. 3 2. 2 3. 4 4. 0

37. Which statement is incorrect ? 1. Ni(CO)4 -tetrahedral, paramagnetic 2. [Ni(CN)4]2- -square planar, diamagnetic 3. Ni(CO)4 -tetrahedral, diamagnetic 4. [Ni(Cl)4]2- tetrahedral, paramagnetic 38. Shape of [Fe(CO)5] is 1. octahedral 2. square planar 3. trigonal bipyramidal 4. square pyramidal 39. Which one of the following have electronic configuration of metal in presence of ligands

as t 5g2

1. [Fe(C2O4)6]3− 2. [Fe(CN)6]3− 3. [Fe(CN)6]4− 4. [Fe(H2O)6]2+ 40. In an octahedral crystal field, the t2g orbitals have 1. Raised energy by 0.4 2. Lowered energy by 0.4 3. Raised energy by 0.6 4. Lowered energy by 0.6 41. Predict the order of Δo for the following compounds (I) [Fe(H2O)6]2+ (II) [Fe(CN)2(H2O)4] (III) [Fe(CN)4(H2O)2]2− Codes :

1. I < II < III 2. III < II < I 3. II < I < III 4. III < I < II 42. The hybridization involved in [CoF6]3− and [CoCl6]3− respectively 1. d2sp3, d2sp3 2. sp3d2, sp3d2 3. d2sp3, sp3d2 4. sp3d2, d2sp3 43. In which of the following coordination entities the magnitude of Δ0 (CFSE in octahedral

field) will be maximum ? (At No Co = 27) 1. [Co(H2O)6]3+ 2. [Co(NH3)6]3+ 3. [Co(CN)6]3– 4. [CoF6]3–


Page No. - 11

44. The d electron configurations of Cr2+, Mn2+, Fe2+ and Ni2+ are 3d4, 3d5, 3d6 and 3d8 respectively. Which one of the following aqua complexes will exhibit the minimum paramagnetic behaviour?

(At. no. of Cr = 24, Mn = 25, Fe = 26, Ni = 28)

1. [Fe(H2O)6]2+ 2. [Ni(H2O)6]2+ 3. [Cr(H2O)6]2+ 4. [Mn(H2O)6]2+

45. Correct increasing order for the wavelengths of absorption in the visible region the

complexes of Co3+ is :- 1. [Co(H2O)6]3+, [Co(en)3]3+, [Co(NH3)6]3+ 2. [Co(H2O)6]3+, [Co(NH3)6]3+, [Co(en)3]3+ 3. [Co(NH3)6]3+, [Co(en)3]3+, [Co(H2O)6]3+ 4. [Co(en)3]3+, [Co(NH3)6]3+, [Co(H2O)6]3+

46. Match the complex ions given in Column I with the hybridisation and number of unpaired electrons given in Column II and assign the correct code :

Column I (Complex ion)

Column II (Hybridisation, number of unpaired electrons)

(i) [CrCl6]3– (A) dsp2, 1

(ii) [Co(CN)4]2- (B) sp3d2, 5

(iii) [Ni(NH3)6]2+ (C) sp3d2, 3

(iv) [MnF6]4 - (D) sp3, 4

(E) sp3d2, 2

Code : 1. i (C) ii (A) iii (E) iv (B) 2. i (D) ii (C) iii (B) iv (A) 3. i (C) ii (B) iii (D) iv (A) 4. i (D) ii (A) iii (B) iv (C) 47. Pick out the correct statement with respect to [Mn(CN)6]3–

1. It is sp3d2 hybridised and tetrahedral 2. It is d2sp3 hybridised and octahedral 3. It is dsp2 hybridised and square planar 4. It is sp3d2 hybridised and octahedral

D– Effective Atomic Number (EAN) and stability

1. From the stability constant (hypothetical values), given below, predict which is the strongest ligand:

1. Cu2+ + 4NH3 → [Cu(NH3)4]2+ , K = 4.5 × 1011 2. Cu2+ + 4CN– → [Cu(CN)4]2–, K = 2.0 × 1027 3. Cu2++ 2en → [Cu(en)2]2+ , K = 3.0 × 1015 4. Cu2+ ++ 4H2O → [Cu(H2O)4]2+, K = 9.5 × 108


Page No. - 12

2. The EAN of platinum in potassium hexachloroplatinate (IV) is: (At. no. of Pt = 78) 1. 88 2. 86 3. 82 4. 84 3. EAN of the central metal in the complexes – K2[Ni(CN)4], [Cu(NH3)4]SO4 and K2[PtCl6]

are respectively. (At. no. of Ni 28, Cu = 29, Pt = 78) 1. 36, 35, 86 2. 34, 35, 84 3. 34, 35, 86 4. 34, 36, 86 4 Ni(CO)4 and [Ni(NH3)4]2+ do not differ in 1. magnetic moment 2. oxidation number of Ni 3. geometry 4. EAN 5. Following Sidgwick's rule of EAN, Co(CO)x will be 1. Co2(CO)4 2. Co2(CO)3 3. Co2(CO)8 4. CO2(CO)10 6. Which is expected most stable among followings ? 1. [Fe(H2O)6]3+ 2. [Fe(NH3)6]3+ 3. [Fe(C2O4)3]3− 4. [FeCl6]3− 7. Which of the following complexes formed by Cu2+ ions is the least stable? 1. Cu2+ + 4NH3 l [Cu (NH3)4]2+, pK = 11.6 2. Cu2+ + 4CN- l [Cu (CN)4]2-, pK = 27.3 3. Cu2+ + 2en l [Cu (en)2]2+, pK = 15.4 4. Cu2+ + 4H2O l [Cu (H2O)4]2+, pK = 8.9 E– Organo metallic compounds 1. Formula of ferrocene is: 1. [Fe(CN)6]4– 2. [Fe(CN)6]3+ 3. [Fe(CO)5] 4. [Fe(C5H5)2] 2. Which of the following statements about Fe(CO)5 is correct? 1. It is paramagnetic and high spin complex

2. It is diamagnetic and high spin complex 3. It is diamagnetic and low spin complex

4. It is paramagnetic and low spin complex 3. In [Fe(CO)5], the Fe−C bond possesses 1. π-character only 2. Both σ and π characters 3. Ionic character 4. σ-character only

4. Which of the following organometallic compound is σ and π-bonded? 1. [Fe(η5-C5H5)2] 2. [PtCl3(η5-C2H4)] 3. [Co(NH3)6]2+ 4. Fe(CO)5 5. The complex which is expected to have shortest M/C bond 1. Fe(CO) +2

6 2. Cr(CO)6 3. V(CO) −6 4. Mn(CO) +6 6. Ferrocene is 1. Fe(η5-C5H5)2 2. Fe(η2-C5H5)2 3. Cr(η5-C5H5)5 4. Os(η5-C5H5)2


Page No. - 13

7. The C – O bond energies correct decreasing order is represented by 1. [Ni(CO)4] > [Co(CO)4] − > [Fe(CO)4]2–

2. [Fe(CO)4]2– > [Ni(CO)4] > [Co(CO)4] −

3. [Fe(CO)4]2– > [Co(CO)4] − > [Ni(CO)4]

4. [Co(CO)4] − > [Ni(CO)4] > [Fe(CO)4]2– F– Isomerism 1. Which of the ligands can show linkage isomerism: 1. CNS– 2. NO2

– 3. CN– 4. All of these 2. The complexes given below show:

and 1. Optical isomerism 2. Co-ordination isomerism 3. Geometrical isomerism 4. Bridged isomerism 3. [(C6H5)2 Pd (SCN)2] and [(C6H5)2 Pd (NCS)2] are: 1. Linkage isomers 2. Co-ordination isomers 3. Ionisation isomers 4. Geometrical isomers 4. Which of the following complex shows ionization isomerism 1. [Cr(NH3)6]Cl3 2. [Cr(en)2 ]Cl2

3. [Cr(en)3]Cl3 4. [Co(NH3)5Br]SO4 5. Which one of the following square planar complex will be able to show cis-trans

isomerism: 1. MA3B 2. M(AA)2 3. MABCD 4. MA4 6. The total number of possible isomers of the compound [CuII(NH3)4] [PtIICl4] are: 1. 3 2. 5 3. 4 4. 6 7. cis-trans-isomerism is found in square planar complexes of the molecular formula : (A and

B are monodenate ligands): 1. MA4 2. MA3B 3. MA2B2 4. MAB3 8. Coordination isomerism could be shown by 1. [Ag(NH3)2][CuCl2] 2. [Al(H2O)6]Cl3

3. [Fe(NH3)6]2[Pt(CN)6]3 4. [Co(NH3)5Cl]SO4 9. Which complex is likely to show optical activity: 1. trans-[Co(NH3)4Cl2]+ 2. cis-[Co(NH3)4Cl2] + 3. cis-[Co(NH3)2(en)2]3+ 4. trans-[Co(NH3)2(en)2]3+


Page No. - 14

10. The two compounds Br])NH)(SO(Co[ 534 and Cl])NH)(SO(Co[ 534 represent: 1. Linkage isomerism 2. Ionisation isomerism 3. Co-ordination isomerism 4. No isomerism 11. Which of the following statements is correct? 1. Geometrical isomerism is not observed in complexes of C.N.4 having tetrahedral geometry 2. Square planar complexes generally do not show geometrical isomerism 3. The square planar complex of general formulae Ma3b or Mab3 exhibits cis–trans isomerism 4. The platinum glycinato complex, [Pt(Gly)2] does not show geometrical isomerism 12. [Co(en)3]3+ ion is expected to show 1. two optically active isomers: d and l forms 2. three optically active isomers: d, l and meso forms 3. four optically active isomers: cis, d and l isomers and trans d and l isomers 4. can not show isomerism 13. The number of geometrical isomers for octahedral [Co(NH3)2Cl4]–, square planar

[AuCl2Br2]– and [Pt(en)Cl2] are 1. 2, 2, 2 2. 2, 2, no isomerism

3. 3, 2, 2 4. 2, 3, no isomerism 14. Which of the following statements is not true about the complex ion [Cr(en)2Cl2]+ 1. It has two geometrical isomers – cis and trans 2. Both the cis and trans isomers display optical activity 3. Only the cis isomer displays optical activity 4. Only the cis isomer has non–superimpossible mirror image 15. Of the following configurations, the optical isomers are 1. I and II 2. I and III 3. II and IV 4. II and III 16. Identify the geometrical isomers of the following: 1. I with III 2. II with IV 3. I with II 4. All of these


Page No. - 15

17. Other than the X–ray diffractions, how could be the following pairs of isomers be distinguished from one another by

[Cr(NH3)6] [Cr(NO2)6] and [Cr(NH3)4(NO2)2] [Cr(NH3)2(NO2)4] 1. electrolysis of an aqueous solution 2. measurement of molar conductance 3. measuring magnetic moments 4. all of these 18. How the isomeric complexes [Co(NH3)6][Cr(NO2)6] and [Cr(NH3)6][Co(NO2)6] can be

distinguished from one another ? 1. conductivity measurement 2. measuring magnetic moments 3. electrolysis of their aqueous solutions 4. optical measurement 19. Which of the following ions are optically active? 1. I only 2. II only 3. II and III 4. IV only 20. How many isomers are possible for the complex ion [Cr(NH3)(OH)2Cl3]2– 1. 2 2. 3 3. 4 4. 5 21. The complex ion has two optical isomers. Their correct configurations are: 1. 2.

3. 4.

22. Which of the following complex can not exhibit geometrical isomerism 1. [Pt(NH3)2Cl NO2] 2. [Pt(gly)2]

3. [Cu(en)2]+ 4. [Pt(H2O)(NH3)BrCl] 23. Theoretically the No. of geometrical isomers expected for octahedral complex [Mabcdef] is 1. Zero 2. 30 3. 15 4. 9 24. The number of geometrical isomers of the complex [Co(NO2)3(NH3)3]is 1. 4 2. 0 3. 2 4. 3


Page No. - 16

25. [Co(NH3)4(NO2)2]Cl exhibits 1. Ionization isomerism, geometrical isomerism and optical isomerism 2. Linkage isomerism, geometrical isomerism and optical isomerism 3. Linkage isomerism, ionization isomerism and optical isomerism 4. Linkage isomerism, ionization isomerism and geometrical isomerism 26. In [Cr(C2O4)3]3−, the isomerism shown is 1. Ligand 2. Optical 3. Geometrical 4. Ionization 27. Which of the following complexes will show geometrical as well as optical isomerism?

(en = ethylenediamine) 1. [Pt(NH3)2Cl2] 2. [Pt(NH3)2Cl4] 3. [Pt(en)3]4+ 4. [Pt(en)2Cl2]2+

28. The total number of possible structural isomers of the compound [CuII(NH3)4][PtIICl4] are: 1. 3 2. 5 3. 4 4. 6

29. The number of stereo isomers formed by square planar complex K2[PdClBr2I] is 1. 2 2. 3 3. 4 4. 6 30. Which kind of isomerism is exhibited by octahedral [Co(NH3)4Br2]Cl ? 1. Geometrical and Ionization 2. Geometrical and Optical 3. Optical and Ionization 4. Geometrical only 31. Which one of the following has an optical isomer ? (en = ethylenediamine) 1. [Co(H2O)4(en)]3+ 2. [Zn(en)2]2+ 3. [Zn(en) (NH3)2]2+ 4. [Co(en)3]3+ 32. The ionization isomer of [Cr(H2O)4Cl(NO2)] Cl is 1. [Cr(H2O)4(O2N)]Cl2 2. [Cr(H2O)4Cl2]NO2 3. [Cr(H2O)4Cl(ONO)]Cl 4. [Cr(H2O)4Cl2(NO2)2]Cl 33. The existence of two different coloured complexes with the composition of [Co(NH3)4Cl2]+ is due to : 1. coordination isomerism 2. ionization isomerism 3. linkage isomerism 4. geometrical isomerism

34. Which one of the following octahedral complexes will not show geometrical isomerism? (A and B are monodentate ligands)

1. [MA4B2] 2. [MA5B] 3. [MA2B4] 4. [MA3B3] 35. Total number of stereo isomers formed by [Pt Py NH3ClBr] is 1. 2 2. 3 3. 4 4. no isomers


Page No. - 17

36. Geometry of [Ni(CO)4] and [Pt(NH3)4]2+ is 1. [Ni(CO)4] is tetrahedral, [Pt(NH3)4]2+ is squar planar 2. [Ni(CO)4] is squar planar, [Pt(NH3)4]2+ is tetrahedral 3. Both are tetrahedral 4. Both are square planar 37. Which of the following compounds would exhibit co-ordination isomerism? 1. [Cr(H2O)6]Cl2 2. [Cr(NH3)6][Co(CN)6] 3. [Cr(en)2]NO2 4. [Ni(NH3)6][BF4]2 38. The number of geometrical isomers of [Co(NH3)3Cl3] are 1. 0 2. 2 3. 3 4. 4 39. A complex shown below can exhibit

1. optical isomerism only 2. geometrical isomerism only 3. both optical and geometrical isomerism 4. none of these 40. Which one of the following pairs of isomers and types of isomerism are correctly matched? (i). [Co(NH3)5(NO2)]Cl2 and [Co(NH3)5(ONO)]Cl2 ……. Linkage (ii). [Cu(NH3)4][PtCl4] and [Pt(NH3)4] [CuCl4] ………Co-ordination (iii). [Pt(NH3)4Cl2]Br2 and [Pt(NH3)4Br2)]NO2 ……. Ionization Select the correct answer using the codes given below 1. (ii) and (iii) 2. (i), (ii) and (iii) 3. (i) and (iii) 4. (i) and (ii)

41. Which one of the following complexes is not expected to exhibit isomerism ? 1. [Ni(NH3)4 (H2O)2]2+ 2. [Pt(NH3)2 Cl2] 3. [Ni(NH3)2Cl2] 4. [Ni(en)3]2+ 42. The two complexes given below are

1. geometrical isomers 2. position isomers 3. optical isomers 4. identical


Page No. - 18

43. Match the complex species given in Column I with the possible isomerism given in Column II and assign the correct code :

Column I (Complex species)

Column II (Isomerism)

(i) [Co (NH3)4 Cl2]+ (A) Optical

(ii) cis- [CoCl2 (en)2]+ (B) Ionisation

(iii) [Co(NH3)5 (NO3)]Cl2 (C) Coordination

(iv) [Co (NH3)6][Cr(CN)6] (D) Geometrical

(E) Linkage

Code : 1. i (A) ii (B) iii (D) iv (E) 2. i (D) ii (C) iii (B) iv (A) 3. i (D) ii (A) iii (E) iv (C) 4. i (D) ii (A) iii (B) iv (C) G– Application of Coordination compound 1. Name the metal M which is extracted on the basis of following reactions: 4M + 8CN– + 2H2O + O2 → 4[M(CN)2]– + 4OH– 2[M(CN)2]– + Zn → [Zn(CN)4]2– + 2M 1. Nickel 2. Silver 3. Copper 4. Mercury 2. Which compound is formed when excess of KCN is added to aqueous solution of copper

sulphate? 1. Cu(CN)2 2. K2[Cu(CN)4] 3. K[Cu(CN)2] 4. K3[Cu(CN)4] 3. Aqueous solution of FeSO4 gives tests for both Fe2+ and SO4

2– but after addition of excess of KCN, solution ceases to give test for Fe2+. This is due to the formation of

1. the double salt FeSO4.2KCN.6H2O 2. Fe(CN)3 3. the complex ion [Fe(CN)6]4– 4. the complex ion [Fe(CN)6]3– 4. The disodium salt of ethylene diamine tetracetic acid can be used to estimate the following

ion(s) in the aqueous solution 1. Mg2+ ion 2. Ca2+ ion 3. Na+ ion 4. both Mg2+ and Ca2+ 5. The brown ring complex compound is formulated as [Fe(H2O)5NO]SO4. The oxidation

state of Fe is: 1. +1 2. +2 3. +3 4. Zero 6. In solid CuSO4⋅5H2O copper is co-ordinated to 1. four water molecules 2. five water molecules 3. one sulphate molecule 4. one water molecule 7. The probable formula for Prussian blue is 1. Fe3[Fe(CN)6]2 2. Fe2[Fe(CN)6]3 3. Fe4[Fe(CN)6]3 4. Fe3[Fe(CN)6]4


Page No. - 19

8. The geometry and magnetic property of [Rh(PPh3)3Cl] is 1. Square planar and diamagnetic 2. Square planar and paramagnetic 3. Tetrahedral and paramagnetic 4. Tetrahedral and diamagnetic 9. Match the coordination compounds given in Column I with the central metal atoms given in Column II and assign the correct code :

Column I (Coordination compound)

Column II (Central metal atom)

(i) Chlorophyll (A) Rhodium (ii) Blood pigment (B) Cobalt

(iii) Wilkinson catalyst (C) Calcium

(iv) Vitamin B12 (D) Iron

(E) Magnesium

Code : 1. i (E) ii (D) iii (A) iv (B) 2. i (C) ii (D) iii (E) iv (A) 3. i (D) ii (C) iii (B) iv (A) 4. i (E) ii (D) iii (C) iv (B) H– Miscellaneous 1. Among CoF6

3–, NiCl42–, Cu2Cl2 and TiF6

3– the colourless species are: 1. CoF6

3– and NiCl42– 2. TiF6

3–and CoF63–

3. NiCl42– and Cu2Cl2 4. TiF6

3– and Cu2Cl2 2. Which of the following statements is not correct? 1. Ti(NO3)4 is a colourless compound 2. [Cr(NH3)6)]Cl3 is a coloured compound 3. K3[VF6] is a colourless compound 4. [Cu(NCCH3)4]BF4 is a colourless compound

3. Among the following, the compound that is both paramagnetic and coloured is 1. K2Cr2O7 2. (NH4)2[TiCl6] 3. VOSO4 4. K3[Cu(CN)4] 4. Which of the following compounds is expected to be coloured 1. Ag2SO4 2. CuF2 3. MgF2 4. CuCl 5. Complex CrCl3⋅6H2O lose 6.75% of their original mass on treatment with concentrated H2SO4. Formula of the complex is : [At. mass of Cr. 52] 1. [Cr(H2O)6]Cl3 2. [Cr(H2O)5Cl]Cl2⋅H2O 3. [Cr(H2O)4Cl2]Cl⋅2H2O 4. [Cr(H2O)3Cl3]⋅3H2O


Page No. - 20

I– Previous years 1. Among the following complexes the one which shows zero crystal field stabilization

energy (CFSE) is 1. [Mn(H2O)6]3+ 2. [Fe(H2O)6]3+ 3. [Co(H2O)6]2+ 4. [Co(H2O)6]3+ 2. Which of the following complexes is used to be as an anticancer agent? 1. mer-[Co(NH3)3Cl3] 2. cis-[PtCl2(NH3)2] 3. cis-K2[PtCl2Br2] 4. Na2CoCl2 3. A magnetic moment at 1.73 BM will be shown by one among of the following 1. TiCl4 2. [CoCl 6 ]4– 3. [Cu(NH3)4]2+ 4. [Ni(CN)4]2– 4. An excess of AgNO3 is added to 100 mL of a 0.01 M solution of dichlorotetraaquachromium (III)

chloride. The number of moles of AgCl precipitated would be 1. 0.003 2. 0.01 3. 0.001 4. 0.002 5. Crystal field splitting energy for high spin d4 octahedral complex is 1. – 1.2 Δ0 2. – 0.6 Δ0 3. – 0.8 Δ0 4. – 1.6 Δ0 6. In a particular isomer of [Co(NH3)4Cl2], the Cl – Co–Cl angle is 90°, the isomer is known as 1. optical isomer 2. cis-isomer 3. positin isomer 4. linkage isomer 7. The anion of acetylacetone (acac) forms Co (acac)3 chelate with Co3+. The rings of the

chelate are 1. five membered 2. four memberd 3. six membered 4. three membered 8. The correct IUPAC name of [CrF2(en)2] Cl is 1. chlorodifluorideethylenediaminechromium(III) chloride 2. difluoridobis(ethylenediamine)chromium(III) chloride 3. difluorobis(ethylenediamine)chromium(II) chloride 4. chlorodifluoridobis(ethylenediamine)chromium(III) 9. Which among the following is a paramagnetic complex? 1. [Co(NH3)6]3+ 2. [Pt(en)Cl2] 3. [NiCl4]2– 4. [Fe(CN)6]3–

10. Which is diamagnetic? 1. [Co(F6)]3– 2. [Ni(CN)4]2– 3. [NiCl4]2– 4. [Fe(CN)6]3– 11. Which one of the following is an outer orbital complex and exhibits paramagnetic behavior? 1. [Ni(NH3)6]2+ 2. [Zn(NH3)6]2+ 3. [Cr(NH3)6]3+ 4. [Co(NH3)6]3+


Page No. - 21

12. Red precipitate is obtained when ethanol solution of dimethylglyoxime is added to ammonical Ni(II). Which of the following statements is not true?

1. Red complex has a square planar geometry 2. Complex has symmetrical H-bonding 3. Red complex has a tetrahedral geometry 4. Dimethylglyoxime functions as bidentate ligand.

13. Low spin complex of d6-cation in an octahedral field will have the following energy

1. P512

0 +Δ− 2. P3

512

0 +Δ− 3. P2

52

0 +Δ− 4. P

52

0 +Δ−

(Δ0 = crystal field splitting energy in an octahedral field, P = Electron pairing energy) 14. Of the following complex ions, which is diamagnetic in nature? 1. [NiCl4]2– 2. [Ni(CN)4]2– 3. [CuCl4]2– 4. [CoF6]3– 15. The complexes [Co(NH3)6][Cr(CN)6] and [Cr(NH3)6[Co(CN)6] are the example of which

type of isomerism? 1. Linkage isomerism 2. Ionization isomerism 3. Coordination isomerism 4. Geometrical isomerism 16. The complex, [Pt(Py)(NH3)BrCl] will have how many geometrical isomers? 1. 3 2. 4 3. 0 4. 2 17. The d-electron configurations of Cr2+, Mn2+, Fe2+ and Co2+ are d4, d5, d6 and d7

respectively. Which one of the following will exhibit minimum paramagnetic behaviour? 1. [Mn(H2O)6]2+ 2. [Fe(H2O)6]2+ 3. [Co(H2O)6]2+ 4. [Cr(H2O)6]2+ 18. Which of the following carbonyl will have the strongest C – O bond? 1. Mn(CO)6

+ 2. Cr(CO)6 3. V(CO)6 4. Fe(CO)5 19. Which of the following complex compounds will exhibit highest paramagnetic behaviour? 1. [Ti(NH3)6]3+ 2. [Cr(NH3)6]3+ 3. [Co(NH3)6]3+ 4. [Zn(NH3)6]2+ 20. Which of the following complex ions is not expected to absorb visible light? 1. [Ni(CN)4]2– 2. [Cr(NH3)6]3+ 3. [Fe(H2O)6]2+ 4. [Ni(H2O)6]2+ 21. The existence of two different coloured complexes with the composition of

[Co(NH3)4Cl2]+ is due to 1. linkage isomerism 2. geometrical isomerism 3. coordination isomerism 4. ionization isomerism

Dimethylglyoxime = Dimethylglyoxime = H3C – C = N

H3C – C = N

OH

OH


Page No. - 22

22. Which one of the following complexes is not expected to exhibit isomerism? 1. [Ni(NH3)4(H2O)2]2+ 2. [Pt(NH3)2Cl2] 3. [Ni(NH3)2Cl2] 4. [Ni(en)3]2+ 23. Out of TiF6

2–, CoF63–, Cu2Cl2 and NiCl4

2– (Z of Ti = 22, Co = 27, Cu = 29, Ni = 28) the colourless species are

1. Cu2Cl2 and NiCl42– 2. TiF6

2– and Cu2Cl2 3. CoF6

3– and NiCl42– 4. TiF6

2– and CoF63–

24. Which of the following does not show optical isomerism? 1. [Co(NH3)3Cl3]0 2. [Co(en)Cl2(NH3)2]+ 3. [Co(en)3]3+ 4. Co(en)2Cl2]+ 25. Which of the following complex ion is expected to absorb visible light? 1. [Ti(en)2(NH3)2]4+ 2. [Cr(NH3)6]3+ 3. [Zn(NH3)6]2+ 4. [Sc(H2O)3(NH3)3]3+ 26. Which of the following complexes exhibits the highest paramagnetic behaviour? 1. [Co(ox)2(OH)2]3– 2. [Ti(NH3)6]3+ 3. [V(gly)2(OH)2(NH3)2]+ 4. [Fe(en)(bpy)(NH3)2]2+ 27. In which of the following coordination entities the magnitude of Δ0 (CFSE in octahedral

field) will be maximum? 1. [Co(CN)6]3– 2. [Co(C2O4)3]3– 3. [Co(H2O)6]3+ 4. [Co(NH3)6]3+ 28. Which of the following will give a pair of enantiomorphs? 1. [Cr(NH3)6][Co(CN)6] 2. [Co(en)2Cl2]Cl 3. [Pt(NH3)4][PtCl6] 4. [Co(NH3)4Cl2]NO2 29. [Cr(H2O)6]Cl3 (At. no. of Cr = 24) has a magnetic moment of 3.83 B.M.. The correct

distribution of 3d electrons in the chromium of the complex is 1. 1

2z1yz

1xy d3,d3,d3 2. 1

xz1

2z

1

)2y2x(d3,d3,d3

−

3. 1yz

1

)2y2x(

1xy d3,d3,d3

− 4. 1

xz1yz

1xy d3,d3,d3

30. [Co(NH3)4(NO2)2]Cl exhibits 1. linkage isomerism, geometrical isomerism and optical isomerism 2. linkage isomerism, ionization isomerism and optical isomerism 3. linkage isomerism, ionization isomerism and geometrical isomerism 4. ionization isomerism, geometrical isomerism and optical isomerism


Page No. - 23

31. Which one of the following is an inner orbital complex as well as diamagnetic in behaviour?

1. [Zn(NH3)6]2+ 2. [Cr(NH3)6]3+ 3. [Co(NH3)6]3+ 4. [Ni(NH3)6]2+ 32. Which one of the following is expected to exhibit optical isomerism? (en = ethylenediamine) 1. cis-[Pt(NH3)2Cl2] 2. trans-[Pt(NH3)2Cl2] 3. cis-[Co(en)2Cl2] 4. trans-[Co(en)2Cl2] 33. Which of the following coordination compounds would exhibit optical isomerism? 1. Pentaamminenitrocobalt(III) iodide. 2. Diamminedichloroplatinum(II) 3. trans-dicyano-bis(ethylenediamine)chromium(III) chloride 4. tris(ethylenediamine)cobalt(III) bromide 34. Among [Ni(CO)4], [Ni(CN)4]2–, [NiCl4]2– species, the hybridisation states at the Ni atom

are, respectively 1. sp3, dsp2, dsp2 2. sp3, dsp2, sp3 3. sp3, sp3, dsp2 4. dsp2, sp3, sp3 35. CN– is a strong field ligand. This is due to the fact that 1. it carries negative charge 2. it is a pseudohalide 3. it can accept electrons from metal species 4. it forms high spin complexes with metal species 36. Considering H2O as a weak field ligand, the number of unpaired electrons in [Mn(H2O)6]2+

will be (atomic number of Mn = 25) 1. three 2. five 3. two 4. four 37. Which of the following does not have a metal carbon bond? 1. Al(OC2H5)3 2. C2H5MgBr 3. K[Pt(C2H4)Cl3] 4. [Ni(CO)4] 38. In an octahedral structure, the pair of d orbitals involved in d2sp3 hybridisation is 1. 222 zyx d,d

− 2. 22 yxxz d,d

− 3. xzz

d,d 2 4. yzxy d,d 39. The number of unpaired electron is the complex ion (CoF6)3– is 1. 2 2. 3 3. 4 4. zero 40. Among the following which is not the π-bonded organometallic compound? 1. K [PtCl3 (η2 – C2H4)] 2. Fe (η5 – C5H5)2 3. Cr (η6 – C6H6)2 4. [(CH3)4Sn] 41. Atomic number of Cr and Fe are respectively 24 and 26, which of the following is

paramagnetic ? 1. [Cr(CO)6] 2. [Fe(CO)5] 3. [Fe(CN)6]4– 4. [Cr(NH3)6]3+ 42. Consider the coordination compound, [Co(NH3)6]Cl3. In the formation of this complex, the

species which acts as the Lewis acid is 1. [Co(NH3)6]3+ 2. Co3+ 3. Cl– 4. NH3


Page No. - 24

43. Which of the following name formula combinations is not correct Formula Name 1. K[Cr(NH3)2Cl4] Potassium diamminetetrachlorochromate (III)

2. [Co(NH3)4(H2O)I]SO4 Tetraammine aquaiodo cobalt (III) sulphate

3. K2[Pt(CN)4] Potassium tetracyanoplatinate (II)

4. [Mn(CN)5]2– Pentacyanomagnate (II) ion 44. If octahedral complex of Co3+ is diamagnetic, then the hybridization of this complex will

be. (Co = 27) 1. dsp2 2. d2sp2 3. sp3d2 4. d2sp3 45. When concentrated HCl is added to an aqueous solution of CoCl2, its colour changes from

reddish pink to deep blue. Which complex ion gives blue colour in this reaction? 1. [Co(H2O)6]2+ 2. [CoCl6]3– 3. [CoCl6]4– 4. [CoCl4]2–

46. Which of the following complex ions has electrons that are symmetrically filled in both t2g

and eg orbitals? 1. [Mn(CN)6]4– 2. [FeF6]3– 3. [CoF6]3– 4. [Co(NH3)6]2+ 47. The correct statement on the isomerism associated with the following complex ions,

(a) [Ni(H2O)5NH3]2+, (b) [Ni(H2O)4(NH3)2]2+ and (c) [Ni(H2O)3(NH3)3]2+ is : 1. (a) and (b) show only geometrical isomerism 2. (a) and (b) show geometrical and optical isomerism 3. (b) and (c) show geometrical and optical isomerism 4. (b) and (c) show only geometrical isomerism

48. Which one of the following complexes will consume more equivalents of aqueous solution

of Ag(NO3) ? 1. Na3[CrCl6] 2. [Cr(H2O)5Cl]Cl2 3. [Cr(H2O)6]Cl3 4. Na2[CrCl5(H2O)]

49. Identify the correct trend given below :

(Atomic No.=Ti : 22, Cr : 24 and Mo : 42) 1. Δo of [Cr(H2O)6]2+ > [Mo(H2O)6]2+ and Δo of [Ti(H2O)6]3+ > [Ti(H2O)6]2+

2. Δo of [Cr(H2O)6]2+ > [Mo(H2O)6]2+ and Δo of [Ti(H2O)6]3+ < [Ti(H2O)6]2+

3. Δo of [Cr(H2O)6]2+ < [Mo(H2O)6]2+ and Δo of [Ti(H2O)6]3+ > [Ti(H2O)6]2+

4. Δo of [Cr(H2O)6]2+ < [Mo(H2O)6]2+ and Δo of [Ti(H2O)6]3+ < [Ti(H2O)6]2+

50. [Co2(CO)8] displays : 1. no Co–Co bond, six terminal CO and two bridging CO 2. no Co–Co bond, four terminal CO and four bridging CO 3. one Co–Co bond, six terminal CO and two bridging CO 4. one Co-Co bond, four terminal CO and four bridging CO


Page No. - 25

51. In Wilkinson's catalyst, the hybridization of central metal ion and its shape are respectively: 1. sp3d, trigonal bipyramidal 2. d2sp3, octahedral 3. dsp2, square planar 4. sp3, tetrahedral

52. Homoleptic octahedral complexes of a metal ion 'M3+' with three monodentate ligands L1,

L2, L3 absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength is :

1. L2 < L1 < L3 2. L3 < L2 < L1 3. L3 < L1 <L2 4. L1 < L2 < L3 53. The total number of isomers for a square planar complex [M(F)(Cl)(SCN)(NO2)] is : 1. 12 2. 8 3. 16 4. 4 54. The coordination number of Th in K4[Th(C2O4)4(H2O)2] is :- (C2O4

2– = oxalato) 1. 6 2. 10 3. 14 4. 8 55. The metal d-orbitals that are directly facing the ligands in K3[Co(CN)6] are :

1. dxz, dyz and dz2 2. dxy, dxz and dyz 3. dxy and dx2–y2 4. dx2–y2 and dz2

56. Mn2(CO)10 is an organometallic compound due to the presence of :

1. Mn – Mn bond 2. Mn – C bond 3. Mn – O bond 4. C – O bond

57. The one that will show optical activity is :

(en = ethane-1,2-diamine) 1. 2. 3. 4. 58. The degenerate orbitals of [Cr(H2O)6]3+ are :

1. dyz and 2zd 2. 2z

d and dxz 3. dxz and dyz 4. 22 yxd

−and dxy

59. The number of water molecule(s) not coordinated to copper ion directly in CuSO4.5H2O, is: 1. 2 2. 4 3. 1 4. 3 60. The compound that inhabits the growth of tumors is : 1. ( ) ]NHClPt[trans 232− 2. ( ) ]NHClPd[trans 232− 3. ( ) ]NHClPd[cis 232− 4. ( ) ]NHClPt[cis 232−


Page No. - 26

61. The calculated spin-only magnetic moments (BM) of the anionic and cationic species of ( ) ( ) −+ 4

62

62 ]CNFe[and]OHFe[ respectively, are : 1. 2.84 and 5.92 2. 4.9 and 0 3. 0 and 4.9 4. 0 and 5.92 62. Three complexes,

[CoCl(NH3)5]2+ (I), [Co(NH3)5H2O]3+ (II) and [Co(NH3)6]3+ (III) absorb light in the visible region. The correct order of the wavelength of light absorbed by them is : 1. (III) > (I) > (II) 2. (I) > (II) > (III) 3. (II) > (I) > (III) 4. (III) > (II) > (I)

63. The species that can have a trans-isomer is :

(en = ethane-1, 2-diamine, ox = oxalate) 1. [Pt(en)Cl2] 2. [Cr(en)2(ox)]+ 3. [Zn(en)Cl2] 4. [Pt(en)2Cl2]2+

64. In which of the following octahedral complex species the magnitude of Δo will be

maximum? 1. [Co (H2O)6]2+ 2. [Co (CN)6]3– 3. [Co (C2O4)3]3– 4. [Co (NH3)6]3+ 65. The magnetic moment of the complex anion [Cr(NO) (NH3)(CN)4]2– is 1. 5.91 BM 2. 3.87 BM

3. 1.73 BM 4. 2.82 BM 66. Type of isomerism which exists between [Pd(C6H5)2(SCN)2] and [Pd(C6H5)2(NCS)2] is : 1. Coordination isomerism 2. Solvate isomerism 3. Linkage isomerism 4. Ionisation isomerism 67. An octahedral complex with molecular composition M. 5NH3.Cl.SO4 has two isomers, A

and B. The solution of A gives a white precipitate with AgNO3 solution and the solution of B gives white precipitate with BaCl2 solution. The type of isomerism exhibited by the complex is :

1. Linkage isomerism 2. Coordinate isomerism 3. Geometrical isomerism 4. Ionisation isomerism 68. Nickel(Z = 28) combines with a uninegative monodentate ligand to form a diamagnetic

complex [NiL4]2–. The hybridisation involved and the number of unpaired electrons present in the complex are respectively :

1. dsp2, one 2. dsp2, zero 3. sp3, zero 4. sp3, two 69. Which one of the following complexes will most likely absorb visible light?

(At nos. Sc = 21, Li = 22, V = 23, Zn = 30) [Sc(H2O)6]3+ : 1. [Sc(H2O)6]3+ 2. [Zn(NH3)6]2+ 3. [Ti (NH3)6]4+ 4. [V(NH3)6]3+


Page No. - 27

70. Mark the correct statement about [Fe(CN)6]3– and [FeF6]3–, (Z = 26) 1. [Fe(CN)6]3– is diamagnetic and [FeF6]3– is Paramagnetic 2. [Fe(CN)6]3– Paramagnetic and [FeF6]3– is diamagnetic 3. Both are paramagnetic 4. Both are diamagnetic 71. Which molecule/ion among the following cannot act as a ligand in complex compounds?

1. CO 2. CN- 3. CH4 4. Br-

72. The pair of compounds having metals in their highest oxidation state is :

1. MnO2 and CrO2Cl2 2. [Fe(CN)6]3– and [Cu(CN)4]2– 3. [NiCl4]2– and [CoCl4]2– 4. [FeCl4]2– and Co2O3

73. The correct combination is :

1. [NiCl4]2– – square-planar ; [Ni(CN)4]2– – paramagnetic 2. [Ni(CN)4]2– – tetrahedral ; [Ni(CO)4]2– – paramagnetic 3. [NiCl4]2– – paramagnetic ; [Ni(CO)4] – tetrahedral 4. [NiCl4]2– – diamagnetic ; [Ni(CO)4] – square-planar

74. Which of the following complexes will show geometrical isomerism ?

1. Potassium tris(oxalato)chromate(III) 2. Pentaaquachlorochromium(III)chloride 3. Aquachlorobis(ethylenediamine)cobalt(II) chloride 4. Potassium amminetrichloroplatinate(II)

75. The complex that has highest crystal field splitting energy (Δ), is :

1. K3[Co(CN)6] 3. [Co(NH3)5(H2O)]Cl3 3. K2[CoCl4] 4. [Co(NH3)5Cl]Cl2

76. Two complexes [Cr(H2O6)Cl3] (A) and [Cr(NH3)6]Cl3 (B) are violet and yellow coloured, respectively. The incorrect statement regarding them is : 1. Δ0 value of (A) is less than that of (B). 2. Δ0 value of (A) and (B) are calculated from the energies of violet and yellow light, respectively 3. Both absorb energies corresponding to their complementary colors. 4. Both are paramagnetic with three unpaired electrons. 77. A reaction of cobalt(III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) B (green coloured). A can show optial actively, B is optically inactive. What type of isomers does A and B represent ? 1. Geometrical isomers 2. Ionisation isomers 3. Coordination isomers 4. Linkage isomers 78. Wilkinson catalyst is : 1. [(Ph3P)3RhCl] (Et = C2H5) 2. [Et3P)3IrCl] 3. [Et3P)3RhCl] 4. [Ph3P)3IrCl]


Page No. - 28

79. The crystal fied stabilization energy (CFSE) of [Fe(H2O)6]Cl2 and K2[NiCl4], respectively, are :- 1. –0.4Δ0 and –0.8Δt 2. –0.4Δ0 and –1.2Δt 3. –2.4Δ0 and –1.2Δt 4. –0.6Δ0 and

80. Consider the following complex ions, P, Q and R. P = [FeF6]3–, Q = [V(H2O)6]2+ and

R = [Fe(H2O)6]2+. The correct order of the complex ions, according to their spin-only magnetic moment values (in B.M.) is

1. R < Q < P 2. Q < R < P 3. R < P < Q 4. Q < P < R 81. NiCl2{P(C2H5)2(C6H5)}2 exhibits temperature dependent magnetic behaviour

(paramagnetic/diamagnetic). The coordination geometries of Ni2+ in the paramagnetic and diamagnetic states are respectively

1. tetrahedral and tetrahedral 2. square planar and square planar 3. tetrahedral and square planar 4. square planar and tetrahedral

82. As per IUPAC nomenclature, the name of the complex [Co(H2O)4(NH3)2]Cl3 is 1. tetraaquadiaminecobalt(III) chloride 2. tetraaquadiamminecobalt(III) chloride 3. diaminetetraaquacobalt(III) chloride 4. diamminetetraaquacobalt(III) chloride 83. Among the following complexes (K-P), K3[Fe(CN)6](K), [Co(NH3)6]Cl3 (L),

Na3[Co(oxalate)3](M), [Ni(H2O)6]Cl2(N), K2[Pt(CN)4](O) and [Zn(H2O)6](NO3)2(P) the diamagnetic complex are

1. K, L, M, N 2. K, M, O, P 3. L, M, O, P 4. L, M, N, O 84. Geometrical shapes of the complexes formed by the reaction of Ni2+ with Cl–, CN– and

H2O, respectively, are 1. octahedral, tetrahedral and square planar 2. tetrahedral, square planar and octahedral 3. square planar, tetrahedral and octahedral 4. octahedral, square planar and octahedral. 85. The complex showing a spin–only magnetic moment of 2.82 B.M. is 1. Ni(CO)4 2. [NiCl4]2– 3. Ni(PPh3)4 4. [Ni(CN)4]2– 86. The correct structure of ethylenediaminetetraacetic acid (EDTA) is 1. 2. 3.

4.

N–CH = CH–N HOOCCH2 CH2COOH HOOCCH2 CH2COOH

N–CH2 – CH2–N HOOC COOH HOOC COOH

N–CH2CH2–N HOOCCH2 CH2COOH HOOCCH2 CH2COOH

N–CHCH2–N HOOCCH2 H

H CH2COOH CH2

CH2 COOH

HOOC


Page No. - 29

87. The ionization isomer of [Cr(H2O)4Cl(NO2)]Cl is 1. [Cr(H2O)4(O2N)]Cl2 2. [Cr(H2O)4Cl2](NO2) 3. [Cr(H2O)4Cl(ONO)]Cl 4. [Cr(H2O)4Cl2(NO2)].H2O

88. The IUPAC name of [Ni(NH3)4][NiCl4] is 1. tetrachloronickel(II)-tetraamminenickel(II) 2. tetraamminenickel(II) – tetrachloronickel(II) 3. tetraamminenickel(II) – tetrachloronickelate(II) 4. tetrachloronickel(II) – tetraamminenickelate(0) 89. Both [Ni(CO)4] and [Ni(CN)4]2– are diamagnetic. The hybridizations of nickel in these

complexes, respectively, are 1. sp3, sp3 2. sp3, dsp2 3. dsp2, sp3 4. dsp2, dsp2 90. Among the following, the coloured compound is 1. CuCl 2. K3[Cu(CN)4] 3. CuF2 4. [Cu(CH3CN)4]BF4

91. Which of the following is diamagnetic ? 1. [Fe(CN)6]3– 2. [Co(OX)]3– 3. [FeF6]3– 4. [Co(F6)]3–

92. Which kind of isomerism is exhibited by octahedral Co(NH3)4Br2Cl ? 1. Geometrical and Ionization 2. Geometrical and Optical 3. Optical and Ionization 4. Geometrical only 93. The pair of the compounds in which both the metals are in the highest possible oxidation

state is 1. [Fe(CN)6]3–, [Co(CN)6]3– 2. CrO2Cl2, −

4MnO 3. TiO3, MnO2 4. [Co(CN)6]3–, MnO3 94. The species having tetrahedral shape is 1. [PdCl4]2– 2. [Ni(CN)4]2– 3. [Pd(CN4)]2– 4. [NiCl4]2– 95. The complex ion which has no d electrons in the central metal atom is 1. [MnO4]– 2. [Co(NH3)6]3+ 3. [Fe(CN)6]3– 4. [Cr(H2O)6]3+ 96. The geometry of Ni(CO)4 and Ni(PPh3)2Cl2 are 1. both square planar 2. tetrahedral and square planar respectively 3. both tetrahedral 4. square planar and tetrahedral respectively 97. Which of the following is an organometallic compound? 1. Lithium methoxide 2. Lithium acetate 3. Lithium dimethylamide 4. Methyl lithium.

98. Among the following, the compound that is both paramagnetic and coloured is 1. K2Cr2O7 2. (NH4)2(TiCl6) 3. CoSO4 4. K3[Cu(CN)4]

99. Which compound is formed when excess of KCN is added to aqueous solution of copper sulphate ?

1. Cu(CN)2 2. K2[Cu(CN)4] 3. K[Cu(CN)2] 4. K3[Cu(CN)4]


Page No. - 30

100. Amongst Ni(CO)4, [Ni(CN)4]2– and −24NiCl

1. Ni(CO)4 and −24NiCl are diamagnetic [Ni(CN)4]2– is paramagnetic

2. −24NiCl and [Ni(CN)4]2– are diamagnetic and Ni(CO)4 is paramagnetic

3. Ni(CO)4 and [Ni(CN)4]2– are diamagnetic and −24NiCl is paramagnetic.

4. Ni(CO)4 is diamagnetic and −24NiCl and [Ni(CN)4]2 are paramagnetic.

Comprehension Type (Only One Option Correct)

Comprehension – 1 An aqueous solution of metal ion M1 reacts separately with reagents Q and R in excess to give tetrahedral and square planar complexes, respectively. An aqueous solution of another metal ion M2 always forms tetrahedral complexes with these reagents. Aqueous solution of M2 on reaction with reagent S gives white precipitate which dissolves in excess of S. The reactions are summarized in the scheme given below : SCHEME : 101. M1, Q and R, respectively are 1. Zn2+, KCN and HCl 2. Ni2+, HCl and KCN 3. Cd2+, KCN and HCl 4. Co2+, HCl and KCN 102 Reagent S is 1. K4[Fe(CN)6] 2. Na2HPO4 3. K2CrO4 4. KOH

Comprehension – 2

The coordination number of Ni2+ is 4. NiCl2 + KCN (excess) → A (cyano complex) A + conc. HCl (excess) → B (chloro complex) 103. The IUPAC name of A and B are 1. potassium tetracyanonickelate(II), potassium tetrachloronickelate(II) 2. tetracyanopotassiumnickelate(II), tetrachloropotassiumnickelate(II) 3. tetracyanonickel(II), tetrachloronickel(II) 4. potassiumtetracyanoniclel(II), potassiumtetrachloroniclel(II)

104. predict the magnetic nature of A and B. 1. Both are diamagnetic 2. A is diamagnetic and B is paramagnetic with one unpaired electron 3. A is diamagnetic and B is paramagnetic with two unpaired electrons. 4. Both are paramagnetic.

Tetrahedral M1 Square planar Q R excess excess

Tetrahedral M2 Tetrahedral Q R excess excess

White precipitate precipitate dissolves S excess

S, stoichiometric amount


Page No. - 31

105. The hybridisation of A and B are 1. dsp2, sp3 2. sp3, sp3 3. dsp2, dsp2 4. sp3d2, d2sp3 One or More Than One Option Correct Type 106. The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are) 1. [Cr(NH3)5Cl]Cl2 and [Cr(NH3)4Cl2]Cl 2. [Co(NH3)4Cl2]+ and [Pt(NH3)2(H2O)Cl]+ 3. [CoBr2Cl2]2– and [PtBr2Cl2]2– 4. [Pt(NH3)3(NO3)]Cl and [Pt(NH3)3Cl]Br 107. The compound(s) that exhibit(s) geometrical isomerism is(are) 1. [Pt(en)Cl2] 2. [Pt(en)2]Cl2 3. [Pt(en)2Cl2]Cl2 4. [Pt(NH3)2Cl2] 108. In nitroprusside ion, the iron and No exist as FeII and NO+ rather than FeIII and NO. These

forms can be differentiated by 1. estimating the concentration of iron

2. measuring the concentration of CN 3. measuring the solid state magnetic moment 4. thermally decomposing the compound One Integer Value Correct Type 109. EDTA4– is ethylenediaminetetraacetate ion. The total number of N–Co–O bond angles in

[Co(EDTA)]1– complex ion is 110. Total number of geometrical isomers for the complex [RhCl(CO)(PPh3)(NH3)] is 111. The number of water molecule(s) directly bonded to the metal centre in CuSO4.5H2O is


Page No. - 32

Matching List Type

112. Match each coordination compound in List – I with an appropriate pair of characteristics from List – II and select the correct answer using the code given below the lists.

{en = H2NCH2CH2NH2; atomic numbers : Ti = 22; Cr = 24; Co = 27; Pt = 78}

Code : P Q R S 1. 4 2 3 1 2. 3 1 4 2 3. 2 1 3 4 4. 1 3 4 2 113. Match the complexes in Column I with their properties listed in Column II.

List – I List – II P [Cr(NH3)4Cl2]Cl 1 Paramagnetic and exhibits

ionization isomerism Q [Ti(H2O)5Cl](NO3)2 2 Diamagnetic and exhibits

cis-trans isomerism R [Pt(en)(NH3)Cl]NO3 3 Paramagnetic and exhibits

cis-trans isomerism S [Co(NH3)4(NO3)2]NO3 4 Diamagnetic and exhibits

ionization isomerism

Column – I Column – II A [Co(NH3)4(H2O)2]Cl2 P Geometrical isomers B [Pt(NH3)2Cl2 Q Paramagnetic C [Co(H2O)5Cl]Cl R Diamagnetic D [Ni(H2O)6]Cl2 S Metal ion with +2 oxidation

state


Page No. - 33

Answers A– Introduction, Important Terms and Werner’s theory

B – Nomenclature

C– Bonding VBT and CFT

D– Effective Atomic Number (EAN) and stability

E– Organo metallic compounds

F– Isomerism

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 2 2 3 2 3 3 1 4 2 4 Q. No. 11 12 13 14 15 16 17 18 19 20

Answer 2 1 3 3 2 4 2 2 4 2 Q. No. 21 22 23 24 25 26 27 28 29 30

Answer 4 2 4 2 4 4 2 1 3 1 Q. No. 31 32 33 34 35 36 37 38 39 40

Answer 1 2 2 3 2 2 4 3 1 4 Q. No. 41 42 43 44 45 46 47 48 49 50

Answer 2 1 3 2 1 1 3 2 3

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 2 3 4 2 2 3 1 2 2 1

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 3 1 4 2 3 2 3 4 3 4 Q. No. 11 12 13 14 15 16 17 18 19 20

Answer 3 3 2 2 3 2 3 2 4 3 Q. No. 21 22 23 24 25 26 27 28 29 30

Answer 3 4 2 3 4 2 2 3 2 2 Q. No. 31 32 33 34 35 36 37 38 39 40

Answer 2 3 3 3 4 3 1 3 2 2 Q. No. 41 42 43 44 45 46 47

Answer 1 2 3 2 4 1 4

Q. No. 1 2 3 4 5 6 7 Answer 2 2 3 3 3 3 4

Q. No. 1 2 3 4 5 6 7 Answer 4 3 2 4 3 1 1

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 4 3 1 4 3 3 3 1 3 4 Q. No. 11 12 13 14 15 16 17 18 19 20

Answer 1 1 2 2 3 3 2 1 3 2 Q. No. 21 22 23 24 25 26 27 28 29 30

Answer 4 3 3 3 4 2 4 3 1 1 Q. No. 31 32 33 34 35 36 37 38 39 40

Answer 4 2 4 2 2 1 2 2 3 4 Q. No. 41 42 43

Answer 3 4 4


Page No. - 34

G– Application of Coordination compound

H– Miscellaneous

I– Previous years

Q. No. 1 2 3 4 5 6 7 8 9 Answer 2 4 3 4 1 1 3 1 1

Q. No. 1 2 3 4 5 Answer 4 3 3 2 2

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 2 2 3 3 2 2 3 2 3 2 Q. No. 11 12 13 14 15 16 17 18 19 20

Answer 1 3 2 2 3 1 3 1 2 1 Q. No. 21 22 23 24 25 26 27 28 29 30

Answer 2 3 2 1 2 4 1 2 4 3 Q. No. 31 32 33 34 35 36 37 38 39 40

Answer 3 3 4 2 3 2 1 1 3 4 Q. No. 41 42 43 44 45 46 47 48 49 50

Answer. 4 2 4 4 4 2 4 3 3 3 Q. No. 51 52 53 54 55 56 57 58 59 60

Answer 3 3 1 2 4 2 3 3 3 4 Q. No. 61 62 63 64 65 66 67 68 69 70

Answer 3 2 4 2 3 3 4 2 4 3 Q. No. 71 72 73 74 75 76 77 78 79 80

Answer 3 2 3 3 1 2 1 1 1 2 Q. No. 81 82 83 84 85 86 87 88 89 90

Answer. 3 4 3 2 2 3 2 3 2 3 Q. No. 91 92 93 94 95 96 97 98 99 100

Answer 2 1 2 4 1 3 4 3 4 3 Q. No. 101 102 103 104 105 106 107 108 109 110 Answe 2 4 1 2 1 2,4 3,4 3 8 3 Q. No. 111 112 113 Answe 4 2 A(P, Q, S); B(P, R, S); C(Q, S) ; D(Q,S)

PHYSICS

JRS Tutorials, Durgakund, Varanasi-221005, Ph No.(0542) 2311922, 2311777

JRS TUTORIALSELECTROSTATICS (12-IIT)

DPP-07 : Electric potential1. A charge + q is fixed at each of the point x = x0, x = 3x0, x = 5 x0, .......ad inf. on the

x-axis, and charges –q is fixed at each of the point x = 2x0, x = 4x0, x = 6 x0,........ad inf.Here x0 is a positive constant. Then the potential at the origin due to the above system ofcharges is

(A) 0 (B) qx8 20 0 In (C) (D)

q4 x0 0

In 2

2. If two electric charges q and -2q are placed at distance 6a apart, then the locus of point in theplane of charges, where the electric potential is zero, is(A) x2 + 2y2 – 4ax – 12a2 = 0 (B) 2x2 + y2 + 4ax – 12a2 = 0(C) x2 + y2 + 4ax – 12a2 = 0 (D) x2 + y2 + 8ax + 12a2 = 0

3. Positive and negative point charges of equal magnitude are kept at a(0,0, )2 and

a(0,0, )2

,

respectively. The work done by the electric field when another positive point charge ismoved from (–a, 0, 0) to (0, a, 0) is(A) positive (B) negative (C) zero(D) depends on the path connecting the initial and final positions

4. The electric potential at a point (x, y) in the x-y plane is given by V = Kxy. The magnitude offield intensity at a distance r (only in xy–plane), from the origin varies proportional to:

(A) r2 (B) r (C) r1 (D) 2r

1

5. A graph of the x component of the electric field as a function of x in a region of space is shown.The Y and Z components of the electric field are zero in this region. If the electric potential is 10V at the origin, then potential at x = 2.0 m is :

(A) 10 V (B) 40 V (C) – 10 V (D) 30 V6. Two large vertical and parallel metal plates having a seperation of 1 cm are connected to a

DC voltage source of potential difference X. A proton is released at rest midway between thetwo plates. It is found to move at 45° to the vertical just after release.Then X is nearly

(A) 51 10 V (B) 71 10 V (C) 91 10 V (D) 101 10 V

PHYSICS


7. In a uniform electric field, the potential is 10V at the origin of coordinates, and 8V at eachof the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). The potential at the point (1, 1, 1) will be(A) 0 (B) 4 V (C) 8 V (D) 10 V

8. A uniform electric field of 400 V/m exists in space as shown in graph. Two points A and Bare also shown with their co-ordinates. The potential difference VB – VA in volts, is :

16°

B

E=400 V/my

x

(0,3cm)

A (-4cm, 0)

(A) 18 V (B) 15 V (C) 12 V (D) 8 V9. Figure shows an electric line of force which curves along a circular arc. The magnitude of

electric field intensity is same at all points on this curve and is equal to E. If the potential at A isV, then the potential at B is :(A) V – ER

(B) V – E2R sin2

(C) V + ER

(D) V + 2ER sin 2

10. The curve represents the distribution of potential (U) along the straight line joining the twocharges Q1 and Q2 (separated by a distance r) :

1. | Q1 | > |Q2 | 2. Q1 is positive in nature3. A and B are equilibrium points. 4. C is a point of unstable equilibriumThen which of the above statements are correct.(A) 1 and 3 (B) 1, 2 and 3 (C) 1, 2 and 4 (D) 1, 2, 3 and 4

11. A nonconducting ring of radius 0.5 m carries a total charge of 1.11 × 10–10 C distributed non-uniformly on its curcumference producing an electric field E everywhere in space. The value of

the lineintegral l 0

l

E.dl

(l = 0 being centre of the ring) in volts is

(A) +2 (B) –1 (C) –2 (D) zero

PHYSICS


12. The electric field intensity at all points in space is given by E

= j - i 3 volts/metre. The nature

of equipotential lines in x-y plane is given by

(A) x

y

30°

High potential

Low potential

(B) x

y

30°

High potential

Low potential

(C) x

y

60°

High potential

Low potential

(D) x

y

60°

High potential

Low potential

13. A non – conducting semicircular disc (as shown in figure) has a uniform surface charge density. The ratio of electric field to electric potential at the centre of the disc will be :

(A) )ab(a/bn1

(B) 2

(C) )ab()a/b(n1 2

(D) )a/b(n2)ab(

Multiple options correct14. The electric field produced by a positively charged particle, placed in an xy-plane is 7.2 (4i + 3j)

N/C at the point (3 cm, 3cm) and 100 i N/C at the point (2 cm, 0).(A) The x-coordinate of the charged particle is –2cm.(B) The charged particle is placed on the x-axis.(C) The charge of the particle is 10 x 10–12 C.(D) The electric potential at the origin due to the charge is 9V.

15. Six point charges are kept at the vertices of a regular hexagon of side L and centre O, as shown

in the figure. Given that K = 20 L

q4

1 , which of the following statement (s) is (are) correct?

(A) the elecric field at O is 6K along OD

(B) The potential at O is zero

(C) The potential at all points on the line PR is same

(D) The potential at all points on the line ST is same.

16. A wire having a positive uniform linear charge density , is bent in the form of a ring of radiusR. Point A as shown in the figure, is in the plane of the ring but not at the centre. Two elementsof the ring of lengths a1 and a2 subtend very small same angle at the point A. They are at distancesr1 and r2 from the point A respectively.

PHYSICS


a1

a2

r2

r1

A

(A) The ratio of charge of elements a1 and a2 is r1/r2.(B) The element a1 produced greater magnitude of electric field at A than element a2.(C) The elements a1 and a2 produce same potential at A.(D) The direction of net electric field at A is towards element a2.

17. Two concentric rings of radii R1 = 6m and R2 = 4m are placed in y-z plane with their centres atorigin. They have uniform charge –q and +Q = 2 2q on the inner and outer rings respectively..Consider the electrostatic potential to be zero at infinity. Then

+Q-q

R1

R2

x

(A) The electric potential is zero at origin.(B) The electric field intensity is zero at r = 2 m.(C) A positive charged particle disturbed from origin along the x-axis will restore back to origin.(D) Where potential is maximum on the x-axis, field intensity is zero.

Subjective Questions

18. Find the potential at the edge of a thin disc of radius R carrying the uniformly distributedcharge with surface density .

19. A particle of charge 2C and mass 1mg is left from position (5, 0) meters with velocity(10 j ) m/s. The electric potential in the regions is given by the equation V = (x2+ y2 + 5) volts.Find (a) the radius of curvature the path particle initially (b) Will the path of the particle becircular? Support your answer with proper mathematical or logical argument ( in short).

20. Find the potential (x, y) of given electrostatic field ,

(i) E = 2axyi + a(x2 - y2) j (ii) E = ayi + (ax + bz)j + byk,

where a is a constant, i and j are the unit vectors of the x and y axes.

PHYSICS


21. A point charge q & mass 100 gm experiences a force of 100 N at a point at a distance 20 cmfrom a long infinite uniformly charged wire. If it is released then its speed when it is at a distance

40 cm from wire is 20 ln . Find

22. A thin elastic rod (of uniform density) of natural length L and uniform cross-sectional areaA and Young's modulus Y has uniform linear charge density charge per unit length). Therod is placed in gravity free space having uniform electric field of magnitude E and directedparallel to length of the rod. Find the magnitude of extension in length of this rod ?

E

L

23. An infinitely long string uniformly charged with a linear charge density 1 and a segment oflength uniformly charged with linear charge density 2 lie in a plane at right angles toeach other and separated by a distance r0. Determine the force with which these two inter-act.

24. Two infinite rods with linear charge density + are kept apart by distance d. An electron e is keptat the midpoint between the two rod . On being given slight vertical displacement (in the planeperpendicular to the plane of rods). Find the time period of this oscillatory motion. Is itS.H.M.(Neglect gravity).

25. Two coaxially rings each of radius R and R distance apart, each of them carrying a uniformlydistributed charge Q. Another charge q is placed at mid point of the line joining their centres.Prove that the charge q will execute S.H.M. For small oscillation, when displaced along the axisof the rings provided Qq < 0. Find the frequency of oscillation if mass of the object is m.(Neglect any gravitational effect)

PHYSICS


ANSWER KEY1. D 2. C 3. C 4. B 5. D 6. C

7. B 8. C 9. A 10. C 11. A 12. C

13. C

14. BCD 15. ABCD 16. ABCD 17. BCD

18. = 0

R 19. (a) 5 m (b) Yes

20. (i)= ay y

x2

2

3

+ const. (ii) = – y(ax+bz) + const.

21. 2 22. 0

23. F = 1 2

02 n 1

0

r

24.emd2

0

25. 21

30 5mR25

Qq82


JRS TUTORIALS CHEMISTRY 20-21

Coordination compound –DPP-1

Subjective 1. Classify the following in monodentate (but not ambidentate) ligands, bidentate ligands and

ambidentate ligands 1. SCN- 2. NO2

- 3. NO2+ 4. CN- 5. CO 6. NH2NH3

+ 7. NO+ 8. en 9. NH2

- 10. NH4+ 11. NO3

- 12. CH3COO-

13 O22-

2. Draw the structure of following ligands 1. DMG 2. Gly 3. acac 4. EDTA4-

3. Classify the following in neutral ligands, cationic ligands and anionic ligands, 1. methyl amine 2. carbon monoxide 3. en 4. pyridine

5. hydrazinium ion 6. nitrosonium ion 7. nitronium ion 8. hydroxide ion 9. amide ion 10. oxalate ion 11. dmgH 12. glycinate ion

4. Classify the following in one negative charge, two negative charge and neutral ligand

1. nitrate ion 2. oxalate ion 3. amide ion 4. hydride ion 5. peroxide ion 6. oxide ion 7. imide ion 8. triphenyl phosphene 9. diethyltriamine (dien) 10. carbon monoxide

(Only one option is correct) 1. Which of the following species is not expected to be a ligand 1. NO+ 2. NH4

+ 3. NH2– NH3+ 4. CO

2. The neutral ligand is

1. chloride 2. Hydroxide 3. Ammonia 4. Oxalate 3. Select bidentate or didentate ligand from the following .

1. CO 2. SCN– 3. CH3COO- 4. C2O42–

4. To form a coordination bond, one needs a ligand. Which of the following species to be a

ligand (i) NH4

+ (ii) NO+ (iii) C5H5NH2 (iv) NH2NH3+

1. i only 2. i & ii only 3. i & iii only 4. ii, iii & iv only 5. Which of the ligands can not acts as a ambidentate ligand?

1. CNS- 2. NO2- 3. CN- 4. CO

6. ethane-1,2-diamine acts as :

1. Monodentate ligand 2. Chelating ligand 3. Bridging ligand 4. Cationic ligand

7. Diethylene triamine is: 1. Chelating agent 2. Neutral ligand

3. Tridentate ligand 4. All of these


2 8. Which of the following is not chelating agent?

1. thiosulphato 2. oxalato 3. glycinato 4. ethylenediamine 9. Which of the following has five donor (coordinating) sites? 1. Triethylenetetramine 2. Ethylenediaminetetracetate ion 3. Ethylenediaminetriacetate ion 4. Diethylenetriamine 10. The number of donor sites in dimethylglyoxime, glycinato, diethylenetriamine and EDTA

are respectively: 1. 2, 2, 3 and 4 2. 2, 2, 3 and 6 3. 2, 2, 2 and 6 4. 2, 3, 3 and 6 11. Glycinato ligand is 1. -OOC-CH2-NH2 2. Bidentate ligand 3. Two donor sites N and O¯ 4. All 12. Which of the following is π-acid ligand 1. NH3 2. CO 3. F¯ 4. ethylene diamine

Answer

Subjective 1. [monodentate ligands(but not ambidentate) -3,5,6,7,9,11,12,13 bidentate ligands – 8

ambidentate ligands-1,2,4] 2.

O O

(acac)

HON

CH3

CH3

NO

(DMG)

H2NO

O

(Gly)

NN

ΟΟC

ΟΟC

CΟΟ

CΟΟ(EDTA)4–

1. 2.

3. 4.

3. [neutral ligands -1,2,3,4 cationic ligands– 5,6,7 anionic ligands-8,9,10,11,12] 4. Ans [one negative charge – 1,3,4 two negative charge- 2,5,6,7

neutral ligand-8,9,10] (Only one option is correct) Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 2 3 4 4 4 2 4 1 3 2

Q.No. 11 12 Ans 4 2

PHYSICS


JRS TUTORIALSVECTOR (11th IIT)

DPP-02

1. Two forces P and Q are in ratio P : Q = 1 : 2. If their resultant is at an angle tan–1

23

to

vector P, then angle between P and Q is :

(A) tan–1

21

(B) 45° (C) 30° (D) 60°

2. A vector A

is directed along 300 west of north direction and another vector B

along 150 southof east. Their resultant cannot be in _____________ direction.(A) North (B) East (C) North-East (D) South

3. Two forces P and Q act at a point and have resultant R. If Q is replaced by Q)PR( 22

acting in

the direction opposite to that of Q, the resultant(A) remains same (B) becomes half (C) becomes twice (D) none of these

4. ABCD is a quadrilateral. Forces

BA ,

BC ,

CD &

DA act at a point. Their resultant is

(A) 2

AB (B) 2

DA (C) zero vector (D) 2

BA5. If 1 2a and a are two non-collinear unit vectors and is 1 2| a a |

= 3 , then the value of

1 2 1 2(a a ). (2a a ) is.

(A) 2 (B) 3/2 (C) 1/2 (D) 1

6. If ba

is perpendicular to b

and b2a

is perpendicular to a , a = a, b

= b, then

(A) a = b (B) a = 2b (C) b = 2a (D) a = 2b

7. If | |A

= 4 units , A B

= 10 units & A

• ( A

+ B

) = 20 units, find B

(A) 76 units (B) 105 units (C) 21 units (D) zero8. Â B 2i

and Â B 4j

then angle between A and B

is

(A) 127° (B) 143° (C) 53° (D) 37°9. Let u v w, , be the vectors such that u v w 0 , if | | , | | u v 3 4 and | |w 5 then the

value of u v v w w u. . . is :(A) 47 (B) 25 (C) 0 (D) 25

10. If ˆ ˆ Â i 2 j 3k

, ˆ ˆ ˆB i j 4k

& ˆ ˆ ˆC 3i 3 j 12 k

then the angle between the

vectors A B C

and A x B

is :

(A) 30º (B) 60º (C) 0º (D) 90º

PHYSICS


MULTIPLE OPTION CORRECT11. The vector i + xj + 3k is rotated through an angle and doubled in magnitude, then it becomes

4i + (4x – 2) j + 2k. The values of x are

(A) 32

(B) 31

(C) 32

(D) 2

12. Four vectors (A, B,C,D)

all have the same magnitude and lie in a plane. The angle between

adjacent vectors is 45° as shown. Which of the following equation is/are correct ?

45°

45°45°

A B

C

D(A) A C 2 D

(B) B D 2 C 0

(C) A B B D

(D) (A C) / 2 B

13. Given 0dcba

, which of the following statements is/are correct :(A) c,b,a

and d

must each be a zero vector

(B) The magnitude of )ca( equals the magnitude of )db(

.

(C) The magnitude of a can never be greater than the sum of the magnitudes of c,b

and d

.

(D) cb must lie in the plane of a

and d

if a

and d

are not collinear, and in the line of a

and

d

, if they are collinear

INTEGER TYPE QUESTIONS14. Three forces of magnitudes 30, 60 and P newton acting at a point are in equilibrium. If the angle

between the first two is 60º, the value of P is 30 n . Find n

15. A force F

of magnitude 12 N has non-rectangular components P

and Q

. The sum of the

magnitudes of P

and Q

is 18 N. The direction of Q

is at right angles to F

. Find the magnitude

of Q

( in N).16. The resultant of two forces 3P and 2P is R. If the first force is doubled, the resultant is also

doubled. Then find the angle between the two forces (in degrees)17. Consider the two vectors : k3j2i1L

and k6j5i4 l

Find the value of the scalar such that the vector l

L is perpendicular to L

.

PHYSICS


MATCH THE COLUMN18. Three forces 1F

, 2F

and 3F

are represented as shown. Each of them is of equal magnitude.

Column I Column II(Combination) (Approximate Direction)

(A) 321 FFF

(P)

(B) 321 FFF

(Q)

(C) 321 FFF

(R)

(D) 312 FFF

(S)

PASSAGE ( Single or multiple options correct)Two vectors A

and B of unknown magnitudes along D&E

respectively

E

D

19. BA

could be

(A) (B) (C) (D)

20. Then BA

could be

(A) (B) (C) (D)

21. If C is another vector represented as then CBA

could be

(A) (B) Null vector (C) (D)

PHYSICS


ANSWER KEYVECTOR DPP-02

1. D 2. D 3. A 4. D 5. C 6. D

7. A 8. A 9. B 10. D 11. AD 12. ABD

13. BCD 14. 7 15. 5 16. 120 17. 7

18. (A) Q; (B) R; (C) P; (D) S 19. B 20. ABD 21. ABCD

MA/PS/XII/Functions-II/pg-1

JRS TUTORIALS, Durgakund, Varanasi – 221 005 (U.P.) Ph. No. (0542) 3290510, 2311922, 2311777

JRS TUTORIALS Problem Sheet

Functions - II A. Let f : A B, (x, y) f . In each of the following determine whether y is function of x. 1. A = 3,2,1 : B = cba ,, (a) f = ),2(),,2(),,1( cba (b) f = ),3(),,2(),,1( aca (c) f = ),3(),,3(),,2(),,1( cacc 2. A=B=ℝ (a) f = 0|),( 2 yxyx (b) f = 1|),( 22 yxyx (c) f = 32|),( yxyx (d) f = yxyx |),( 3. A= [–1, 1] , B=[0, 1] and y = f (x), where (a) f (x) = x2, (b) f (x) = x3 (c) f (x) = | x – 1 | (d) f (x) = sin x (e) f (x) = cos x 4. A=X, B=ℝ where X is the set of all 2 2 matrices. For M X define f (A) = det (A). B. In each of the following f : A B is a function. Determine whether f is one to one, onto,

both or neither. 1. f : cba ,, 4,3,2,1 , f = )1,(),4,(),1,( cba 2. f : X R, X is the set of all 2 2 matrices f (A) = det (A) 3. f : R R R f (x, y) = x + y 4. Let Z be the set of all integer, Z+ set of all positive integers and Zp = 1...,2,1,0 p

(a) f : Z Z, f (x) =

oddis,2

1evenis,2/

xxxx

(b) f : Z+ Z+, f(x) = x , when [x] integral part of x. (c) f : Z7 Z7, f (x) = 3x (mod 7) where a = b (mod c) c divides a – b 5. (a) f : R R, f (x) = 2x – 3 (b) f : R+ R f (x) = 1x – 1 (c) f : [–2, 3] [0, 4], f (x) = | x + 1| (d) f : [– /6, 5/6] [–2, 2], f (x) = 3 sin x + cos x

(e) f : R [0, 1], f (x) = ||1

1x

MA/PS/XII/Functions-II/pg-2


C. In each of the following find f –1 (x) if f (x) is invertible. 1. f : {a, b, c} {1, 2, 3, 4}, f = { (a, 1), (b, 2), (c, 4)} 2. f : R R, f (x) = 2x – 5

3. f : [–2, ∞) Range (f), f (x) = x2 + 4x + 3 4. f : R\ 2 R \ 3, f (x) = 213

xx

5. f (x) = x + 1/x, 1 < x < 3 6. f (x) = ln (x2 – 2x), x < 0

7. 5/1374 xxf 8. f (x) =

0,0,2

xxxx

ANSWERS

A. 1. (a) is not a function (b) is a function (c) is not a function 2. (a) is a function (b) is not a function (c) is a function (d) is not a function 3. (a) is a function (b) is not a function (c) is not a function (d) is not a function

(e) is a function B. 1. neither 11 nor onto 2. neither 11 nor onto 3. neither 11 nor onto 5. (a) Bijective (b) One-one (c) onto (d) neither 1-1 nor onto (e) neither one-one nor onto

C. 1. not invertible 2. f1 (x) = 2

5x 3. f1 (y) = 2+ 1y

4. ( ) = 5. ( ) = √ 6. ( ) = 1 − √ + 1

7. f1 (y) = 7 + (4 y5)1/3 8. ( ) = √ , ≥ 0, < 0



Functions – III 1. Find the domain of definitions of the following functions.

(i) xxxf 1223 (ii) 211 xxf

(iii) 2/32 1 xxxf (iv) xx

xxxf

11

22

(v) xxxf 2tantan (vi) 1( )1 cos

f xx

(vii) 22( ) 2 log [ 1]f x x (viii) 1 1( ) cos

3 2 | |f x

x

(ix) 푓(푥) = 푙표푔푠푖푛( 푥 + 3) + (x) 푓(푥) =( √ √ )

2. Find the range of the following functions.

(i) 1 4 3 | |( ) sec2

xf x

(ii) 푓(푥) = 4 − 2 + 1

(iii) x

xf3cos2

1

(iv) 48

22

xxxxf

(v) 4242

2

2

xxxxxf (vi) 2

2

16sin3 xxf

(vii) 푓(푥) = sin (푙푛 √ ) (viii) 52 24 xxxf

(ix) 푓(푥) = , n is even (x) 푓(푥) =

3. Find the domain of following functions:

(i) 2

1

4( )cos 2

xf xx

(ii) f(x) = cos log 2x 1 x

(iii) 1( )1 | ln |

f xx

(iv) f(x) = log2

2( 3)3 2

++ +

xx x

(v) ( ) ln | ln |f x x (vi) 21log

1

10

xx

xf

(vii)

213sin321 1 xxxf (viii)

212

1sin

xxf x

(ix) 푓(푥) = 푙표푔 푙표푔/

MA/PS/XII/Functions-III/pg-2


4. Let RR :f be given by .1,1)1()( 2 xxxf Then, the set of values of x for which f (x) = f –1 (x) is given by {0, – 1}.

5. Find the range of following functions:

(i) ( ) =f x 23 4 5 x x (ii) f(x) = 2

2

14 3

x xx x

(iii) f(x) = x2 + 21

1x (iv) f (x) = sin(sin–1{x})({.}denotes fractional part of x)

(v) 21 xxxf

(vi) 216 xxf

(vii) x

xfsin34

1

(viii) 392

x

xxf (ix) xnxf 1sin

6. Let Bf

6,

3: defined by .12sin3cos2 2 xxxf Find the B such that

f -1 exists. Also find f -1 (x).

7. Find all real values of ‘a’ for which the range of the function 1

12

xa

xxf does

not contain any values belonging to the interval 3/1,1 . 8. Let f be a one-one function with domain zyx ,, and range 3,2,1 . It is given that

exactly one of the following statements is true and the remaining two are false. .2;1;1 zfyfxf Determine f -1 (1)

9. A function RRf : where R is the set of real numbers is defined by,

.86

862

2

xxxxxf

Find the interval of values of for which f is onto. Is the

function one-to-one for = 3? Justify your answer.

10. If 2 2 = : , = y: 1 1 and ( ) = cos(5 + 2)5 5

A x x B y f x x

then prove that the

mapping : AB is one - one and onto .

11. Find the range of each of the following functions

(i) xx cos4sin3 (ii) x

xx

x22 cot1

costan1

sin

12. Check whether following pairs of functions are identical or not ? (i) 22 & xxgxxf

(ii) xececxgxxf 11 coscos&secsec

(iii) xxgxxf cos&2

2cos1

(iv) and n xf x x g x e



13. Draw the graph of the function 342 xxxf and also find the set of values of ‘a’ for which the equation f (x) = a has exactly four distinct real roots.

14. Let f (x) = 2x and g (x) = 2,21

x

xx . Find inverse of f ∘g(x) and g∘ f (x)

15. Let ,: RRf be defined by 2

22 xx eexf

. Is f (x) invertible ? If yes, then find

its inverse

INTEGER TYPE QUESTION

1. If

1/2 1/2 1/4 1/4 1/8 1/8 1/8 1/8 cos sin cos sin cos sin cos sin( ) 4

sin cos

x x x x x x x xf x

x x

,

then number of integral values in the range of f are …………. 2. Let 2222)( bxxaxf . Let M is the largest value of f. If 62 M , then number of ordered pairs (a , b), where a and b are integers ……

3. Fundamental Period of the function 5 5 52 4( ) sin sin sin3 3

f x x x x

can be

written as b

a in lowest fraction. Value of a + b is ………

4. Let a and b be real numbers and let 3( ) sin 4, f x a x b x x R . If 3loglog 1010f = 5, then value of 10loglog 310f is……. 5. Total number of integral values in the interval [2,10] satisfying the equation

2 2| 2 | | 2 |x x x x , are ……….

6. Let f is a continuous function satisfying 12

,))((

bfxbxff . Then value of

21

23 ff is equal to ………..

7. Let ( )f x is an odd function satisfying ( 4) ( ) (4).f x f x f Then value of (12)(4)

ff

=

8. Let f be a function defined for all x > 1 such that 1214 8 ( 1) logxf f x x

x

, then

value of 4( (10) (13) (17))f f f is

9. Let 2 2 2 2( ) 1 tan (1 sec 2 ) (1 sec 2 )f . Then value of 548

f

can be written as

2( )a b where ,a b are square free natural numbers. Value of | |a b is ….

10. The number of solutions of the equation 1 2 2 2tan | | ( 1) 4x x x is ……….



ANSWERS 1. (a) [0, 1] (b) [–1, 1] (c) (d) (e) [n, n + /4], n is an integer. (f) \ {2n | n an integer}

(g) (– 4, 4) (h) \ {x | 1 < |x| < 2} (i) (−3,휋 − 3) (j) , 1 , 푥 ≠

2. (a) [0, /3] (/2,] (b)

,41 (c) [1/3, 1]

(d) \ (– 1/4, – 1/20) (e) [1/3, 3] (f) 2/3,0 (g) [– 1, 1] (h) ,4 (i) [0, ] (j) [−5,− ] 3. (i) [2, 3] (ii) R (iii) (1/e, e) (iv) (–3, ) – {–2, –1}

(v) (0, ) – {1} (vi) [–2, 0) (0, 1) (vii) [–1, 1] – {0} (viii)

(ix) 1 3, 0 1,2 2

5. (i) 11 ,3

(ii) 2 7 2 7, ,

2 2

(iii) [1, ) (iv) [0, 1)

(v) 1 1,2 2

(vi) [0, 4] (vii) 1 , 1

7

(viii) R – {6} (ix) , ln2

6.

622sin

21;4,0 11 xxfB

7.

41,a 8. yf 11 9. ;14,2 for ,3 f is not one-one

11. (i) [–4, 3] (ii) [–1, 1]

12. (i) No (ii) yes (iii) No (iv) No 13. 15. 푓 :ℝ → ℝ,푓 (푥) = (1/2 )푙푛( 푥 + √푥 + 1)

INTEGER TYPE QUESTION

1. 9 2. 4 3. 5 4. 3 5. 9 6. 2 7. 3 8. 3 9. 4 10. 4



Functions – IV A. Objective. Only one correct. 1. Let RRf : be defined by ,43)( xxf then )(1 xf

1. )4(31

x 2. )4(31

x 3. 3x + 4 4. not defined

2. Mapping RRf : which is defined as Rxxxf ,cos)( will be: 1. either into or onto 2. one-one 3. onto 4. one-one onto 3. The composite mapping f o g of the maps RRf : , .)(,:,sin)( 2xxgRRgxxf

1. 2sin xx 2. 2)(sin x 3. 2sin x 4. 2sin

xx

4. Given A ={x, y, z},B = {u, v, w}, the function BAf : defined by f (x) = u, f (y) = v, f (z) = w is: 1. surjective 2. bijective 3. injective 4. None

5. If ,1)(,103)( 2 xxgxxf then 1)( gof is equal to :

1. 2/1

37

x 2.

2/1

37

x 3.

2/1

75

x 4.

2/1

73

x

6. If ),cos(log)( xxf then

)(

21)()( xyf

yxfyfxf

1. 0 2. 1 3. 2 4. – 1 7. If ,21)( xxf then )(xfofof is: 1. 3)21( x 2. x85 3. x67 4. x87

8. If 2)( 2 xxxg and ,252)(21 2 xxxfog then f (x) =

1. 32 x 2. 32 x 3. 132 2 xx 4. 132 2 xx

9. If

21

2121 1)()(

xxxxfxfxf for ),1,1(, 21 xx then )(xf =

1.

xx

11log 2.

xx

11tan 1 3.

xx

11log 4.

xx

11tan 1

10. The function RRf : defined by )3()2()1()( xxxxf is: 1. one-one but not onto 2. onto but not one-one 3. both one-one and onto 4. neither one-one nor onto 11. If |sin|)]([ xxfg and ,)(sin)]([ 2xxgf then: 1. xxgxxf )(,sin)( 2 2. ||)(,sin)( 2 xxgxxf 3. xxgxxf sin)(,sin)( 2 4. f and g can not be determined

MA/PS/XII/Functions-IV/pg-2


12. If the function ,1,1f is defined by ,2)( )1( xxxf then )(1 xf is:

1. )1(

21

xx

2. ]log411[21

2 x

3. ]log411[

21

2 x

4. Not defined

13. Let .1,1

)(

xx

xxf Then for what value of , is xxff ))(( ?

1. 2 2. – 2 3. 1 4. – 1

14. Let ][1)( xxxg and 000

,1,0,1

)(

xxx

xf Then for all x, f (g (x)) =

1. x 2. 1 3. f (x) 4. g (x)

15. If ),2[),1[: f is given by ,1)(x

xxf then )(1 xf

1. 2

42 xx 2. 21 xx

3. 2

42 xx 4. 41 2 x

16. Let E = {1, 2, 3, 4} and F = { 1, 2}. Then the number of onto functions from E to F is 1. 14 2. 16 3. 12 4. 8 17. Let function RRf : be defined by .sin2)( Rxxxxf then f is: 1. one to one and onto 2. one to one but not onto

3. onto but not one-one 4. neither one-one nor onto

18. x

xxff

1

)(),,0[),0[: is :

1. one-one and onto 2. one-one but not onto 3. onto but not one-one 4. neither one-one nor onto

19. The value of b and c for which the identity 38)()1( xxfxf is satisfied, where ,)( 2 dcxbxxf are: 1. b = 2, c = 1 2. b = 4, c = – 1 3. b = – 1, c = 4 4. None

20. If xxx

fxf ,13)(2 2

is not equal to zero, then f (2) is equal to

1. 25 2.

47

3. – 1 4. None of these

21. If ,]cos[]cos[)( 22 xxxf where [x] stands for the greatest integer function, then:

1. 12

f 2. 1)( f 3. 0)( f 4. 2

4

f

22. The graph of the function )1(cos)2cos(cos 2 xxx is: 1. a straight line passing through )1sin,0( 2 with slope 2. 2. a straight line passing through (0, 0) 3. a parabola with vertex )1sin,1( 2

4. a straight line passing through the point

1sin,

22 and parallel to the x-axis.



23. The domain of the function )2(

)3()1()(

xxxxf

1. ),3[)2,1[ 2. ),3[)2,1( 3. ),3[]2,1[ 4. None of these 24. For a real number x, [x] denotes the integral part of x. The value of

10099

21...

1002

21

1001

21

21 is

1. 49 2. 50 3. 48 4. 51

25. If the function

xxxxxf

3cos.cos

3coscos)( 22

is constant(independent of x), then the value of this constant is:

1. 34 2. 1 3. 0 4.

43

26. If xxg 1)( and ,23)]([ xxxgf then f(x) = 1. 221 x 2. 22 x 3. x1 4. x2 27. If ,)()( /1 nnxaxf then )]([ xff equal to 1. nx /1 2. nx 3. xa 4. x 28. The number of surjections from A = {1, 2, ..., n}, 2n on to B = { a, b } is: 1. 2pn 2. 22 n 3. 12 n 4. None of these

29. Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is:

1. 10 ! 2. 1010 3. 102 4. 1210

30. Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from A to B is:

1. 144 2. 12 3. 24 4. 64 31. |sin|)( xxf has an inverse if its domain is: 1. ],0[ 2. ]2/,0[ 3. ]4/,4/[ 4. None of these 32. The number of bijective function from set A to itself when A contains 106 elements is: 1. 1062 -1 2. 22106 3. 106 ! 4. 1062 33. If ,112111 nifnfnfandf then f ( n ) is equal to 1. 12 n 2. 2 n 3. 2 n – 1 4. 2 n – 1 – 1

34. If y = f ( x ) satisfies the condition 푓 푥 + = 푥 + (푥 ≠ 0)푡ℎ푒푛푓(푥) = 1. -x2 + 2 2. -x2 – 2 3. x2 + 2 4. x2 – 2 35. Which of the following pair of functions are identical 1. 푓(푥) = 푠푖푛 푥 + 푐표푠 푐 푎푛푑 푔(푥) = 2. 푓(푥) = 푡푎푛 푥 + 푐표푡 푥 푎푛푑 푔(푥) = 3. 푔(푥) = 푠푒푐 푥 + 푐표푠 푒 푐 푥 푎푛푑 푔(푥) = 4. All of these 36. If ,14/53/coscos3/sinsin 22 gandxxxxxf then (gof)

(x) is equal to 1. 1 2. 0 3. sin x 4. none of these



37. Let f (x) be a function whose domain is .7,5 Let .52 xxg Then domain of (fog) (x) is

1. 1,4 2. 1,5 3. 1,6 4. none of these 38. The function Yf ,2: defined by 542 xxxf is both one-one & onto if 1. Y = R 2. Y = ,1 3. Y = ,4 4. Y = ,5

39. Let RRf : be a function defined by 102752

2

2

xxxxxf then f is:

1. one – one but not onto 2. onto but not one – one 3. onto as well as one – one 4. neither onto nor one – one

40. To domain of definition of the function 2)1(log

110

xx

y is:

1. [– 2, 1] 2. [– 2, 1[ 3. [1,0][0,2[ 4. None of these

41. Let f : R [0,1) be a function defined by f(x) = xx

x|x|

eeee

. Then

1. f is both one – one and onto. 2. f is one –one but not onto. 3. f is onto but not one – one. 4. f is neither one –one nor onto. 42. The function f(x) = |sinx| + 2| cos x| + g() has period equal to / 2 if is 1. 2 2. 1 3. 3 4. none of these 43. Let f : (-, 1] (- , 1] such that f(x) = x(2 – x), then f-1 (x) is 1. 2 + x2 2. 1 - x1 3. x21 4. none of these 44. Total number of solutions of |||x| – 2| - 1| = 1/2 is 1. 1 2. 2 3. 8 4. 6 45. Range of f(x) = sin-1x + tan-1 x + cos-1x is

1. [0, ] 2.

23

4, 3.

43

4, 4. [-, ]

46. If f(x) = 1+ x, 0 is the inverse of itself, then the value of is 1. -2 2. -1 3. 0 4. 2

47. Let f(x) = 24

4x

x

. Then f(x) + f(1 – x) is equal to

1. 0 2. 1 3. –1 4. none of these 48. If f(x) + 2f(1 - x) = 2x + 1 x R, then inverse of f(x) is given as

1. 635 x 2.

365 x 3.

656 x 4. none of these

49. Range of f(x) = cos(tan-1x) is;

1. (0, 1] 2.

22, 3. (, ) 4. [0, 1)

50. The range of the function for real x of y = is

1. ≤ 푦 ≤ 1 2. − ≤ 푦 < 1 3. > 푦 > 1 4. > 푦 > 1



B. Objective. One or more than one correct.

1. Let 21},1),1(min{)( xxtttxf

1. range of f(x) is

2,

41 2. f(x) is a 1– 1 function

3. graph of f(x) is symmetric about 21

x 4. f(x) is constant in [1, 2]

2. Let ,14)( 2 xxxf then 1. f(x) > 0 for all x 2. f(x) > 1 when 0x 3. 1)( xf for 1x 4. )()4( xfxf for all x

3. Let f(x) = x(x-1) and g(x)= { x }, frctional part of x, then fog(x) is:

1. a bijective mapping from

0,

41to1,

23 2. is an even function

3. is a periodic function 4. is always negative

4. Let 1sin21sin2)( 2

2

xxxf

1. f(x) is an even function 2. f(x) is a periodic function

3. Range of f(x) is [–1, 1/3] 4. f(x) is invertible for 2

32

x

5. Let f(x) be function defined over [0, 1] then the domain of 1. ]4/,0[is)(tan xf 2. )1,(is)( xef

3.

211x

f is R 4. ])([ 2 xxf is (–2, –1]

6. Let xxgxxf sin)(and2)( then

1. domain of gof(x) contains [0, 2] 2. domain of fog(x)contains [0, 2] 3. range of gof(x) contained in [0, 1] 4. range of fog(x) is contained in [1, 2]

7. Let .:,: DCgBAf Let S = Range )( f Domain(g). Then: 1. gof(x) is well defined if S is not empty. 2. Domain of gof(x) will be the preimage of S under g. 3. Range of gof(x) will be the image of S under g. 4. gof(x) is injective if f is injective

8. A function f(x) satisfies the relation 2

21)(112

xxxxf

xxf

then

1. 2

21)(xxxxf

2. 2

21)(2xxxxf

3. 2

21)(3xxxxf

4. None of these



9. If a set A has an m elements and a set B has n element then : 1. total number of function from A to B is nm 2. total number of function from A to B is mn 3. total number of one-one function from A to B is 4. total number of one-one functions from A to B is nmmPn , 10. A function y = f(x) satisfies the following xyy ||2 : 1. Domain of f(x) is ‘ 2. f(x) is a one-one function 3. If 31 x then range of f(x) is [– 3, 1] 4. For 42 x f(x) is its own inverse

11. If f(x + y) = f(x) + f(y) for all x, y then

1. f (n) = nf(1), n∊ℕ 2. f (p) = pf(1), p∊ℚ, set of rationals

3. f (x) is odd 4. f (x) is even

12. If f(x – 1) + f(x + 1) = 4 then

1. f(x) is periodic with period 4 2. f(x) is periodic with period 2

3. f (x) is odd and periodic 4. f (x) is even and periodic

13. A function f(x) satisfies the relation 3f(x) + a f(1/x) = x.

1. If f(2)=0 then a=18 2. If f(2)=1 then f(1/2)=2/3

3. If a =1 then f(2)=11/16 4. If a =1 then f(1/2)= 1/16

14. If f(x) is a polynomial satisfying f(x) + f(1/x) = f(x) f(1/x) then f(x) is

1. 1)( nxxf 2. 1)( 3 xxf

3. nxxf 1)( 4. 31)( xxf

15. If f(x) + f(x + a) + f(x + 2a) = 6 then

1. f(x) is periodic with period 4a 2. f(x) is periodic with period 3a

3. f (x) is odd and periodic 4. f (x) is even and periodic

16. If f(x + a) = )()(21 2 xfxf for all x ∊ Dom(f) then

1. 1)(21

xf 2. f(x) may be constant.

3. f(x) is periodic with period 4a 4. f(x) is periodic with period 2a

mnnPm ,



17. If the graph of f(x) is symmetric about x = a and x = b, then

1. f(x) is periodic with period | b – a | 2. f(x) is periodic with period 2| b – a |

3. f(x) is even if | b – a | = | a | 4. f(x) is odd if | b – a | = | b |

18. If )1(2

)1(11 2

xx

xxf

then

1. 61)3( f 2.

61)3( f 3.

87)(

7

1

rf

r 4. Dom(f)=ℝ\{- 1}

19. Let 13|,2|1)( xxxf and ,2|1|)( xxg ,22 x then

1. domain of )(xgf ,22 x 2. Range of )(xgf ,22 x 3. domain of )(xfg 02 x 4. Range of )(xfg 02 x 20. p(x) is a polynomial such that )()()()()(2 xypypxpypxp then 1. 2or1)1( p 2. nxxp 1)( 3. p(x) + p(1/x) = p(x) p(1/x) 4. If 26)3( p then 7)2( p

ANSWERS A.

11321 14112 12421 12222 (13)4124 24223 23342 13243 32233 22111

B.

14(123)3 (1234)(13)1(23)(12) (123)1(23)(234)2 (124)(23)(23)(14)(123)

JRS TUTORIALS Durgakund Varanasi 221005 Ph. No. 2311922, 2311777, 3290510


Trigonometry – IV

1. Prove that, 28

7cos8

5cos8

3cos8

cos 2222

2. Prove that, 23

87sin

85sin

83sin

8sin 4444

3a. If ,2

3,43tan

xx find the value of 2

cosand2

sin xx

3b. If ,2

,41sin

xx find the values of

2tanand

2cos xx

3c. If ,2

3,31cos

xx find the values of 2

tanand2

sin xx

4. Prove that 2

tan1tan1

2sin12sin1

AA

AA 5. Show that 4

10cos3

10sin1

6. Prove that cosec A – 2cot 2A cos A = 2 sinA

7. Prove that AecAAA 2cos2cot4tancot 22

8. Prove that

A

AAAA

AA

4tan

sincossincos

2cos2sin1

9. Prove that

AAAA 2sin

4112cossincos 266

10. Prove that 23

3cos

3coscos 222

11. If ,15

prove that cos 2 cos 4 cos 8 cos 14 = 161

12. Prove that xxxxx 4sincos46sin4sin22sin 2

13. Prove that 12 2cos...2cos2coscos2

sin2sin nn

n

14. Show that 13)cos(sin4)cos(sin6)cos(sin3 6624 xxxxxx

15. Show that 01)cos(sin3)cos(sin2 4466 xxxx

16. Show that )(coscoscos2)(coscos 22 is independent of .


PS/Trig–IV/Page No. - 2

17. Prove that )20sin10(cos3)20sin10(cos4 33

18. Prove that 4sin)sincoscos(sin4 33

19. Prove that 4sin3)3cossin3sin(cos4 33

20. Prove that 3tan3)120tan()60tan(tan

21. Prove that 4 sin

3sin3

2sin3

sin

22. Prove that cot + cot (60 + ) + cot (120 + ) = 3 cot 3

23. Prove that )sin(cos)sin(cos)cos(cos)cos(cos84cos4cos

24. Prove that

42

3

tantan61tan4tan44tan

25. If ,135cosand

54sin prove that one value of

658

2cos

26. If ,tan21tan 22 prove that cos 2 = 1 + 2 cos 2

27. If and are acute angles and

2cos3

12cos32cos prove that tan = 2 tan

28. Prove that (a) 8

1512cos48sin 22 (b) 4 (sin24 + cos 6) = 3 + 15

29. Prove that (a) cot 6 cot 42 cot 66 cot 78 = 1 (b) tan12tan24tan48tan84 = 1

30. Prove that sin 165

54sin

53sin

52sin

5

31. If

cos1 cos costhatProve,

2tan

11

2tan

ee

ee

32. If ,41sinsinand

31coscos prove that

245

2cos

33. If ,2

tan2

tan2

prove that

cos35cos53cos

34. If cos = ,coscos1coscos

prove that one of the values of .

2tan

2tanis

2tan

35. If ,90 show that the maximum value of 21iscoscos .

36. Prove that tan tan (60 – ) tan (60 + ) = tan 3


PS/Trig–IV/Page No. - 3

37. If ,3

1sin,2

1cos show that 625or6252

cot2

tan

38. If and be two different roots of the equation a cos + b sin = c then prove that

(i) 푡푎푛 = (ii) 푐표푠(훼 + 훽) = (iii) 푡푎푛(훼 + 훽) =

39. If + = then show that + =( )

40. If 푐표푠(훼 + 훽) = and 푠푖푛(훼 − 훽) = , where , lie between 0 and 4 then prove

that tan(2훼) =

41. Prove that tan 20 tan 80 = 50tan3 .

42.

43.

44. (a) Prove that the value of 33

cos3cos5

lies between - 4 and 10.

(b) Find the maximum and the minimum values of 7 cos + 24sin .

(c) If ,4

cos4

sin1)(

f find the range of values of 푓(휃).

45. If a right angle be divided into three parts , , prove that

tantantantan1tan

46. If + = 60 prove that 43coscoscoscos 22

47. prove aaaaaa

aaecaa 22

2222

2222 sincos2cossin1cossin

sincos1

cossec1

48. prove )sec(coscottan2)sec(cot)cos(tan 22 BAecBAABBecA

49. Prove that : to n terms

= .

50. Show that

Answers: 3(a) sin =√

, cos = −√

3(b) cos = √ , tan = √√

3(c) sin = , tan = −√2

44(b) -25, 25 44(c) [-1, 3]

3 cos 4 cos2 4cos8 sin8.

1 cos2x cos 4x cos 6x 4 cos x cos 2x cos 3x

tan tan 2 tan2 tan3 tan3 tan4 ...

n 1 cot tann 1

tan9 . tan27 . tan45 . tan 63 tan81 1

PHYSICS


JRS TUTORIALSVECTOR (11th IIT)

DPP-01

1. A physical quantity which has a direction :

(A) cannot be a vector (B) must be a vector (C) must be a scalar (D) may be a vector

2. The magnitude of a vector cannot be :

(A) positive (B) unity (C) negative (D) zero

3. The forces, each numerically equal to 5 N, are acting as shown in the Figure. Find the anglebetween forces?(A) 90°

(B) 120°

(C) 0°

(D) 60°

4. For the figure shown.

(A) A B C

(B) B C A

(C) C A B

(D) A B C 0

5. Six vectors, a through f

have the mangitudes and directions indicated in the figure.Which of

the following statements is true ?

`

(A) b + c = f

(B) d + c = f

(C) d + e = f

(D) b + e = f

6. A man moves 10 m in a direction 30° East of North.The displacement of man is [assuming east

as positive X axis and north as positive Y axis]

(A) ˆ ˆs 5 3 i 5 j m

(B) ˆ ˆs 5i 5 3 j m

(C) ˆ ˆs 5 3i 5 j m

(D) ˆ ˆs 5 i 5 3 j m

PHYSICS


7. A person pushes a box kept on a horizontal surface with force of 100 N. In unit vector notationforce F

can be expressed as :

(A) 100 ˆ ˆ(i j)

(B) 100 ˆ ˆ(i j)

45°

y

xF

(C) 250 ˆ ˆ(i j)

(D) 50 2 ˆ ˆ(i j)

8. Just after firing, a bullet is found to move at an angle of 37° to horizontal. Its acceleration is 10m/s2 downwards. Find the component of acceleration in the direction of the velocity.

(A) – 6 m/s2

(B) – 4 m/s2

(C) – 8 m/s2

(D) – 5 m/s2

9. A particle moves along a path ABCD as shown in the figure. Then the magnitude of netdisplacement of the particle from position A to D is :(A) 10 m

(B) 25 m(C) 9 m(D) 27 m

10. Find the resultant of three vectors OA

, OB

and OC

and each of magnitude R

(A) 2R

(B) R(1 + 2 )

(D) R 2

(D) R( 2 – 1)

11. Find resultant force as vector in ˆ ˆai bj format.

(A) ˆ ˆ225 i 300 j

(B) ˆ ˆ475 i 900 j

(C) ˆ ˆ475 i 600 j

(D) ˆ ˆ475 i 900 j12. An insect crawls 10 m towards east, turns to its right, crawls 8 m, and again turns to its right,

Now crawling a distance of 2 m it turns to its right and stop after moving 2 m more. Find its netdisplacement.(A) 10 m , 37° S of E (B) 10 m , 37° E of S(C) 5 m , 37° S of E (D) 5 m , 37° W of N

PHYSICS


13. A sail boat sails 2 km due East, 5 km 37o South of East and finally an unknown displacement .If the final displacement of the boat from the starting point is 6 km due East, the third displace-ment is ______(A) 3 km North (B) 3 km South (C) 4 km South (D) 4 km East

14. Two horizontal forces of magnitudes 10 N & P N act on a particle. The force of magnitude 10 Nacts due west & the force of magnitude P N acts on a bearing of 30° east of north as shown infigure. The resultant of these two force acts due north. Find the magnitude of this resultant.(A) 310 N

(B) 20 N(C)10 N(D) 10 / 3 N

15. As shown in figure, find the magnitude of the unknown forces X and Y if sum of all forces iszero.(A) 5N, 5N(B) 5N, 10N(C) 10N, 5N(D) 10N, 10N

16. Three forces acting on a body are shown in the figure. To have the resultant force only along the

y-direction, the magnitude of the minimum additional force needed is:

(A) 0.5N (B) 1.5N (C) 3 N

4(D) 3N

INTEGER TYPE QUESTIONS

17. The rectangular components of a vector are (2, 2). The corresponding rectangular components

of another vector are (1, 3 ). Find one third of the angle between the two vectors in degree.

18. A vector B

which has a magnitude 8.0 is added to a vector A

which lie along the x-axis. Thesum of these two vectors is a third vector which lie along the y-axis and has a magnitude that is

twice the magnitude of A

. The magnitude of A

is x5 then find x .

PHYSICS


MATCH THE COLUMN19. Column-I show vector diagram relating three vectors a, b

and c . Match the vector equation in

column-II, with vector diagram in column-I

Column-I Column-II

(I)a

bc(P) 0)cb(a

(II)a

cb (Q) acb

(III)a b

c(R) cba

(IV)b

ca (S) cba

PASSAGEThree forces of 3N, 2N and 1N act on a particle as shown in the figure. Calculate the

20. Net force along the x-axis.

(A) 6 N (B) 3 N (C) 32 N (D)

32

N

21. Net force along the y-axis.

(A) 6 N (B) 3 N (C) 32 N (D)

32

N

22. Single additional force required to keep the body in equilibrium.

(A)3 3ˆ ˆF i j

2 2

N (B)3 3ˆ ˆF i j

2 2

N

(C)3 3ˆ ˆF i j2 2

N (D)3 3ˆ ˆF i j2 2

N

PHYSICS


ANSWER KEY

VECTOR DPP-01

1. D 2. C 3. B 4. C 5. C 6. D

7. C 8. A 9. D 10. B 11. D 12. A

13. A 14. A 15. B 16. A 17. 5 18. 8

19. (I)-R ; (II)-S ; (III)-P ; (IV)-Q 20. C 21. D 22. A


PHYSICS


DPP-04 : Coulomb’s Law

1. An infinite number of charges, each of charge 1 C, are placed on the x-axis with co-ordinates

x = 1, 2, 4, 8, .... . If 1 C is kept at the origin, then what is the net force acting on 1 C charge

(A) 9000 N (B) 12000 N (C) 24000 N (D) 36000 N2. Given are four arrangements of three fixed electric charges. In each arrangement, a point labeled

P is also identified — test charge, +q, is placed at point P. All of the charges are the samemagnitude, Q, but they can be either positive or negative as indicated. The charges and point Pall lie on a straight line. The distances between adjacent items, either between two charges orbetween a charge and point P, are all the same.

I. II.

III. IV.

Correct order of choices in a decreasing order of magnitude of force on P is(A) II > I > III > IV (B) I > II > III > IV (C) II > I > IV > III (D) III > IV > I > II

3. Four positive point charges are arranged as shown in the accompanying diagram. The forcebetween charges 1 and 3 is 6.0 N; the force between charges 2 and 3 is 5.0 N; and the forcebetween charges 3 and 4 is 3.0 N. The magnitude of the total force on charge 3 is most nearly

(A) 6.3 N

(B) 8.0 N

2 3 4

1

(C) 10 N

(D) 11 N4. A point charge +Q is placed at the centroid of an equilateral triangle. When a second charge +Q

is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge

is 4N. What is the magnitude of the net force on the central charge when a third charge +Q is

placed at another vertex of the triangle?

(A) zero (B) 4 N (C) 4 3N (D) 8 N5. Three identical spheres each having a charge q and radius R, are kept in such a way that

each touches the other two. The magnitude of the net electric force on any sphere is

(A) 2

0

314 4

qR

(B) 2

0

212 4

qR

(C) 2

0

214 4

qR

(D) 2

0

312 4

qR


PHYSICS6. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at

each of the other two corners. If the net electrical force on Q is zero, then Q/q equals

(A) – 22 (B) – 1 (C) 22 (D) –21 [AIEEE-2009]

7. Given figure shows an arrangement of six charged particles. The net electrostatic force F acting

on charge +q at the origin due to other charges is

(A) 20

2

a4q6

(B) zero (C) 20

2

a2q7

(D)

3

23

a4q

20

2

8. The magnitude of electric force on 2 C charge placed at the centre O of two equilateraltriangles each of side 10 cm, as shown in figure is P. If charge A, B, C, D, E & F are 2 C,2 C, 2 C, -2 C, - 2C, - 2 C respectively, then P is:(A) 21.6 N

(B) 64.8 N OA

B

C

D

E

F

(C) 0

(D) 43.2 N9. Through the exact centre of a hydrogen molecule, an -particle passes rapidly, moving on

a line perpendicular to the internuclear axis. The distance between the two hydrogen nucleiis b. The maximum force experienced by the -particle is

(A) 2

20

43 3

eb (B)

2

20

83

eb (C)

2

20

83 3

eb (D)

2

20

43

eb

10. Which of the following graphs best represents the force acting on a charged particle kept at

distance x from the centre of a square and on the axis of the square whose corners haveequal charges.

(A) (B) (C) (D)


PHYSICS11. Three charges +Q1, +Q2 and q are placed on a straight line such that q is somewhere in between

+Q1 and +Q2. If this system of charges is in equilibrium, what should be the magnitude and sign

of charge q ?

(A) ve,)QQ(

QQ2

21

21 (B) ve,

2QQ 21

(C) ve,)QQ(

QQ2

21

21 (D) ve,

2QQ 21

12. Three charges + 4q, -q and +4q are kept on a straight line at position (0, 0, 0), (a, 0, 0) and(2a, 0, 0) respectively. Considering that they are free to move along the x-axis only(A) all the charges are in stable equilibrium(B) all the charges are in unstable equilibrium(C) only the middle charge is in stable equilibrium(D) only middle charge is in unstable equilibrium

13. A mass particle (mass = m and charge = q) is placed bewteen two point charges of charge

q separtion between these two charge is 2L. The frequency of oscillation of mass particle,

if it is displaced for a small distance along the line joining the charges–

(A) 30Lm

12q

(B) 30Lm

42q

(C) 30Lm4

12q

(D)2q

30mL161

14. Two positive point charges are fixed at some distance apart. A third negative charge ' q ' is placedat the centre of the line joining the two charges. Then the number of lines along which ' q ' canperform SHM for small displacements is(A) 1 (B) 2 (C) 3 (D)

15. Four point positive charges are held at the vertices of a square in a horizontal plane. Theirmasses are 1 kg, 2 kg, 3 kg & 4 kg. Another point positive charge of mass 10 kg is kept onthe axis of the square. The weight of this fifth charge is balanced by the electrostatic forcedue to those four charges. If the four charges on the vertices are released such that they canfreely move in any direction (vertical, horizontal etc) then the acceleration of the centre ofmass of the four charges immediately after the release is: (Use g = 10 m/s2)

(A) 10 m/s2 (B) 20 m/s2 (C) zero (D) 10 m/s2 16. Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an

elliptical orbit.Find out the correct statement(s). [JEE -2009](A) The angular momentum of the charge –q is constant.(B) The linear momentum of the charge –q is constant.(C) The angular velocity of the charge – q is constant.(D) The linear speed of the charge –q is constant.


PHYSICS17. A ring of radius R is made out of a thin metallic wire of area of cross section A. The ring has a

uniform charge Q distributed on it. A charge q0 is placed at the centre of the ring. If Y is theyoung’s modulus for the material of the ring and R is the change in the radius of the ring, then

(A) R = RAY4Qq

0

0

(B) RAY4QqR

0

0

(C) RAY8

QqR 20

0

(D) RAY8

QqR0

20

18. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap

film of side ‘ ’. The surface tension of the soap film is . The system of charges and planar

film are in equilibrium, and = k1/N2q

, where ’k’ is a constant. Then N is

(A) 3 (B) 2 (C) 4 (D) 6 [JEE-2011]

MULTIPLE CORRECT ANSWERS19. Three charged particles are in equilibrium under their electrostatic forces only

(A) The particles must be collinear.(B) All the charges cannot have the same magnitude.(C) All the charges cannot have the same sign.(D) The equilibrium is unstable.

20. Two equal negative charges –q each are fixed at the points (0, a) and (0, -a) on the y-axis .Apositive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will:(A) At origin velocity of particle is maximum.(B) Execute simple harmonic motion about the origin(C) Move to infinity(D) Execute oscillatory but not simple harmonic motion.

21. A negative point charge placed at the point A is

(A) in stable equilibrium along x-axis

(B) in unstable equilibrium along y-axis

(C) in stable equilibrium along y-axis

(D) in unstable equilibrium along x-axis22. Two identical charges +Q are kept fixed some distance apart. A small particle P with charge q is

placed midway between them. If P is given a small displacement , it will undergo simpleharmonic motion if(A) q is positive and is along the line joining the charges.(B) q is positive and is perpendicular to the line joining the charges.(C) q is negative and is perpendicular to the line joining the charges.(D) q is negative and is along the line joining the charges.


PHYSICSParagraph

Three charged particles each of +Q are fixed at the corners of anequilateral triangle of side ‘a’. A fourth particle of charge –q andmass m is placed at a point on the line passing through centroid of triangle and perpendicular to the plane of triangle at a distance xfrom the centre of triangle

23. Force on the fourth particle is

(A) 2/3220 )ax3(

Qx394

1 (B) 2/322

0 )ax3(Qx33

41

(C) 2/3220 )ax2(

Qx224

1 (D) 2/322

0 )ax2(Qx24

41

24. Value of x for which the force is maximum is

(A) 3a

(B) 2a

(C) 6a

(D) 5a

MATCH THE COLUMN25. Four charge Q1,Q2,Q3, and Q4,of same magnitude are fixed along the x axis at x = –2a –a, +a

and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0.Four options of the signs of these charges are given in List-I . The direction of the forces on thecharge q is given in List- II Match List-1 with List-II and select the correct answer using thecode given below the lists [JEE (ADV)-2014]

List-I List-IIP. Q1,Q2,Q3, Q4, all positive 1. +xQ. Q1,Q2 positive Q3,Q4 negative 2. –xR. Q1,Q4 positive Q2, Q3 negative 3. +yS. Q1,Q3 positive Q2, Q4 negative 4. –yCode :(A) P-3, Q-1, R-4,S-2 (B) P-4, Q-2, R-3, S-1(C) P-3, Q-1, R-2,S-4 (D) P-4, Q-2, R-1, S-3


PHYSICS26. In the following Fig. charges, each +q, are fixed at L and M. O is the mid point of distance LM.

X- and Y –axes are as shown. Consider the situations given in column I and match them with

the information in column II

Column I Column –II(A) Let us place a charge +q at O, displace it (P) force on the charge is zero slightly along X-axis and release. Assume that it is allowed to move only along X-axis. At position O,(B) Place a charge –q at O, Displace it slightly (Q) potential energy of the system along X-axis and release. Assume that it is maximum is allowed to move only along X-axis. At position O,(C) Place a charge +q at O. Displace it slightly (R) potential energy of the system is along Y-axis and release. Assume that it is minimum allowed to move only along Y-axis. At position O,(D) Place a charge –q at O. Displace it slightly (S) the charge is in equilibrium along Y-axis and release. Assume that it is allowed to move only along Y-axis. At position O,

ANSWER KEYELECTROSTATICS DPP-04

1. B 2. C 3. A 4. B 5. A 6. A

7. B 8. D 9. C 10. C 11. C 12. B

13. A 14. D 15. B 16. A 17. D 18. A

19. A,B,CD 20. A,D 21. C,D 22. A,C 23. A

24. C 25. A 26. (A- P, R, S) ( B – P, Q, S) (C –P, Q, S) (D – P, R, S)


PHYSICS



1. Two identical conducting spheres (of negligible radius), having charges of opposite sign,attract each other with a force of 0.108 N when separated by 0.5 meter. The spheres areconnected by a conducting wire, which is then removed (when charge stops flowing), andthereafter repel each other with a force of 0.036 N keeping the distance same. What werethe initial charges on the spheres?[Ans. ± 1.0 x 10-6 C, 3 x 10-6 C ]

2. Two identical balls of mass m = 0.9 g each are charged by the same charges, joined by a threadand suspended from the ceiling (Figure). What is the charge (in µC) should both balls have sothat the tension in both the threads is the same? The distance between the centers of balls R = 3m.

R

[Ans. 3]

3. Two spherical bobs of mass m each & identically charged with charge q each are suspendedon strings of length L each. They are suspended from a point O where there is a third chargeq. Find q, if the angle between the strings in equilibrium position is Can you find thevalue of charge at O, if it is not q but q1. If yes, find? If no, explain the physical significanceof it.

[Ans. q =2

tanmg2

sin4 0

]

4. Two small equally charged identical conducting balls are suspended from long threadssecured at one point. The charges and masses of the balls are such that they are in equilibrium.When the distance between them is a = 10 cm (the length of the threads L >> a). One of theballs is discharged. How will the balls behave after this? What will be the distance b betweenthe balls when equilibrium is restored?[Ans. The balls will first go down, touch each other and then move apart by a distance

b = a

( ) /4 1 3]


PHYSICS5. Two positive point charges each of magnitude 10 C are fixed at positions A & B at a separation

2 d = 6 m. A negatively charged particle of mass m = 90 gm & charge of magnitude 10 106 C is revolving in a circular path of radius 4 m in the plane perpendicular to the line ABand bisecting the line AB. Neglect the effect of gravity. Find the angular velocity of theparticle. If gravity is also considered will it still move in the circular path assuming AB tobe horizontal.

[ Ans : 400 rad/s ]

6. Two small identical balls having the same mass and charge are located in the same verticalline at heights h1 and h2 from ground are thrown in the same direction along the horizontalat the same velocity v. The first ball touches the ground at a distance from the initialvertical line. At what height H2 will the second ball be at this instant? Neglect the effect ofair friction on motion of the balls.

[Ans2

212 vghhH

]

7. An electrometer consists of a fixed vertical metal bar OB at the top of which is attached a thinrod OA which gets deflected from the bar under the action of an electric charge (fig.). The rodcan rotate in vertical plane about fixed horizontal axis passing through O. The reading is takenon a quadrant graduated in degrees . The length of the rod is and its mass is m . What will bethe charge when the rod of such an electrometer is deflected through an angle in equilibrium.Find the answer using the following two assumptions:(i) the charge on the electrometer is equally distributed between the bar & the rod(ii) the charges are concentrated at point A on the rod & at point B on the bar.

[ Ans : q = 4

2

sinmg4 0 sin 2 ]


PHYSICS8. A rigid insulated wire frame in the form of a right angled triangle ABC, is set in a vertical

plane as shown. Two bead of equal masses m each and carrying charges q1 & q2 are connectedby a cord of length & slide without friction on the wires . Considering the case when thebeads are stationary, determine.

(a) The angle .(b) The tension in the cord &(c) The normal reaction on the beads .(d) If the cord is now cut, what is the product of the charges for which the beads continue to remain stationary .

[Ans. (a) 60º (b) mg + 2

21qqk

(c) 3 mg , mg (d) q1 & q2 should have unlike charges

for the beads to remain stationary & q1q2 = k

mg 2 ]

9. The distance between two fixed positive charges 4e and e is . How should a third charge‘q’ be arranged for it to be in equilibrium? Under what condition will equilibrium of thecharge ‘q’ be stable (for displacement on the line joining 4e and e) or will it be unstable?

[Ans. 23 from charge 4 e ( If q is positive stable, If q is negative unstable)]

10. Two equally charged particles A and B, each having a charge Q are placed a distance dapart. Where should a third particle of charge q be placed on the perpendicular bisector ofAB so that it experiences maximum force? Also find the magnitude of the maximum force.

[Ans. d

2 2, 2

0d33Qq4πε

]

11. Four charges q1 = 1 c, q2 = 2 c, q3 = 3 c and q4 = 4 c are placed at (0, 0, 0), (1, 0, 0), (0,

1, 0), (0, 0, 1) respectively. Let F i be the net electric force acting on ith charge of the given

charges then F i = _____________.

[Ans. 0 ]

12. Calculate the magnitude of electrostatic force on a charge placed at a vertex of a triangularpyramid (4 vertices, 4 faces), if 4 equal point charges are placed at all four vertices ofpyramid of side ‘a’.

[Ans. 20

2

a4q6

]


PHYSICS



1. Two copper balls, each having weight 10 g are kept in air 10 cm apart. If one electron from every

106 atoms is transfered from one ball to the other, the coulomb force between them is (atomic

weight of copper is 63.5)

(A) 2.0 × 108 N (B) 2.0 × 106 N (C) 2.0 × 1010 N (D) 2.0 × 104 N2. The figure below shows the forces that three charged particles exert on each other. Which of the

four situations shown can be correct.

(I) (II) (III) (IV)

(A) all of the above (B) II, III & IV (C) II, III (D) none of the above3. Two charges 8 C and –6 C are placed with a distance of separation ‘d’ between them and exert

a force of magnitude F on each other. If a charge 8 C is added to each of these and they are

brought nearer by a distance 3d

, the magnitude of force between them will be-

(A) F31

(B) F49

(C) F23

(D) F32

4. Two identical spheres A and B having charge Q are placed at a distance r apart. The forceacting between them is F. An identical uncharged sphere C comes into contact with A. Afterthat it comes into contact with B and is then placed in middle of A and B. The net forceacting on the C is

(A) 83F

(B) F (C) 4

3F (D) 3F

5. Two identical positive charges are fixed on the y-axis, at equal distances from the origin O. Aparticle with a negative charge starts on the x-axis at a large distance from O, moves along the +x-axis, passes through O and moves far away from O. Its acceleration a is taken as positivealong its direction of motion. The particle’s acceleration a is plotted against its x-coordinate.Which of the following best represents the plot?

(A) (B) (C) (D)


PHYSICS6. Two pith balls with mass m are suspended from insulating threads. When the pith balls are

given equal positive charge Q, they hang in equilibrium as shown.

Q Q

We now increase the charge on the left pith ball from Q to 2Q while leaving its mass essentially

unchanged. Which of the following diagrams best represents the new equilibrium configuration?

(A)

2Q Q

(B) 2Q

Q

(C)

2QQ

(D)

2Q Q

7. Two identical small balls each have a mass m and charge q. When placed in a hemisphericalbowl of radius R with frictionless, nonconductive walls, the beads move, and at equilibriumthe line joining the balls is horizontal and the distance between them is R.Neglect any

induced charge on the hemispherical bowl. Then the charge on each bead is: (K = 04

1 )

(A) 2/1

3KmgRq

(B)

2/1

3KmgRq

(C)

2/1

Kmg3Rq

(D)

2/1

Kmg3Rq

8. Two identical charged spheres suspended from a common point by two massless strings oflength are initially a distance d(d << 1) apart because of their mutual repulsion. The chargebegins to leak from both the spheres at a constant rate. As a result the charges approach eachother with a velocity v. Then as a function of distance x between them, [AIEEE-2011](A) v x–1/2 (B) v x–1 (C) v x1/2 (D) v x

9. In the figure shown, A is a fixed charged. B (of mass m) is given a velocity V perpendicularto line AB. At this moment the radius of curvature of the resultant path of B is

(A) 0 (B) (infinity)

(C) 2

220

qmvr4

(D) r


PHYSICS10. In gravity free space a ring of mass m and charge +q can move on a smooth circular wire

track of radius R. A point charge –q is fixed at the centre of the track and another charge +q isfixed on the track at the position shown. If the ring is released from the rest at the position A,then just after the release, the tangential acceleration and normal force on the ring will berespectively

(A) 132F,

m2F

(B) 2F,

m23F (C) 0,

m23F (D) 0, F/2

11. A simple pendulum of mass m and charge + q is suspended vertically by a massless threadof length . At the point of suspension, a point charge + q is also fixed. If the pendulum isdisplaced slightly from equilibrium position, its time period will be

(A) T = 2 2

2

mkqg

(B) T = 2 (C) T = 2 g

(D) will be greater than 2 g

12. An insulating long massless rod of length L, pivoted at its centre and balanced with a weight Wat a distance x from the left end, is shown in the figure. Charges q and 2q are attached at the leftand right ends of the rod. At a distance h directly below each of these charges is a positive chargeQ. The distance x in terms of q, Q, L and W is

(A) WhWLhqQL

20

20

(B)

Wh8WLhqQL4

2

20

(C) Wh8

WLh4qQL2

0

20

(D)

WhWLh4qQL

2

20

13. Two identical spheres of same mass and specific gravity (which is the ratio of density of asubstance and density of water) 2.4 have different charges of Q and – 3Q. They are suspendedfrom two strings of same length fixed to points at the same horizontal level, but distant fromeach other. When the entire set up is transferred inside a liquid of specific gravity 0.8, it isobserved that the inclination of each string in equilibrium remains unchanged. Then the dielec-tric constant of the liquid is(A) 2 (B) 3 (C) 1.5 (D) 4


PHYSICS14. Two point charges are kept separated by 4 cm of air and 6 cm of a dielectric of relative permittivity

4. The equivalent dielectric separation between them so far their colombian interaction isconserved is(A) 10 cm (B) 8 cm (C) 5 cm (D) 16 cm

15. Force between two identical charges placed at a distance of r in vacuum is F. Now a slab ofdielectric constant K = 4 is inserted between these two charges. The thickness of the slab is r/2.The force between the charges will now become -(A) F/4 (B) F/2 (C) 5

3 F (D) 9

4 F

Paragraph

Three charges are placed as shown in Fig. The magnitude of q1 is 2.00 mC, but its signand the value of the charge q2 are not known. Charge q3 is +4.00 C, and the net forceon q3 is entirely in the negative x-direction

y

x

q3

3cm4cm

q1 q2

F

5 cm

16. As per the condition given in the problem the sign of q1 and q2 will be

(A) +, + (B) +, (C) , + (D) , 17. The magnitude of q2 is

(A) C6427

(B) C3227

(C) C3213

(D) 6413

C

18. The magnitude of force acting on q3 is(A) 25.2 N (B) 32.2 N (C) 56.2 N (D) 13.5 N


1. A 2. C 3. C 4. C 5. B 6. D

7. A 8. A 9. C 10. B 11. C 12. C

13. C 14. B 15. D 16. C 17. B 18. C


PHYSICS

JRS TUTORIALSELECTROSTATICS (12-IIT)DPP-01 : Charge and its properties

1. Find the charge on an iron particle of mass 2.24 mg, if 0.02 % of electrons are removed from it.(A) 0.01996 (B) 0.01996 C (C) 0.02 C (D) 2.0 C

2. In 1 gm of a solid, there are 5 1021 atoms. If one electron is removed from everyone of 0.01%atoms of the solid, the charge gained by the solid is (given that electronic charge is 1.6 10–19 C)(A) + 0.08 C (B) + 0.8 C (C) – 0.08 C (D) – 0.8 C

3. The direction of electrostatic forces which are possible in the system of three charges A, Band C is :

(A) (B) (C) (D) None of these

4. Five Styrofoam balls are suspended from insulating threads. Several experiments are performedon the balls and the following observation are made

(i) Ball A repels C and attracts B

(ii) Ball D attracts B and has no effect on E

(iii) A negatively charged rod attracts both A and E. An electrically neutral Styrofoam ball getsattracted if placed nearby a charged body due to negative charge. What are the charges, if any on

each ball ?

A B C D E A B C D E

(A) + + 0 + (B) + + + 0

(C) + + 0 0 (D) + 0 0


PHYSICS5. Five balls, numbered 1 to 5, are suspended using separate threads. Pairs (1, 2), (2, 4), (4, 1) show

electrostatic attraction, while pairs (2, 3) and (4, 5) show repulsion. Therefore ball 1 :(A) Must be positively charged (B) Must be negatively charged(C) May be neutral (D) Must be made of metal

6. Consider three identical metal spheres A, B & C. Sphere A carries charge + 6 q and sphere

B carries charge 3 q. Sphere C carries no charge. Spheres A & B are touched together and

then separated. Sphere C is then touched to sphere A and separated from it. Finally the

sphere C is touched to sphere B and separated from it. The final charge on the sphere C is:

(A) 3 q (B) 0.75 q (C) 1.25 q (D) 1.125 q7. A common concept on charge is given, Select the odd statement.

(A) Charge gained by an uncharged body by conduction from a charged body is equal to half of the total charge initially present(B) Magnitude of charge does not with its velocity(C) Charge cannot be coexisted without matter although matter can exist without charge(D) Between two substance repulsion is true test of presence of charge

8. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere.The net charge on the sphere is then, [JEE-2007](A) negative and distributed uniformly over the surface of the sphere(B) negative and appears only at the point on the sphere closest to the point charge(C) negative and distributed non-uniformly over the entire surface of the sphere(D) zero

9. A positively charged insulator is brought near (but does not touch) two metallic sphere that arein contact. The metallic spheres are then separated. The sphere which was initially farthest fromthe insulator will have(A) no net charge (B) a negative charge(C) a positive charge (D) either a negative or a positive charge.

10. A circle of radius r has a linear charge density = 0 cos2 along its circumference. Totalcharge on the circle is

(A) 0(2 r) (B) 0( r) (C) 0r

2 (D) 0

r4

11. The charge density of a spherical charge distribution is given by

nr0

nrr)r(0

.

What is the total charge on the distribution

(A) B C 0

3

34

D 03

32


PHYSICS12. The volume charge density as a function of distance x from one face inside a unit cube is

varying as shown in figure. Find charge stored in cube.

0

41

43 )min(x

y

1y

x1x

(A) 0

4

(B) 0

2

(C) 034

(D) 0

13. When an isolated body is connected to earth, electrons from the earth flow into the body.This means the body is :(A) charged negatively (B) an insulator(C) uncharged (D) charged positively

14. When a negatively charged rod is brought near, but does not touch, the initially unchargedelectroscope shown below, the leaves spring apart (I). When the electroscope is then touchedwith a finger, the leaves collapse (II). When next the finger and finally the rod are removed, theleaves spring apart a second time (III). The charge on the leaves is

I II III

- - - -- - - - --

(A) positive in both I and III (B) negative in both I and III

(C) positive in I, negative in III (D) negative in I, positive in III


PHYSICSParagraphA leaf electroscope is a simple apparatus to detect any charge on a body. It consists of twometal leaves OA and OB, free to rotate about O. Initially both are very slightly separated.When a charged object is touched to the metal knob at the top of the conducting rod, chargeflows from knob to the leaves through the conducting rod. As the leaves are now chargedsimilarly, they start repelling each other and get separated, (deflected by certain angle).

The angle of deflection in static equilibrium is an indicator of the amount of charge on thecharged body.

15. When a + 20 C rod is touched to the knob, the deflection of leaves was 5°, and when anidentical rod of – 40 C is touched, the deflection was found to be 9°. If an identical rod of+30 C is touched, then the deflection may be :(A) 0 (B) 2° (C) 7° (D) 11°

16. If we perform these steps one by one.

(i) A positively charged rod is brought closer to initially (A)

++++++

uncharged knob

(ii) Then the positively charged rod is touched to the knob (B)

++++++

(iii) Now the +vely charged rod is removed, and a negatively charged. (C)

- - -- - -

rod of same magnitude is brought closer at same distance

In which case, the leaves will converge (come closer), as compared to the previous state ?(A) (i) (B) (i) and (iii)(C) only (iii) (D) In all cases, the leaves will diverge


PHYSICS

ANSWER KEY PHYSICS DPP-01

1. B 2. A 3. C 4. C 5. C 6. D

7. A 8. D 9. C 10. B 11. B 12. C

13. D 14. D 15. C 16. C



Trigonometry – I

Section -I Prove the following identities:

1. .tantansecsec 2424 2. .sec2sin1

cossin1

cos

3. .cossin31cossin 2266 4. .cotcoscos1cos1

ec

5. )cos1()sin1(2)cossin1( 2 AAAA 6. .cosseccottan 22 AecAAA 7. .cossec)cot1(cos)tan1(sin AecAAAAA

8. 1 1 1 1 .cos cot sin sin cos cotec ec

9. .cos21sec

tan1sec

tan

ec

10. .sin5sec2)1tan2()2(tancos 11. .secsec)tan(tan)tantan1( 2222

12. 22

22

22

tantancoscoscoscos 13. .cot

cossinsin1coscossin2

22

Section - II

Do as required in each of the following. 1a. Which trigonometric ratios are negative for the following angles

(i) 315 2. – 210 3. 6

5

1b. Find the values of the following trigonometric functions.

(i) sin 1830 (ii) sin 765 (iii) cos (– 1710) (iv)

311sin

(v) 3

31sin (vi)

415cot (vii)

313cot

2. Find the values of the other five trigonometric functions in the following

(i) 2

3,178cos

(ii) ,21cos lies is the third quadrant

(iii)

2

,5

12cot (iv)

22

3,5

13sec

3. If cos = – ,2

3and53

find the value of

cotcostansec

ec

4. If ,2

32

and21tan,

53sin

show that 8 tan – .27sec5


5. Show that

(i) cos 70 cos 10 + sin 70 sin10 = 21 (ii)

2318sin78cos18cos78sin

6. Find the value of the following: (i) sin 105 + cos105 (ii) sin 300 cosec 1050 – tan ( – 120) (iii). sin 690 cos 930 + tan (– 765) cosec (– 1170)

(iv) 6

tan36

5cos6

cot 22

ec (v) 4

cot6

5sin43

sec6

sin3

7. Prove that 4

2675sin

8. Find 15tan and hence show that .415cot15tan

9. Evaluate ,4

)1(tan

n when n is an integer.

10. If sin 5

1sin,101

(, and + are acute angles). Show that .4

11. If ,2

0,2

0,419cosand

53sin

BABA Find the value of the following

(i) sin (A + B) (ii) cos (A + B) (iii) sin(A – B) (iv) cos (A – B)

12. if ,2

0and2

where,23cos,

21sin

BABA find the following

(i) tan (A + B) (ii) tan (A – B)

13. If ,2

and2

where,1312cos,

53sin

yxyx show that

6556)sin( yx .

14. Evaluate: (i) 2 2cos sin4 4

x x

(ii) )15(sin)15(sin 22 AA (iii)

28sin

28sin 22 AA

15. Prove that

(i) 1)2cot(2

3cot)2cos(2

3cos

xxxx

(ii)

2cot

2cos)sin(

)cos()cos(

16. Show that

(i) 21)10sin()40cos()10cos()40sin(

(ii) xxnxnxnxn cos)2cos()1cos()2sin()1sin(


(iii) )sin(4

sin4

sin4

cos4

cos yxyxyx

(iv) 0cos)cos3(cossin)sin3(sin xxxxxx

17. Prove that 25tan

20sin20cos20sin20cos 18. Prove that cos9 + sin9 = .54sin2

19. Prove that )sin()sin(

tantantantan

BABA

BABA

20. Prove that (i) tan 8 – tan 6 – tan 2 = tan 8 tan 6 tan 2 (ii) tan 9 + tan 36 + tan 9 tan 36 = 1 (iii) tan 3x – tan 2x – tan x = tan 3x tan 2x tan x 21. If sin sin – cos cos = 1, show that tan + tan = 0.

22. If sin ( + ) = 1 and sin ( – ) = ,21 where 0 , ,

2 then find the values of

tan ( +2) and tan (2 + ).

SECTION – III 1. If AAAAppAA ifsinand,sec,tanfind,0,tansec is acute angle.

2. If A and B are acute angles and ,3tantanand2

sinsin

BA

BA find A and B.

3. If tan + cot = 2 find sin .

4. If sin x + cos x = a, then prove that .2where,)1(431cossin 22266 aaxx

5. Eliminate from the following equations: (i) sin,cos bkyahx (ii) byxayx cossin,sincos

6. If sin x + cos x = m and sec x + cosec x = n, prove that n (m2 – 1) = 2m.

7. If x = r sin . cos , y = r sin . sin , z = r cos , show that x2 + y2 + z2 = r2

8. Prove that xyyx

4sin

22

is possible for real values of x and y only if x = y and x 0.

9. Show that 2cossin 22 ec 10. Prove that sec + cos .23

11. If .0cossinandcossincossin 33 yxyx prove that x2 +y2 = 1.

12. Show that xy

yx2

sin22

2 is possible for real values of x and y only when x = y 0.

13. Show that the equation x

x 1sin is impossible if x is real

14. If .cos2sincos Prove that: sin2sincos


15. If ,1sinsin 24 AA prove that (i) 1tan

1tan

124

AA (ii) 1tantan 24 AA

16. If .cossincossinthatshow,tan 22

22

baba

baba

ba

17. If ,1tan 22 k show that .)2(costansec 2/323 kec 18. If ,tansincos 222 ABB prove that .tansincos1cos2 2222 BAAA 19. If .cossin nn

nT prove that .0132 46 TT 20. Can, 02sin7sin6 2 , hold for any real value of ?

21. Prove that if cos 2x – 4 cos x + 1 = 8 sin x – 2 sin 2x, then )2/tan(x

22. If the product of the sines of the angles of a triangle is p and the product of their

cosines is q, show that the tangents of the angles are the roots of the equation

.

23. If then prove that 222cossin cbaAbAa

24. If ,1sinsin

coscos

2

4

2

4

BA

BA prove that

(i) ;sinsin2sinsin 2244 BABA (ii) ,1sinsin

coscos

2

4

2

4

AB

AB

25. If mxx cossin and necxx cossec show that mmn 2)1( 2

ANSWERS Section: II

1a. (i) sin , tan, cot , and cosec (ii) cos , tan , cot , and sec

(iii) sin , cos , sec and cosec

1b. (i) 2 (ii) 2

1 (iii) 0 (iv) 23 (v)

23 (vi) 1 (vii)

31

2. (i) 1517cos,

817sec,

158cot,

815tan,

1715sin ec

(ii) 3

2cos,2sec,3

1cot,3tan,23sin ec

(iii) 1213cos,

1312sec,

125tan,

1312cos,

135sin ec

(iv) 1213cos,

125cot,

512tan,

135cos,

1312sin ec

qx3 px2 1 qx p 0

a cos A b sinA c,


6. (i) 2

1 (ii) 0 (iii) 143 (iv) 6 (v) 1

8. 1313

9. ( 1)n

11. (i) 205187 (ii)

20584

(iii) 205133

(iv) 205156

12. (i) 0 (ii) 3

14. (i) 0 (ii) A2sin21 (iii) Asin

21 22.

31,3

Section – III

1. 2

222

11sin,

21sec,

21tan

ppA

ppA

ppA

2. 30,45 BA

3. 2

1 5. (i) 1

22

bky

ahx (ii) 2222 yxba



Solid State XII – (IIT and PMT)–DPP-2

1. The formula for determination of density of unit cell is

1. 303

cmgMNNa −

××

2. 3

03 cmg

NaMN −

×× 3. 3

0

3

cmgNNMa −

×× 4. 3

30 cmg

NaNM −

××

2. The packing efficiency of two dimensional square unit cell shown

below is

1. 32.97 % 2. 68%

3. 74% 4. 78.5%

3. A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is

'a', the closest approach between two atoms in metallic crystal will be :-

1. 2a 2. a22 3. a2 4. 2

a

4. Body centered cubic lattice has a coordination number of 1. 4 2. 8 3. 12 4. 6

5. The element crystallizes in a body centered cubic lattice and the edge of the unit cell is 0.351 nm. The density is 0.533 g/cm3. What is the atomic weight?

1. 12.0 2. 6.94 3. 9.01 4. 10.8

6. An element crystallizes in a structure having fcc unit cell of an edge 200 pm. Calculate the density, if 100g of this element contains 12 × 1023 atoms

1. 41.66 g/cm3 2. 4. 166 g/cm3 3. 10.25 g/cm3 4. 1.025 g/cm3 7. The number of close neighbour in a body centred cubic lattice of identical sphere is 1. 8 2. 6 3. 4 4. 2 8. In the closest packed structure of a metallic lattice, the number of nearest neighbours

of a metallic atom is 1. Twelve 2. Four 3. Eight 4. Six 9. The number of atoms in 100 gm of an bcc crystal with density d = 10 g/cm3 and cell

edge equal to 100 pm, is equal to 1.

25104× 2. 25103× 3.

25102× 4. 25101×

10. The number of atoms in primitive cubic unit cell, body-centred cubic unit cell and face-

centred cubic unit cell are A, B and C, respectively. Select the correct values.

A B C A B C

1. 1, 2, 3 2. 1, 2, 4

3. 1, 1, 3 4. 2, 3, 4

L


2

11. The following crystallographic data were obtained for a protein. Volume of unit cube = 1.50 × 10–19 cm3, Density = 1.35 g cm–3 Z = 4 and protein fraction = 0.75. Thus, molar mass of protein is 1. 2.3 × 104 g mol–1 2. 3.048 × 104 g mol–1 3. 1.725 × 104 g mol–1 4. None of these 12. A element is having body centred unit cell arrangement. Length of body diagonal is

350 pm. Density of unit cell is 6 gm/cm3. Find how many atoms are present in 500 gm of element.

1. 20 NA 2. 25 NA 3. 34 NA 4. 40 NA 13. A metal crystallises in f.c.c. lattice with unit cell edge length of 4 . If 100 gm of this

metal contains 3 × 1023 atom, its density is 1. 1.44 gm/cm3 2. 14.4 gm/cm3 3. 10.4 gm/cm3 4. 20.8 gm/cm3

14. What are the number of atoms per unit cell and the number of nearest neighbours in a

sample cubic structure? 1. 1, 6 2. 4, 12 3. 2, 8 4. 2, 6 15. % of empty space in body centered cubic unit cell is nearly 1. 52.36 2. 68 3. 32 4. 26 16. Lithium has a bcc structure. Its density is 530 kg m–3 and its atomic mass is 6.94 gmol–1.

Calculate the edge length of a unit cell of Lithium metal. (NA = 6.02 × 1023) 1. 154 pm 2. 352 pm 3. 527 pm 4. 264 pm

17. A solid has a structure in which W atoms are located at the corners of a cubic lattice,

O atoms at the centres of edges and Na atom at the centre of the cube. The formula of the compound is

1. NaWO2 2. NaWO3 3. Na2WO3 4. NaWO4

18. A metal crystallizes with a face-centred cubic lattice. The edge of the unit cell is 408 pm. The diameter of the metal atom is

1. 288 pm 2. 408 pm 3. 144 pm 4. 204 pm

Answer DPP-2 Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 2 4 4 2 2 1 1 1 3 2

Q.No. 11 12 13 14 15 16 17 18 Ans 2 3 4 1 3 2 2 1




1. Which of the following is not a crystalline solid ? 1. Common salt 2. Sugar 3. Iron 4. Rubber 2. A pseudo solid is : 1. Glass 2. pitch 3. KCl 4. Glass and pitch both 3. Solid CO2 is an example of, 1. Ionic crystal 2. Covalent crystal 3. Metallic crystal 4. Molecular crystal 4. A molecular crystalline solid, 1. is very hard 2. is volatile 3. has a high melting point 4. is a good conductor 5. Select the correct statement 1. Crystalline solids are anisotropic 2. Amorphous solids are isotropic 3. Both 1 and 2 4. None of the above 6. Amorphous materials are infact considered as 1. supercooled liquids 2. spercooled solids 3. covalent network 4. molecular crystals 7. The sharp melting point of crystalline solids compared to amorphous solids is due to 1. same arrangement of constituent particles in different directions 2. different arrangement of constituent particles in different directions

3. a regular arrangement of constituent particles observed over a long distance in the crystal lattice

4. a regular arrangement of constituent particles observed over a short distance in the crystal lattice

8. As it cools, olive oil solidifies and forms a solid over a wide range of temperature.

Which term best describes the solid? 1. Ionic 2. Covalent network 3. Metallic 4. amorphous solid 9. Which of the following can be regarded as molecular solids? 1. SiC 2. AlN 3. C(diamond) 4. Ne 10. A solid can be characterized by 1. definite mass, volume and shape 2. short intermolecular distances 3. strong intermolecular forces 4. All of the above 11. Which of the following are the correct axial distances and axial angles for rhombohedral

system ? 1. a = b = c, α =β = γ ≠ 90° 2. a = b ≠ c, α =β = γ = 90° 3. a ≠ b = c, α =β = γ = 90° 4. a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90°


2 12. Select incorrect statement for polar molecular solids,

1. molecules have polar covalent bonds 2. molecules are held by relatively stronger dipole-dipole interactions 3. molecules are held by weak London forces 4. higher melting point as compared to non-polar molecular solids, is observed 13. a ≠ b ≠ c, α = γ = 90° β ≠ 90° represents 1. tetragonal system 2. orthorhombic system 3. monoclinic system 4. triclinic system 14. Bravais lattices are of, 1. 10 types 2. 8 types 3. 7 types 4. 14 types 15. In a simple cubic cell, each point on a corner is shared by, 1. 2 unit cells 2. 1 unit cell 3. 8 unit cells 4. 4 unit cells 16. In face centred cubic cell, an atom at the face centres is shared by, 1. 4 units cells 2. 2 unit cells 3. One unit cell 4. 6 unit cells 17. In a body centred cubic cell, an atom at the body centre is shared by, 1. 1 unit cell 2. 2 unit cell 3. 3 unit cells 4. 4 unit cells 18. Match Column A with B and select the correct option. Column A Column B

A. Ionic solid I. ZnS B. Metallic solid II. Au C. Covalent solid III. Diamond) D. Molecular solid IV. Ice 1. A - I, B - II, C - IV, D - III 2. A - I, B - II, C - III, D - IV 3. A - III, B - II, C - I, D - IV

4. A - II, B - IV, C - I, D - III

Answer DPP-1 Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 4 4 4 2 3 1 3 4 4 4

Q.No. 11 12 13 14 15 16 17 18 Ans 1 3 3 4 3 2 1 2


JRS TUTORIALS MATHEMATICS PROBLEMS SHEET

Functions - I 1. Find f∘g(x) in each of the following :

(a) f (x) = 1x , g(x) = x2 – 2x

(b) f (x) = x2 – 1, g(x) = 1x

(c) f (x) = ln x g(x) = x + 12 x

2. Find f (x) in each of the following

(a) f (g(x)) = 2x – 4, g(x) = x + 1 (b) f (g (x)) = x2 – 3x + 2, g(x) = x + 1 (c) g(f (x)) = x2 + 1, g (x) = x2 + 2x – 1 3. Find f (g (x)) and g (f (x)) if ( ) = 2 – 3, – 2 1 and ( ) = + 1, – 1 2

4. If f (x) =

0,0,

2 xxxx

Find f (f (x).

5. Let f (x) = x1

1 find ∘ ∘ ( ). What is domain?

6. Let f (x) =

20,3202,1

xxxx

find f∘f (x).

7. If 24

4

x

x

xf , then show that 11 xfxf

8. Let f be a function defined for all x > 1 such that 1214 8 ( 1) logxf f x xx

, then value of

4( (10) (13) (17))f f f is

9. f (x + y, x – y) = xy, then the arithmetic mean of f (x, y) and f (y, x) is 0.

10. If 11)(

xxxf then show that f (f (ax)) in terms of f (x) is equal to

)1)((1)(

xfaxf

.

11. Determine if the following functions are periodic if yes find their period

(i) 2cos32 xxf (ii) xxxxf tancos3sin 2

(iii) 3

sin4

sin xxxf (iv) .

72sin

53cos xxxf

(vii) xxf sin (viii) xxxf sin


12. Determine whether the following functions are even or odd or neither even nor odd :

(i)

11

x

x

aaxxf (ii) 1log 2 xxxf

(iii) xxxf cossin (iv) xxxf 12

13. If

1)1ln(10cos

xxxxxx

xf

then extend the definition of 0,xforxf such that f (x) becomes (i) An even function (ii) An odd function 14. If f (x + y) = f (x) + f (y) – 1 for all ,1)1(and, fyx R then the number of solutions of

Nnnnf ,)( is one. 15. Let be a function with domain [–3, 5] and let g(x) = 3x + 4, find the domain of (og) (x). 16. The function f (x) = sin 5x + cos 3 x is non-periodic. Why?

17. Let f be a real valued function with domain R satisfying 21)(0 xf and for some fixed a,

,))(()(21)( 2 R xxfxfaxf then the period of the function f (x) is 2a.

18. Let f (x) = max R xxx ,2,1,1 . Then 1

111

,1,2,1

xx

x

x

xxf .

19. If ,)})({()(and))(()(,11)( xfffxhxffxgx

xf

then the value of

xhxgxf is – 1.

20. Determine a function f satisfying the functional relation

2 1 211 1

xf x f

x x x

21. Determine f(x) such that (| |) + | ( )| = 3 + 4. 22. If 3f(x) + af(1/x) = x and f(2) = 0 find a. 23. If f(x) is a polynomial satisfying f(x) + f(1/x) = f(x)f(1/x) determine f(x). 24. If f(x + y) = f(x) + f(y) for all x, y then f is odd, show. 25. If f(x - 1) + f(x + 1) = 4 then f(x) is periodic.


ANSWERS

1. (A) |x-1| (B) x (C) ln 1x2

2. (A) 2x 6 (B) x2 5x + 6 (C) 1 ± 3x2

3. ( ) = 2 − 1, −1 ≤ ≤ 0, ( ) = 2 − 2, = 1

4. ( ( ) = , < 0 ( ( ) = , ≥ 0

5. ∘ ∘ ( ) = , ≠ 0,1

6. ( ) =

⎩⎪⎨

⎪⎧ + 2, −2 ≤ < −1

2 − 1, −1 ≤ < 02 − 2, ≤ <

4 − 9, 3/2 ≤ ≤ 2

11. (A) T = 2 (B) T = 2 (C) T = 24 (D) T = 70

(E) not periodic (F) not periodic

12. (A) even (ii) odd (C) neither (D) even

15. −3, 20. ( ) = , ≠ 0,1 21. ( ) =, ≥ 0

, − ≤ < 0

22. 12 23. ( ) = 1 ±

Page No. - 1


Mob. : 9794757100, 7317347706 e-mail : [email protected] Web site : www.jrstutorials.ac.in

JRS TUTORIALS JEE PRACTICE SHEET No. – 1

Mathematics – Target & XII Time : 1 Hr.

1. The value of such that

8

9ln

)1x()x(

dx2

1

is

A. – 3 B. 2

1 C. –

2

1 D. 3

2. If

then,2

dxxsecxtan

xtan2/

0

=

A. 1 B. – 1 C. 2

1 D. –

2

1

3. The value of

n2

0

Nn,4dx)]x3cos1(x2[sin and [t] denotes the greatest integer

function then the value of n = ……..

A. 2 B. 3 C. 4 D. 5

4. Let x

0

dt)t(g)x(f , where g is not zero function as well as even. If f(x + 5) = g(x)

then x

0

dt)t(f

A.

5

5x

dt)t(g5 B. 5x

5

dt)t(g C. 5x

5

dt)t(g2 D.

5

5x

dt)t(g

5. The integral

1

x3x2

dxxlnx

e

e

x is equal to

then,

e

e

1 3

2= …………..

A. 3 B. 5 C. 7 D. 9

6. If xcos)xx1(ln2

xcos)xx1ln(2)x(f

2

2

and g(x) = ln x, (x > 0) when the value of the integral

4/

4/

dx))x(f(g is

A. ln 3 B. ln 1 C. ln 2 D. ln 3

Page No. - 2



7. Let

b

a

24 dx)xx(I . If I is minimum in the interval (–2, 2) then | a | + | b | = ………

(where N)

A. 2 B. 4 C. 6 D. 8

8. The value of

2/

2/

x

2

dxe1

xcosx is equal to

A. 24

2

B. 24

2

C. 2/2 e D. 2/2 e

9. The value of

1

3

23 dx)}2xcos()2x()10x12x6x({ is equal to ………..

A. 0 B. 3 C. 4 D. 1

10. Let

........,3,2,1,0n,dxxsin)e1(

nxsinI

xn

I1 + I2 + I3 + ………… + In = 99 and maximum of n = N then the value of

.....12

2N

11. The value of

1

0

2

44

n

mdx

x1

)x1(x

(where HCF (m, n) = 1) then (m – 3n) = ……….

12. If L

dt)atcosat(sine

dt)atcosat(sine

0

50100t

8

0

50100t

Where a is an even natural number then the value of ...........)L2.()1e(

)1e(8

13. Let 2448 tan3xtan3xtan7xtan7)x(f

for all L)x(fxand2

,2

x

4/

0

then

the value of L4

1= …………..

Page No. - 3



14. The value of integral

2/1

0

4/162 ])x1()1x[(

dx)31( is …………..

15. The value of

dx)x1(dx

dx)x1(5050

10150

1

0

1

0

10050

then (L – 5050) = ………..

16. Let f : [1, ) [2, ) be differential function.

If 1xx)x(fx3dt)t(f6 3

x

1

If | f(x) | = K has maximum number of solution for K (0, a) then the value of a

1=……

17. If f(x) = x + sin x and y = g(x) is the inverse of y = f(x).

If

2

3dx)x(g

2

then + = ……………

18. If ......I

Ithendx))x1(x(gIanddx))x1(x(gxI,

e1

e)x(f

1

2

2)a(f

2)a(f

2

2)a(f

2)a(f

1x

x

19. Let f(x) be continuous and differentiable in the interval (a, b) and ,1)x(flimax

.3)x(flim 4/1

bx

If )x(f

1)x(f)x(f 3 then value of [24(b – a)] = ……………

Where [t] is greatest integer function.

20. Let 2

2187

v

uif,dx)x1(xvanddx)x3(xu

n

n

1

0

nn

n

2/3

0

nn

n then n = ……….

Page No. - 4



JRS TUTORIALS JEE PRACTICE SHEET No. – 1

Answer

Question Answer Question Answer

1 B 11 1

2 A 12 2

3 C 13 3

4 D 14 2

5 B 15 1

6 B 16 9

7 B 17 4

8 A 18 2

9 C 19 3

10 9 20 3


JRS TUTORIALS MATHEMATICS FOUNDATION COURSE

PRACTICE SHEET: TRIGONOMETRY II

1. The value of cos 135 sin 135 is

1. 0 2. < (1) 3. > 1 4. None

2. cot 1. cot 2. cot 3…….cot 89 =

1. 2. 0 3. 1 4. 2

1

3. Which of the following is correct?

1. cos 1 > cos 1 2. cos 1 < cos 1

3. cos 1 = cos1 4. cos 1 = 1cos180

4.

75tan1

75tan12

2

1. 2

1 2.

2

3 3.

3

2 4.

3

2

5. sin 75 =

1. 22

13 2.

22

13 3. 32 4. 32

6. If

sinthen4

3cot

1. 5

4notbut

5

4 2.

5

4or

5

4

3. 5

4notbut

5

4 4. None

7. cot 15 tan 15 =

1. 32 2. 32 3. 32 4. None

8.

11sin11cos

11sin11cos

1. tan 45 2. tan 34 3. tan 60 4. cot 11

9.

14sin

14

3sin

14

5sin

1. 8

1 2.

4

1 3.

4

1 4.

8

1

10. The minimum value of ,cos24sin7 for all real values of is

1. 1 2. 24 3. 25 4. 31


Page No. 2

11. is45cos45sin 1. cos2 2. sin2 3. non zero constant 4. 0

12.

4tan .

4tan =

1. 1 2. 0 3. 1 4. infinite

13. If cos =

24

costhen2

3,

5

4

1. 5

1 2.

10

1 3.

5

1 4.

10

1

14. If and3

1cot lies in the 3rd quadrant, then cosec

1. 10

1 2. 10 3.

3

10 4.

3

10

15. If

costhen2

,5

3sinand

20,

13

12sin

1. 65

56 2.

65

16 3.

65

56 4.

65

16

16. cos 40 cos 20 + sin 10 =

1. 1 2. 0 3. 2

1 4. 2

17. 20sin20cos3

1. 2 2.

40sin

20sin2 3. 40sin2 4. None

18. If cos (B A) = 5

3 and tan A = 2 cot B then

1. 5

1coscos

BA 3.

5

1sinsin

BA

3. 5

1cos

BA 4.

5

4sinsin

BA

19. If tan = tan 60 then the value of in the 3rd quadrant is 1. 240 2. 210 3. 200 4. 220 20. Which of the following is correct? 1. sin + sin 2 + sin 3 = 3 is true for some real value of 2. If = 155 then sin + cos is negative 3. cos 11 cos 2 is positive

4. cos (1044) = 4

15


Page No. 3

21. The maximum value of 8 + 4 cos x + 3 sin x is 1. 12 2. 13 3. 8 4. 5

22. If sec 2 = 7

9 then sin =

1. 3

1notbut

3

1 2.

3

1notbut

3

1

4. 3

1or

3

1 4. None

23. sin 420 cos 390 cos (300) sin 330 =

1. 0 2. 1 3. 1 4. 2

13

24. tan 760 cot 760 + tan 225 cos 450 = 1. 0 2. 1 3. 2 4. 2

25. The signs of 5

12sin

5

12cosand

7

13sin

are respectively

1. +, + 2. , 3. +, 4. , +

26.

6

17sin

3

11cos

3

13sin

6

19cos

1. 1 2. 2

1 3.

2

1 4. 1

27. tan 6

11sin

4

17

1. 2

1 2. 1 3.

2

1 4.

2

3

28. cos 5

13

1. 5

2cos

2.

5

2sin

3.

10sin

4.

10

cos4

29. If 5 then to....3sin2sin(sin 222 18 terms) is equal to

1. 7 2. 8 3. 9 4. 2

19

30. Which of the following is a rational number? 1. sin 15 2. cos 15

3. sin 15 cos 15 4. sin 15 cos 75

31. 22 coscossinsin

1. 2cos4 2. 2sin4 3. 2

cos4 2 4. 2

sin4 2


Page No. 4

32. If tanthen1cossin

1. 1 2. 2

1 3. 0 4. none

33. If n tanthen2sinsin m

1. m

m

1

1 2.

nm

nm

3. nm

nm

4. None

34. If 22thensincosandcossin banbamba

1. m + n 2. mn 3. m2 + n2 4. mn

35. If 2

cotthen1cos2cos2cos

1. 2

cot3

2. 2

cot

3. 2

cot3

1 4.

2cot

3

1

36. If 0 < A, B < lyrespectiveareBandAthen2

1sinand

2

1cos,

2 BABA

1. 45, 45 2. 60, 45 3. 45, 15 4. 45, 60 37. The minute-hand of a clock is of length 10 cm. How far the tip of the hand move in

10 minutes?

1. cm3

10 2. cm

27

11160 3. cm

27

113050 4. None

38. If the angles of a triangle are in A.P. and the greatest angle is 2

then the smallest angle is

1. 3

2.

6

3.

4

4.

39. If sincosthensin2sincos

1. cos2 2. sin2 3. sincos2 4. None

40. If

sin

cos1,

cos

sin1

yx then

1. xy + 1 = x y 2. xy + 1 = 2y 3. xy +1 = x + y 4. xy +1 = y x

ANSWERS 1. 2 2. 3 3. 1 4. 4 5. 2 6. 2 7. 1 8. 2 9. 4 10. 3 11. 4 12. 3 13. 1 14. 3 15. 1 16. 2 17. 3 18. 3 19. 1 20. 2 21. 2 22. 3 23. 3 24. 2 25. 2 26. 4 27. 4 28. 3 29. 4 30. 3 31. 1 32. 3 33. 4 34. 3 35. 4 36. 3 37. 1 38. 2 39. 1 40. 4


PHYSICS



1. An infinite number of charges, each of charge 1 C, are placed on the x-axis with co-ordinates

x = 1, 2, 4, 8, .... . If 1 C is kept at the origin, then what is the net force acting on 1 C charge

(A) 9000 N (B) 12000 N (C) 24000 N (D) 36000 N2. Given are four arrangements of three fixed electric charges. In each arrangement, a point labeled

P is also identified — test charge, +q, is placed at point P. All of the charges are the samemagnitude, Q, but they can be either positive or negative as indicated. The charges and point Pall lie on a straight line. The distances between adjacent items, either between two charges orbetween a charge and point P, are all the same.

I. II.

III. IV.

Correct order of choices in a decreasing order of magnitude of force on P is(A) II > I > III > IV (B) I > II > III > IV (C) II > I > IV > III (D) III > IV > I > II

3. Four positive point charges are arranged as shown in the accompanying diagram. The forcebetween charges 1 and 3 is 6.0 N; the force between charges 2 and 3 is 5.0 N; and the forcebetween charges 3 and 4 is 3.0 N. The magnitude of the total force on charge 3 is most nearly

(A) 6.3 N

(B) 8.0 N

2 3 4

1

(C) 10 N

(D) 11 N4. A point charge +Q is placed at the centroid of an equilateral triangle. When a second charge +Q

is placed at a vertex of the triangle, the magnitude of the electrostatic force on the central charge

is 4N. What is the magnitude of the net force on the central charge when a third charge +Q is

placed at another vertex of the triangle?

(A) zero (B) 4 N (C) 4 3N (D) 8 N5. Three identical spheres each having a charge q and radius R, are kept in such a way that

each touches the other two. The magnitude of the net electric force on any sphere is

(A) 2

0

314 4

qR

(B) 2

0

212 4

qR

(C) 2

0

214 4

qR

(D) 2

0

312 4

qR


PHYSICS6. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at

each of the other two corners. If the net electrical force on Q is zero, then Q/q equals

(A) – 22 (B) – 1 (C) 22 (D) –21 [AIEEE-2009]

7. Given figure shows an arrangement of six charged particles. The net electrostatic force F acting

on charge +q at the origin due to other charges is

(A) 20

2

a4q6

(B) zero (C) 20

2

a2q7

(D)

3

23

a4q

20

2

8. The magnitude of electric force on 2 C charge placed at the centre O of two equilateraltriangles each of side 10 cm, as shown in figure is P. If charge A, B, C, D, E & F are 2 C,2 C, 2 C, -2 C, - 2C, - 2 C respectively, then P is:(A) 21.6 N

(B) 64.8 N OA

B

C

D

E

F

(C) 0

(D) 43.2 N9. Through the exact centre of a hydrogen molecule, an -particle passes rapidly, moving on

a line perpendicular to the internuclear axis. The distance between the two hydrogen nucleiis b. The maximum force experienced by the -particle is

(A) 2

20

43 3

eb (B)

2

20

83

eb (C)

2

20

83 3

eb (D)

2

20

43

eb

10. Which of the following graphs best represents the force acting on a charged particle kept at

distance x from the centre of a square and on the axis of the square whose corners haveequal charges.

(A) (B) (C) (D)


PHYSICS11. Three charges +Q1, +Q2 and q are placed on a straight line such that q is somewhere in between

+Q1 and +Q2. If this system of charges is in equilibrium, what should be the magnitude and sign

of charge q ?

(A) ve,)QQ(

QQ2

21

21 (B) ve,

2QQ 21

(C) ve,)QQ(

QQ2

21

21 (D) ve,

2QQ 21

12. Three charges + 4q, -q and +4q are kept on a straight line at position (0, 0, 0), (a, 0, 0) and(2a, 0, 0) respectively. Considering that they are free to move along the x-axis only(A) all the charges are in stable equilibrium(B) all the charges are in unstable equilibrium(C) only the middle charge is in stable equilibrium(D) only middle charge is in unstable equilibrium

13. A mass particle (mass = m and charge = q) is placed bewteen two point charges of charge

q separtion between these two charge is 2L. The frequency of oscillation of mass particle,

if it is displaced for a small distance along the line joining the charges–

(A) 30Lm

12q

(B) 30Lm

42q

(C) 30Lm4

12q

(D)2q

30mL161

14. Two positive point charges are fixed at some distance apart. A third negative charge ' q ' is placedat the centre of the line joining the two charges. Then the number of lines along which ' q ' canperform SHM for small displacements is(A) 1 (B) 2 (C) 3 (D)

15. Four point positive charges are held at the vertices of a square in a horizontal plane. Theirmasses are 1 kg, 2 kg, 3 kg & 4 kg. Another point positive charge of mass 10 kg is kept onthe axis of the square. The weight of this fifth charge is balanced by the electrostatic forcedue to those four charges. If the four charges on the vertices are released such that they canfreely move in any direction (vertical, horizontal etc) then the acceleration of the centre ofmass of the four charges immediately after the release is: (Use g = 10 m/s2)

(A) 10 m/s2 (B) 20 m/s2 (C) zero (D) 10 m/s2 16. Under the influence of the Coulomb field of charge +Q, a charge –q is moving around it in an

elliptical orbit.Find out the correct statement(s). [JEE -2009](A) The angular momentum of the charge –q is constant.(B) The linear momentum of the charge –q is constant.(C) The angular velocity of the charge – q is constant.(D) The linear speed of the charge –q is constant.


PHYSICS17. A ring of radius R is made out of a thin metallic wire of area of cross section A. The ring has a

uniform charge Q distributed on it. A charge q0 is placed at the centre of the ring. If Y is theyoung’s modulus for the material of the ring and R is the change in the radius of the ring, then

(A) R = RAY4Qq

0

0

(B) RAY4QqR

0

0

(C) RAY8

QqR 20

0

(D) RAY8

QqR0

20

18. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap

film of side ‘ ’. The surface tension of the soap film is . The system of charges and planar

film are in equilibrium, and = k1/N2q

, where ’k’ is a constant. Then N is

(A) 3 (B) 2 (C) 4 (D) 6 [JEE-2011]

MULTIPLE CORRECT ANSWERS19. Three charged particles are in equilibrium under their electrostatic forces only

(A) The particles must be collinear.(B) All the charges cannot have the same magnitude.(C) All the charges cannot have the same sign.(D) The equilibrium is unstable.

20. Two equal negative charges –q each are fixed at the points (0, a) and (0, -a) on the y-axis .Apositive charge Q is released from rest at the point (2a, 0) on the x-axis. The charge Q will:(A) At origin velocity of particle is maximum.(B) Execute simple harmonic motion about the origin(C) Move to infinity(D) Execute oscillatory but not simple harmonic motion.

21. A negative point charge placed at the point A is

(A) in stable equilibrium along x-axis

(B) in unstable equilibrium along y-axis

(C) in stable equilibrium along y-axis

(D) in unstable equilibrium along x-axis22. Two identical charges +Q are kept fixed some distance apart. A small particle P with charge q is

placed midway between them. If P is given a small displacement , it will undergo simpleharmonic motion if(A) q is positive and is along the line joining the charges.(B) q is positive and is perpendicular to the line joining the charges.(C) q is negative and is perpendicular to the line joining the charges.(D) q is negative and is along the line joining the charges.


PHYSICSParagraph

Three charged particles each of +Q are fixed at the corners of anequilateral triangle of side ‘a’. A fourth particle of charge –q andmass m is placed at a point on the line passing through centroid of triangle and perpendicular to the plane of triangle at a distance xfrom the centre of triangle

23. Force on the fourth particle is

(A) 2/3220 )ax3(

Qx394

1 (B) 2/322

0 )ax3(Qx33

41

(C) 2/3220 )ax2(

Qx224

1 (D) 2/322

0 )ax2(Qx24

41

24. Value of x for which the force is maximum is

(A) 3a

(B) 2a

(C) 6a

(D) 5a

MATCH THE COLUMN25. Four charge Q1,Q2,Q3, and Q4,of same magnitude are fixed along the x axis at x = –2a –a, +a

and +2a, respectively. A positive charge q is placed on the positive y axis at a distance b > 0.Four options of the signs of these charges are given in List-I . The direction of the forces on thecharge q is given in List- II Match List-1 with List-II and select the correct answer using thecode given below the lists [JEE (ADV)-2014]

List-I List-IIP. Q1,Q2,Q3, Q4, all positive 1. +xQ. Q1,Q2 positive Q3,Q4 negative 2. –xR. Q1,Q4 positive Q2, Q3 negative 3. +yS. Q1,Q3 positive Q2, Q4 negative 4. –yCode :(A) P-3, Q-1, R-4,S-2 (B) P-4, Q-2, R-3, S-1(C) P-3, Q-1, R-2,S-4 (D) P-4, Q-2, R-1, S-3


PHYSICS26. In the following Fig. charges, each +q, are fixed at L and M. O is the mid point of distance LM.

X- and Y –axes are as shown. Consider the situations given in column I and match them with

the information in column II

Column I Column –II(A) Let us place a charge +q at O, displace it (P) force on the charge is zero slightly along X-axis and release. Assume that it is allowed to move only along X-axis. At position O,(B) Place a charge –q at O, Displace it slightly (Q) potential energy of the system along X-axis and release. Assume that it is maximum is allowed to move only along X-axis. At position O,(C) Place a charge +q at O. Displace it slightly (R) potential energy of the system is along Y-axis and release. Assume that it is minimum allowed to move only along Y-axis. At position O,(D) Place a charge –q at O. Displace it slightly (S) the charge is in equilibrium along Y-axis and release. Assume that it is allowed to move only along Y-axis. At position O,


1. B 2. C 3. A 4. B 5. A 6. A

7. B 8. D 9. C 10. C 11. C 12. B

13. A 14. D 15. B 16. A 17. D 18. A

19. A,B,CD 20. A,D 21. C,D 22. A,C 23. A

24. C 25. A 26. (A- P, R, S) ( B – P, Q, S) (C –P, Q, S) (D – P, R, S)



MOLE CONCEPT –DPP-1

Subjective 1. Find out number of moles in 0.0036 gram of water?

2. Find out number of atoms in following a. 5 moles of oxygen b. 5 moles of water c. 5 moles of glucose d. 5 moles of CuSO4.5H2O

3. Find out number of atoms in following A. 25 moles of nitrogen B. 0.24 moles of methane C. 1.2 moles of glucose D. 200 milimoles of water Hint: 1 mole = 1000 millimoles

4. Convert following into moles A. 3.011 × 1023 molecules of water B. 1.2044 × 1025 molecules of water C. 3.011 × 1020 molecules of oxygen D. 2.4088 × 1022 molecules of nitrogen

5. Find out number of electrons in following A. 6.022 × 103 molecules of water B. 10 moles of water C. 0.0024 moles of carbon dioxide D. 400 milimoles of oxygen

6. What is mass of five sodium atoms in amu

7. What should be mass of one molecule of water in gram?

8. Find out mass of one Mg atom in gram

9. One atom of an element X weighs 6.644 × 10–23 g. Calculate the number of moles of X in 40 kg of it

10 4.6 × 1022 atoms of an element weigh 13.8 gm. The gram atomic mass of the element

is: (NA = 6 × 1023)

11. Find out number of moles of CH4 in 5.6 L of CH4 at STP.

12. Find out volume of 10 moles methane at STP.

Objective (Only one option is correct) 1. The mass of 3.2 ×105 atoms of an element is 8.0 ×10–18 g. the atomic mass of the

element is about (NA = 6×1023) 1. 2.5 ×10–22 2. 15 3. 8.0×10–18 4. 30 2. Number of electrons in 18 g H2O 1. 6.022 × 1022 2. 6.022 × 1023 3. 6.022 × 1024 4. 6.022 × 1025 3 The number of neutrons present in 9 mg of O18 is

1. 10 2. 5NA 3. 0.005 NA 4. 0.0005 NA


2 4. Which of the following have largest number of atoms?

1. 4 gm oxygen (at mass O = 16) 2. 16 gm sulphur (at mass S = 32) 3. 35.5 gm chlorine (at mass Cl = 35.5) 4. 14 gm lithium (at mass Li = 7) 5. Number of oxygen molecules having weight equal to weight of 20 molecules of SO3. 1. 100 2. 50 3. 15 4. 8 6. The weight of 3.2 × 105 atoms of an element is 8.0 × 10–18 gm. The atomic weight of

the element should be about 1. 2.5 × 10–22 2. 15 3. 1.5 4. 150

7. The number of molecules of water in 333 g of Al2(SO4)3. 18H2O is

1. 18.0 × 6.02 × 1023 2. 9.0 × 6.02 × 1023

3. 18.0 4. 36.0 8. The mass of 2 gram atoms of calcium (atomic mass = 40) 1. 2 g 2. 0.05 g 3. 0.5 g 4. 80 g 9. The number of molecules present in 88 g of CO2 (Relative molecular mass of

CO2 = 44) 1. 1.24 × 1023 2. 3.01 × 1023 3. 6.023 × 1024 4. 1.2046 ×1024

10. One a.m.u. is equivalent to 1. 1.66 × 10–24 kg 2. 1.66 × 10–25 kg 3. 1.66 × 10–26 kg 4. 1.66 × 10–27 kg 11. The number of atoms present in 0.05g of water is 1. 1.67 × 1023 2. 1.67 × 1022 3. 5.02 × 1021 4. 1.67 × 1021 12. How many moles of Magnesium phosphate Mg3(PO4)2 will contain 0.25 mole of

oxygen atoms? 1. 0.02 2. 3.125 × 10–2 3. 1.25 × 10–2 4. 2.5 × 10–2

13. Which has the maximum no. of atom? 1. 6 g C 2. 1 g H2 3, 12 g Mg 4. 30 g Ca

Answers – Mole concept –DPP-1 Subjective 1. [0.0002] 2. [(a ) 6.022 × 1024 (b) 9.033 × 1024 (c) 7.2264 × 1025 (d) 6.323 × 1025 3. [A. 25× 2 × NA B. 0.24 × 5 × NA C. 1.2× 24× NA D. 200× 10–3× 3× NA ] 4. [A. 0.5 B. 20 C. 5 × 10–4 D. 0.04] 5. [A. 6.022 × 104 B. 10 ×10 × 6.022 × 1023 C. 3.17 × 1022 D. 3.85 × 1024 ] 6. [115 amu] 7. [29.88 × 10-24 gram] 8. [39.84 × 10-24 gram] 9. [1000] 10. [180]11. [0.25] 12. [224]

Objective

Q. No. 1 2 3 4 5 6 7 8 9 10 Answer 2 3 3 4 2 2 2 4 4 4 Q. No. 11 12 13 Answer 3 2 2



Trigonometry – III 1. Express each of the following products into sums or difference of sines and cosines. (i) 2 cos 3 sin 2 (ii) 2 sin 5 cos 3 (iii) cos 9 cos 4 (iv) sin 75 cos 15

2. Prove that )140(sin21115cos25sin

3. Prove that : (i) 16380sin60sin40sin20sin

(ii) 8180cos40cos20cos (iii) 380tan60tan40tan20tan

4. Prove that : (i) 16370cos50cos30cos10cos

(ii) tan 20 tan 30 cos40 cos80 = 1

5. Prove that : (i)

3cos3

cos3

coscos4

(ii) 2

5sin5sin2

9cos3cos2

cos2cos xxxxxx

6. show that: 0)(cos)(sin)(cos)(sin)(cos)(sin DCBADBACDACB



9. If ,3

1sin,2


cot2

tan

10. Express each of the following as product of sines and cosines (i) cos 9 + cos 3 (ii) sin 2 + cos 4 (iii) cos 12 – cos 4 (iv) sin 9 + sin 5 11. Prove that (i) 20cos265cos65sin (ii) 17cos77cos47sin 12. Prove that

(i) xxxxx cot

5sin7sin5cos7cos

(ii)

xx

xxxx

10cos2sin

3sin17sin5cos9cos

(iii) xxxxx 2tan

3coscos3sinsin

(iv) )3sin5(sincot)3sin5(sin4cot xxxxxx

(v) xxx

xx sin2cossin

3sinsin22


13. Prove that

(i) cos10 sin10 tan 35cos10 sin10

(ii) 020cos40cos80cos

(iii) 80sin70sin50sin40sin20sin10sin

(iv) 0140cos100cos20cos

14. Prove that

(i) 05

7cos5

6cos5

2cos5

cos

(ii) 1cos sin

12 12 2

(iii) 9

sin39

4cos185sin

(iv) xxx sin24

3cos4

3cos

(v) xxx cos24

cos4

cos

15. Prove that

(i) cos + cos + cos + cos( + + ) = 2

cos2

cos2

cos4

16. (i) 2

tancoscossinsin yx

yxyx

(ii)

2tan

coscossinsin yx

yxyx

(iii)

2cot

2tan

coscossinsin yxyx

yxyx

17. Prove that

(i) sin 3x + sin 2x – sin x = 4 sin x cos 2x cos

23x

(ii) xxxxxxx 4sin2coscos47sin5sin3sinsin

(iii) 3tan

5cos3coscos5sin3sinsin (iv) cos 4 cos3 cos 2 cot 3

sin 4 sin 3 sin 2

(v) sin 2sin 3 sin 5 sin 3sin 3 2sin 5 sin 7 sin 5

(vi) 3tan2sin2cos

5cos3cos2cos7cos5cos23cos

(vii)

tancos5cos

sin3sin25sin


18. If cosec A + sec A = cosec B + sec B, Prove that tan A tan B = 2

cot BA

19. Prove that

(i) (cos – cos )2 + (sin – sin )2 = 4 sin2

2

(ii) sin + sin + sin – sin ( + + ) = 4 sin

2sin

2sin

2

20. If ,0)cos()cos(

)cos()cos(

DCDC

BABA prove that 1tantantantan DCBA

21. If ,4

BA show that .2)1(cot)1(cot BA

22. If 0.cot 7cot that show,8

23. If x tantan and ,cotcot y prove that xy

yx )cot(

24. If ,tan2tan show that .3)sin()sin(

25. If ,cossinandsincos nBAmBA prove that. .2)sin(2 22 nmBA

26. If ,33

2tan3

tantan

xxx then prove that 1tan31

tantan32

3

x

xx

27. If a right angle be divided in to three parts , and , prove that cot cot cot cot cot cot 28. If sin sin – cos cos = 1, show that tan + tan = 0.



tan ( +2) and tan (2 + ).

30. If m tan ( – 30) = n tan ( + 120). Show that )(2

2cosnm

nm

31. If sin 2A = sin 2B, prove that 11

)tan()tan(

BABA

32. If cos ( + ) sin ( + ) = cos ( – ) sin ( – ), prove that cot cot cot = cot 33. If y sin = x sin (2 + ) show that (x + y) cot ( + ) = (y – x) cot

34. If + and ,tantan

yx

prove that .sin)sin(

yxyx

35. If and are the solutions of the equation a cos + b sin = C. then show that

(i) 22

22

)cos(baba

(ii) 22

222 )(2)cos(ba

bac


36. Find the maximum and minimum values of the following expressions: (i) a cos – b sin (ii) 7 cos + 24 sin 37. Show that

(i) AAAAA

2cotcot3cot

1tan3tan

1

(ii) AAAAA

4cotcot3cot

1tan3tan

1

38. Prove that

(i) xxxx 8sin4sin6cos2cos 22 (ii)

22

22

sincossinsin)tan()tan(

39 Prove that (i) 0)sin()sin()sin()sin()sin()sin( ACACCBCBBABA (ii) .0})12tan{(})12{(tan nn

40. If ,12

1tan,1

tan

mm

m prove that .4

ANSWERS

1. (i) sin 5 – sin (ii) sin 8 – sin 2 (iii) )5cos13(cos21

10. (i) 2 cos 6 cos 3 (ii)

3

4cos

4cos2 (iii) – 2sin 8 sin 4

(iv) 2 sin 7 cos 2 36. (i) maximum = ,22 ba minimum = – 22 ba (ii) maximum = 25, minimum = – 25

Page No. - 1

JRS TUTORIALS, Durgakund, Varanasi – 221 005 (U.P.) Ph. No. (0542) 2311922, 2311777 Mob. : 9794757100, 7317347706 e-mail : [email protected] Web site : www.jrstutorials.ac.in

JRS TUTORIALS Mathematics

Vectors (Collinearity and Coplanarity) DPP – 1

1. Prove that points A(1, 3, 2), B(–2, 0, 1) and C(4, 6, 3) are collinear. 2. If position vectors of points A, B, C are baba 23,, respectively (where a and b are

non-collinear vectors). Then prove that A, B, C are collinear points. 3. Points P, Q, R, S have position vectors cb32,c4b33a5,c4a2 and

ca2 respectively. Prove that line segment PQ is parallel to line segment RS. (where candb,a are linearly independent vectors).

4. If points (1, x, 3), (3, 4, 7) and (y, –2, –5) are collinear. Prove that 1 yx . 5. a and b are non-collinear vectors. Find ‘x’ for which (x–2) ba)1x2(,ba are

collinear vectors. 6. Let candb,a are three vectors of which every pair is non-collinear. If ba is collinear

with cbandc is collinear with a . Prove that 0cba . 7. Prove that vectors k4j3i7,kj3i2,kji are non-coplanar. 8. If vectors k5jai3andk3j2i,kji2 are coplanar. Prove that | a | = 4. 9. If candb,a are non-coplanar, prove that vectors cbacba 432,32 and c2b are coplanar. 10. If candb,a are non-coplanar vectors. Prove that four points ,c3b2a,cb3a2 c2b4a3 and c6b6a are coplanar.

Page No. - 2

JRS TUTORIALS, Durgakund, Varanasi – 221 005 (U.P.) Ph. No. (0542) 2311922, 2311777 Mob. : 9794757100, 7317347706 e-mail : [email protected] Web site : www.jrstutorials.ac.in

11. Let b)1y3x2(a)2x2y(qandb)1yx2(a)y4x(p where banda are non-collinear and q2p3 . Find x and y.

12. Find ‘a’ if points j52iaandj8i40,j3i60 are collinear. 13. kjic,k4j3i4b,kjia where candb,a are linearly dependent

and 1|| c then prove that = 1, = 1. 14. k5j2i3randk3ji2c,k2j3ib,kji2a 1 . If crbqapr1

then prove that p = q + r. 15. Let candb,a are three non-zero vectors, no two of which are collinear. If b7a3 is

collinear with c2b3andc is collinear with a . Prove that 0c14b21a9 . 16. )kxj5i4(Dand)k2ji(C),k4j3i2(B),kj2i3(A are coplanar points.

Find x. 17. Let candb,a are three non-coplanar vectors, such that acbrcbar 21 , , cbarandbacr 4323 . If 321 rzryrxr then prove that x + z = 3. 18. If vectors kji2andkji,k2ji are coplanar. Then find .

19. Let a, b and c are distinct non-negative numbers. If vectors andki,kcjaia kbjcic lie in a plane then prove that c is geometric mean of a and b. 20. The vectors jiandjiji 865,32 have their initial points at (1, 1). Find the

value of so that the vectors terminate on one straight line.

ANSWERS

5. 31 11. x = 2 and y = –1 12. a = – 40

16. 17146 18. = –2, 1 3 20. 9




Subjective 1. A solid contains A+ and B¯ ions. The structure of solid is fcc for B¯ ions and A+ ions are

present in one fourth of tetrahedral voids as well as in one fourth of octahedral voids. What is the simplest formula of solid ?

2. A cubic solid is made by atoms A forming close pack arrangement, B occupying one.

Fourth of tetrahedral void and C occupying half of the octahedral voids. What is the formula of compound

3. Spinel is a important class of oxides consisting of two types of metal ions with the oxide

ions arranged in CCP pattern. The normal spinel has one-eight of the tetrahedral holes occupied by one type of metal ion and one half of the octahedral hole occupied by another type of metal ion. Such a spinel is formed by Zn2+, Al3+ and O2–, with Zn2+ in the tetrahedral holes. Give the formulae of spinel

4. A closed packed structure of uniform spheres has the edge length of 534 pm. Calculate

the radius of sphere, if it exist in (a) simple cubic lattice (b) BCC lattice (c) FCC lattice

5. An element crystallizes into a structure which may be described by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its body diagonals. If the volume of this unit cell is 24×10–24 cm3 and density of element is 7.2 g cm–3, calculate the number of atoms present in 200 g of element.

6. A cubic unit cell contains manganese ions at the corners and fluoride ions at the center of each edge. (a) What is the empirical formula of the compound? (b) What is the co-ordination number of the Mn ion? 7. An element (atomic mass = 100) having BCC structure has unit cell edge length 400

pm. The density of this element will be (NA = 6 × 1023) 8. A solid has three types of atoms X, Y and Z. ‘X’ forms a FCC lattice with ‘Y’ atoms

occupying all the tetrahedral voids and ‘Z’ atoms occupying half the octahedral voids. The simplest formula of solid is

9. Lithium metal crystallizes in a body-centred cubic crystal. If the length of the side of the

unit cell of lithium is 351 pm, the atomic radius of lithium will be 10. A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge

of 400 pm. If the density of the substance in the crystal is 8 g cm–3, Calculate the number of atoms present in 256 g of the crystal :


Page-2

Only one option is correct 1. Copper crystallizes in a face-centred cubic lattice with a unit cell length of 361 pm.

What is the radius of copper atom in pm? 1. 157 2. 181 3. 108 4. 128 2. If the radius of the anion in an ionic solid is 200 pm, what would be the radius of the

cation that fits exactly into a cubic hole 1. 146.4 pm 2. 82.8 pm 3. 45 pm 4. 60.8pm

3. The decreasing order of size of the void is 1. cubic > octahedral > tetrahedral > Trigonal 2. trigonal > tetrahedral > octahedral > cubic 3. Trigonal > octahedral > tetrahderal > cubic 4. cubic > tetrahedral > octahedral > trigonal 4. For the structure given below the site marked as S is a 1. Tetrahedral void 2. Cubic void 3. Octahedral void 4. None of these 5. If a stands for the edge length of the cubic system: simple cubic, body centred cubic and

face centred cubic, then the ratio of radii of the spheres in these systems will be respectively

1. a22:a

23:a

21 2. 1a : a3 : a2

3. a22

1:a43:a

21 4. aaa

21:3:

21

6. In which of the following substances the carbon atom is arranged in a regular tetrahedral structure. 1. Diamond 2. Benzene 3. Graphite 4. Carbon black 7. For a solid with the following structure, the co-ordination number

of the point B is 1. 3 2. 4 3. 5 4. 6 8. In a hexagonal close packed (hcp) structure of spheres, the fraction of the volume occupied by the sphere is A. In a cubic close packed structure, the fraction is B. The relation for A and B is 1. A = B 2. A < B 3. A > B 4. A is equal to the fraction in a simple cubic lattice. 9. In a close packed array of N spheres, the number of tetrahedral holes are 1. 2/N 2. 4N 3. 2N 4. N

S

A B


Page-310. If the radius ratio is in the range of 0.225–0.414, then the coordination number

will be 1. 2 2. 4 3. 6 4. 8

11. In a solid C atom are forming CCP lattice with A atoms

occupying all tetrahedral voids and B atoms occupying all octahedral voids. Which of the following arrangement is obtained along the plane shown in diagram?

1. 2. 3. 4.

19. A metallic crystal crystallizes into a lattice containing a sequence of layers AB AB

AB....Any packing of spheres leaves out voids in the lattice. What percentage of volume of this lattice is empty space, 1. 74% 2. 26% 3. 50% 4. 40%

13. The fraction of octahedral voids filled by Al3+ ions in Al2O3 )43.0/( 23 =−+ OAl

rr is 1. 0.43 2. 0.287 3. 0.667 4. 1

14. Which of the following expressions is correct for an NaCl unit cell with lattice parameter a

1. 2a

rr ClNa =+ −+ 2. −+ + ClNa rr = 4a

3. 4a

r ClNa r =+ −+ 4. a43

rr ClNa =+ −+

15. In a unit cell atoms (A) are present at all corners atom(B) are present at 50% faces and all edge centre, Atoms(C) are present at face centres left from (B) and 1 at each body diagonal at distance of 1/4 th of body diagonal from corner. Formula of the given solid is

1. A3B8C7 2. AB4C6 3. A6B4C8 4. A2B9C11

16. Which of the following statements is correct for 3CsBr 1. It is a covalent compound

2. It contains +3Cs and −Br ions 3. It contains +Cs and −

3Br ions. 4. It contains +Cs , −Br and lattice 2Br molecule

17. A crystal is made of particles X and Y. X forms fcc packing and Y occupies all the

octahedral voids. If all the particles along one body diagonal are removed then the formula of the crystal would be

1. X4Y3 2. X5Y4 3. X4Y5 4. X3Y4

CCP unit cell

C C

C C

B

B

B B A

B A

C C C

C C C

B B B

C C C

C C C

B B B A A A A

C C C

C C C

B B B


Page-4

18. In a face centred cubic arrangement of A and B atoms when A atoms are at the corner of the unit cell and B atoms of the face centres. One of the A atom is missing from one corner in unit cell. The simplest formula of compound is

1. 37BA 2. 3AB 3. 247BA 4. 38/7 BA

19. Ferrous oxide has a cubic structure and each edge of the unit cell is 5.0 Å. Assuming density of the oxide as 4.0 g 3cm−− , then the number of +2Fe and −2O ions present in each unit cell will be 1. Four +2Fe and four −2O 2. Two +2Fe and four −2O 3. Four +2Fe and two −2O 4. Three +2Fe and three −2O

20. For an octahedral arrangement the lowest radius ratio limit is 1. 0.155 2. 0.732 3. 0.414 4. 0.225

Answer DPP-3

Subjective 1. [A3 B4] 2. [A4B2C2] 3. [ZnAl2O4] 4. [ 267pm , 231.2pm ,188.8pm

5. [3.472 × 1024 atoms] 6. [ (a) MnF3 (b) 6 ] 7. [5.2 g/ml]

8. [X2Y4Z] 9. [151.8 pm] 10. [2 × 1024]

Only one option is correct

Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 4 1 1 3 3 1 4 1 3 2

Q.No. 11 12 13 14 15 16 17 18 19 20 Ans 3 3 3 1 4 3 2 3 1 3




Subjective 1. Cesium chloride forms a body centered cubic lattice. Cesium and chloride ions are in

contact along the body diagonal of the unit cell. The length of the side of the unit cell is 412 pm and Cl– ion has a radius of 181 pm. Calculate the radius of Cs+ ion.

2. If the radius of Mg2+ ion, Cs+ ion, O2– ion, S2– ion and Cl– ion are 0.65 Å , 1.69 Å, 1.40

Å, 1.84 Å, and 1.81 Å respectively. Calculate the co-ordination numbers of the cations in the crystals of MgS, MgO and CsCl.

3. KCl crystallizes in the same type of lattice as does NaCl. Given that 5.0=−

+

Cl

Na

rr

and

7.0=+

+

K

Na

rr

Calculate:

(a) The ratio of the sides of unit cell for KCl to that for NaCl and (b) The ratio of densities of NaCl to that for KCl. 4. A unit cell of sodium chloride has four formula units. The edge of length of the unit

cell is 0.564 nm. What is the density of sodium chloride. 5. In a cubic crystal of CsCl (density = 3.97 gm/cm3) the eight corners are occupied by Cl–

ions with Cs+ ions at the centre. Calculate the distance between the neighbouring Cs+ and Cl– ions.

6. An ionic compound AB has ZnS type structure. if the radius A+ is 22.5 pm, then

calculate the ideal radius of B- would be 7. KF has NaCl structure. What is the distance between K+ and F– in KF if density of KF is

2.48 gm/cm3. 8. NaH crystallizes in the same structure as that of NaCl. The edge length of the cubic unit

cell of NaH is 4.88 Å. (a) Calculate the ionic radius of H–, provided the ionic radius of Na+ is 0.95 Å. (b) Calculate the density of NaH.

9. AgCl has the same structure as that of NaCl. The edge length of unit cell of AgCl is

found to be 555 pm and the density of AgCl is 5.561 g cm–3. Find the percentage of sites that are unoccupied.

10 A crystal of lead(II) sulphide has NaCl structure. In this crystal the shortest distance

between Pb+2 ion and S2– ion is 297 pm. What is the length of the edge of the unit cell in lead sulphide? Also calculate the unit cell volume.


Page-2

Only one option is correct 1. A binary solid (AB) has a rock salt structure. If the edge length is 400 pm, and radius of

cation is 80 pm the radius of anion is 1. 100 pm 2. 120 pm 3. 250 pm 4. 325 pm 2. In which case, can we see 12 as coordination number : 1. ZnS 2. CaF2 3. NaCl 4. Ag 3. In CsCl structure, the coordination number of +Cs is 1. Equal to that of −Cl , that is 6 2. Equal to that of −Cl , that is 8 3. Not equal to that of −Cl , that is 6 4. Not equal to that of −Cl , that is 8 4. Which of the following statement (s) is incorrect

1. The coordination number of each type of ion in CsCl crystal is 8 2. A metal that crystallizes in bcc structure has a coordination number of 12 3. A unit cell of an ionic crystal shares some of its ions with other unit cells. 4. The adge length of the unit cell in NaCl is 552 pm ( +Na

r = 95 pm; −Clr = 181 pm)

5. If the radius of Cs+ = 1.69 Å and Br- = 1.95 Å, then which of the following is correct

statement? 1. Edge length of until cell is 8.2 Å 2. Coordination number of Cs+ is 6 3. CsBr has BCC type structure 4. Br– ions touch each other along the edge 6. RbCl has NaCl type lattice and its unit cell length is 0.30 Å greater than that for KCl.

If +Kr = 1.33 Å , the ionic radius of Rb+ is

1. 1.48 Å 2. 1.63 Å 3. 1.03 Å 4. 1.75Å 7. 8 : 8 co-ordination is noticed in – 1. MgO 2. Al2O3 3. CsCl 4. All 8. A certain sample of cuprous sulphide is found to have composition Cu1.8S, because of

incorporation of Cu2+ ions in the lattice. What is the mole % of Cu2+ in total copper content in this crystal?

1. 99.8% 2. 11.11% 3. 88.88% 4. 94% 9. A solid +A −B has a body centred cubic structure. The distance of closest approach between the two ions is 0.767 Å. The edge length of the unit cell is

1. 23 pm 2. 142 = 2 pm 3. 2 pm 4. 81.63 pm.

10. For an ionic crystal of the general formula AX and co-ordination number 6, the radius ratio value will be, 1. greater than 0.73 2. between 0.73 and 0.41

3. between 0.41 and 0.22 4. less than 0.22 11. NH4Cl crystallizes in a body-centered cubic type lattice with a unit cell edge length of

387 pm. The distance between the oppositively charged ions in the lattice is 1. 335.1 pm 2. 83.77 pm 3. 274.46 pm 4. 137.23 pm 12. If the distance between Na+ and Cl– lons in NaCl crystal is 'a' pm, what is the length of

the cell edge? 1. 2a pm 2. a/2 pm 3. 4a pm 4. a/4 pm


Page-3

13. Which statement is correct in antifluorite structure of Na2O 1. O2– ions have CCP arrangement 2. It has 4 :8 coordination 3. Na+ ions occupy all the tetrahedral sites 4. All are correct 14. The number of nearest neighbours and next nearest neighbours of a Na+ ion in a crystal

of NaCl are respectively : 1. 6Na+, 12Cl– 2. 6Cl–, 12Na+ 3. 12Cl–, 6Na+ 4. 6Cl–, 6Na+ 15. In solid CsCl each Cl– is closely packed with how many Cs+ 1. 8 2. 6 3. 10 4. 2 16. For an ionic crystal of the general formula AX and coordination number 6, the value of radius ratio will be 1. Greater than 0.73 2. In between 0.73 and 0.41 3. In between 0.41 and 0.22 4. Less than 0.22. 17. Which of the following statements is correct in the zinc-blende type structure of an ionic

compound? 1. Coordination number of each cation and anion is two 2. Coordinate number of each cation and anion is four 3. Coordination number of each cation and anion is six 4. Coordination number of each cation and anion is eight 18. Select the incorrect statement 1. CsCl changes to NaCl structure on heating 2. NaCl changes to CsCl structure on applying pressure 3. Coordination number increases on applying pressure

4. Coordination number increases on heating

19. CsBr has bcc type structure with edge length 4.3 pm. The shortest inter ionic distance in between Cs+ and Br– is

1. 3.72 pm 2. 1.86 pm 3. 7.44 pm 4. 4.3 pm

20. In a solid ‘AB’ having the NaCl structure, ‘A’ atoms occupy the corners of the cubic unit cell. If all the face centered atoms along one of the axes are removed, then the resultant stoichiometry of the solid is :

1. AB2 2. A2B 3. A4B3 4. A3B4

Answer –DPP-4

Subjective

1. [175.8 pm] 2. [4, 6, 8] 3. [(a) 1.143, (b) 1.172] 4. [2.16 gm/cm3]

5. [3.57 Å] 6. [100pm] 7. [2.685 Å] 8. [(a) 1.49 Å, (b) 1.37 g/cm3] 9. [0.24%]

10. [a =5.94 ×10–8 cm, V=2.096×10–22 cm–3]

Only one option is correct

Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 2 4 2 2 3 1 3 2 4 2

Q.No. 11 12 13 14 15 16 17 18 19 20 Ans 1 1 4 2 1 2 2 4 1 4

PHYSICS



DPP-05 : ELECTRIC FIELD1. Two charges 10 C and 25 C are placed at (1,0) and (4,0), electric field at (0,3) =

(A) ˆ ˆ(63 27 )i j

(B) 2 ˆ ˆ10 (63 27 )i j

(C) ˆ ˆ(27 63 )i j

(D) 2 ˆ ˆ10 (27 6 )i j2. Four charges are placed on the circumference of a circle of radius R, 90° apart as shown in the

fig. The electric field strength at the centre of the circle is

(A) 20 R

Q524

1 , making angle tan–12 with the – ve x-axis.

(B) 20 R

Q524

1 , making angle tan–12 with the + ve y-axis.

(C) 20 R

Q244

1 , making angle tan–1

21

with the – ve x-axis.

(D) 20 R

Q244

1 , making angle tan–1

21

with the + ve y-axis.

3. A point charge q is placed at origin. Let AE

, BE

and CE

be the electric field at three pointsA (1, 2, 3), B (1, 1, – 1) and C (2, 2, 2) due to charge q. Then [i] AE

BE

[ii] | BE

| = 4 | CE

|select the correct alternative(A) only [i] is correct (B) only [ii] is correct(C) both [i] and [ii] are correct (D) both [i] and [ii] are wrong

4. A positive charge +Q located at the origin produces an electric field E0 at point P (x = +1, y = 0).A negative charge –2Q is placed at such a point as to produce a net field of zero at point P. Thesecond charge will be placed on the

(A) x-axis where x > 1

(B) x-axis where 0 < x < 1

y

x+Q (1,0)

P-x(C) x-axis where x < 0

(D) y-axis where y > 05. Charges q, 2q, 4q, 8q, ..... are placed along x-axis at r, 2r, 4r, 8r, ..... from origin respectively.

The net electric field at origin is

(A) Infinite (B) 20

q4 r (C) 2

0

q2 r (D) 2

0

q8 r

PHYSICS


6. Four point charges q, q, Q and 2Q are placed in order at the corners A, B, C and D of a square.

If the field at the midpoint of CD is zero then the value of Qq

is

(A) 1 (B) 25

(C) 5

22(D)

255

7. Two point charges q and 2q are placed at (a, 0) and (0, a). A point charge q1 is placed at a pointP on the quarter circle of radius a as shown in the diagram so that the electric field at the originbecomes zero:

(A) the point P is

3a2,

3a

(B) q1 = – 5q s

(C) the point P is

5a2,

5a

(D) both (B) and (C)

8. An equilateral triangle wire frame of side L having 3 point charges at its vertices is kept in x-yplane as shown. Component of electric field due to the configuration in z direction at (0, 0, L)is [origin is centroid of triangle]

(A) 2L8kq39

(B) zero

(C) 2L8kq9

(D) None

9. Six charges q,q,q, – q, –q and –q are to be arranged on the vertices of a regular hexagon PQRSTUsuch that the electric field at centre is four times the field produced when only charge ‘q’ isplaced at vertex R. The sequence of the charges from P to U is(A) q, –q, q, q, –q, –q(B) q, q, q, –q, –q, –q(C) –q, q, q, –q, –q, q(D) –q, q, q, q, –q, –q

10. Two point like charges Q1 and Q2 of whose strength are equal in absolute value are placed at acertain distance from each other. Assuming the field strength to be positive in the positive directionof x-axis, the signs of the charges Q1 and Q2 for the graphs (field strength versus distance)shown in Fig.

(A) (Q1 positive; Q2 negative); (both positive); (Q1 negative; Q2 positive); (both negative)(B) (Q1 negative; Q2 positive); (Q1 positive; Q2 negative); (both positive); (both negative)(C) (Q1 positive; Q2 negative; (both negative); (Q1 negative; Q2 positive); (both positive)(D) (both positive; (Q1 positive, Q2 negative); (Q1 negative, Q2 positive); (both negative)

PHYSICS


11. Four equal positive charges are fixed at the vertices of a square of side L. Z-axis is perpendicularto the plane of the square. The point z = 0 is the point where the diagonals of the square intersecteach other. The plot of electric field due to the four charges, as one moves on the z-axis.

(A) (B) (C) (D)

12. A wire is bent in the form of a regular hexagon of side a and a total charge Q is distributeduniformly over it. One side of the hexagon is removed. The electric field due to the remainingsides at the centre of the hexagon is

(A) 20

Q12 3 a (B) 2

0

Q16 3 a (C) 2

0

Q8 3 a (D) 2

0

Q12 3 a

13. The direction () of E at point P due to uniformly charged finite rod will be

(A) at angle 300 from x-axis(B) 450 from x - axis(C) 600 from x-axis(D) none of these

14. The charge per unit length of the four quadrant of the ring is 2 , – 2 , and – respectively..The electric field at the centre is

(A) – iR2 0

(B) j

R2 0

(C) iR4

2

0

(D) – 0

i4 R

15. In x-y plane a circular wire AB, of radius R is uniformly charged with linear charge density(0) which is constant, is shown in the figure. Centre of the arc conside with the origin. Theelectric field intensity at the origin is :

(A) ji3R2

K 0 (B) ji

R2K3 0

(C) j3iR2

K 0 (D) ki3

R2K 0

16. The ratio of the magnitude of electric field at O due to inner (r1 to r2) and outer (r3 to r4) partof the disc :

(A) )r/r(n)r/r(n

43

12

(B) )r/r(n)r/r(n

43

21

(C) )r/r(n)r/r(n

34

21

(D) )r/r(n)r/r(n

31

42

PHYSICS


17. The electric field at the centre of a hemispherical surface having uniform surface chargedensity is

(A) 0

σε (B)

0

σ2ε (C)

0

σ4ε (D)

0

σ8ε

18. The maximum electric field at a point on the axis a uniformly charged ring is E0. At how manypoints on the axis will the magnitude of electric field be E0/2(A) 1 (B) 2 (C) 3 (D) 4

19. The column I gives the two point charge system separated by 2a and the column II gives thevariation of magnitude of electric field intensity along x-axis.Match the situation in Column Iwith the results in Column II

Column – Column –

(A) + +(0, 0) a

q q

(a, 0)(-a, 0)xx' (p) Increases as x increases

in the interval 0 x < a

(B) + –(0, 0) a

q -q

(a, 0)(-a, 0)xx' (q) Decreases as x increases

in the interval 0 x < a

(C)

++

(0, 0)

q

q

(0,+a)

(0,–a)

x

y

(r) Zero at x = 0

(D)

–

+

(0, 0)

–q

q

(0,+a)

(0,–a)

x

y

(s) Decreases as x increasesin the interval a < x <

ANSWER KEY1. B 2. A 3. C 4. C 5. C 6. D7. C 8. B 9. D 10. A 11. D 12. A13. A 14. A 15. A 16. B 17. C 18. D19. (A) (p, r, s), (B) (p, s), (C) (r, s), (D) (q, s)



Trigonometry – III 1. Express each of the following products into sums or difference of sines and cosines. (i) 2 cos 3 sin 2 (ii) 2 sin 5 cos 3 (iii) cos 9 cos 4 (iv) sin 75 cos 15

2. Prove that )140(sin21115cos25sin

3. Prove that : (i) 16380sin60sin40sin20sin

(ii) 8180cos40cos20cos (iii) 380tan60tan40tan20tan

4. Prove that : (i) 16370cos50cos30cos10cos

(ii) tan 20 tan 30 cos40 cos80 = 1

5. Prove that : (i)

3cos3

cos3

coscos4

(ii) 2

5sin5sin2

9cos3cos2

cos2cos xxxxxx

6. show that: 0)(cos)(sin)(cos)(sin)(cos)(sin DCBADBACDACB



9. If ,3

1sin,2


cot2

tan

10. Express each of the following as product of sines and cosines (i) cos 9 + cos 3 (ii) sin 2 + cos 4 (iii) cos 12 – cos 4 (iv) sin 9 + sin 5 11. Prove that (i) 20cos265cos65sin (ii) 17cos77cos47sin 12. Prove that

(i) xxxxx cot

5sin7sin5cos7cos

(ii)

xx

xxxx

10cos2sin

3sin17sin5cos9cos

(iii) xxxxx 2tan

3coscos3sinsin

(iv) )3sin5(sincot)3sin5(sin4cot xxxxxx

(v) xxx

xx sin2cossin

3sinsin22


13. Prove that

(i) cos10 sin10 tan 35cos10 sin10

(ii) 020cos40cos80cos

(iii) 80sin70sin50sin40sin20sin10sin

(iv) 0140cos100cos20cos

14. Prove that

(i) 05

7cos5

6cos5

2cos5

cos

(ii) 1cos sin

12 12 2

(iii) 9

sin39

4cos185sin

(iv) xxx sin24

3cos4

3cos

(v) xxx cos24

cos4

cos

15. Prove that

(i) cos + cos + cos + cos( + + ) = 2

cos2

cos2

cos4

16. (i) 2

tancoscossinsin yx

yxyx

(ii)

2tan

coscossinsin yx

yxyx

(iii)

2cot

2tan

coscossinsin yxyx

yxyx

17. Prove that

(i) sin 3x + sin 2x – sin x = 4 sin x cos 2x cos

23x

(ii) xxxxxxx 4sin2coscos47sin5sin3sinsin

(iii) 3tan

5cos3coscos5sin3sinsin (iv) cos 4 cos3 cos 2 cot 3

sin 4 sin 3 sin 2

(v) sin 2sin 3 sin 5 sin 3sin 3 2sin 5 sin 7 sin 5

(vi) 3tan2sin2cos

5cos3cos2cos7cos5cos23cos

(vii)

tancos5cos

sin3sin25sin


18. If cosec A + sec A = cosec B + sec B, Prove that tan A tan B = 2

cot BA

19. Prove that

(i) (cos – cos )2 + (sin – sin )2 = 4 sin2

2

(ii) sin + sin + sin – sin ( + + ) = 4 sin

2sin

2sin

2

20. If ,0)cos()cos(

)cos()cos(

DCDC

BABA prove that 1tantantantan DCBA

21. If ,4

BA show that .2)1(cot)1(cot BA

22. If 0.cot 7cot that show,8

23. If x tantan and ,cotcot y prove that xy

yx )cot(

24. If ,tan2tan show that .3)sin()sin(

25. If ,cossinandsincos nBAmBA prove that. .2)sin(2 22 nmBA

26. If ,33

2tan3

tantan

xxx then prove that 1tan31

tantan32

3

x

xx

27. If a right angle be divided in to three parts , and , prove that cot cot cot cot cot cot 28. If sin sin – cos cos = 1, show that tan + tan = 0.



tan ( +2) and tan (2 + ).

30. If m tan ( – 30) = n tan ( + 120). Show that )(2

2cosnm

nm

31. If sin 2A = sin 2B, prove that 11

)tan()tan(

BABA

32. If cos ( + ) sin ( + ) = cos ( – ) sin ( – ), prove that cot cot cot = cot 33. If y sin = x sin (2 + ) show that (x + y) cot ( + ) = (y – x) cot

34. If + and ,tantan

yx

prove that .sin)sin(

yxyx

35. If and are the solutions of the equation a cos + b sin = C. then show that

(i) 22

22

)cos(baba

(ii) 22

222 )(2)cos(ba

bac


36. Find the maximum and minimum values of the following expressions: (i) a cos – b sin (ii) 7 cos + 24 sin 37. Show that

(i) AAAAA

2cotcot3cot

1tan3tan

1

(ii) AAAAA

4cotcot3cot

1tan3tan

1

38. Prove that

(i) xxxx 8sin4sin6cos2cos 22 (ii)

22

22

sincossinsin)tan()tan(

39 Prove that (i) 0)sin()sin()sin()sin()sin()sin( ACACCBCBBABA (ii) .0})12tan{(})12{(tan nn

40. If ,12

1tan,1

tan

mm

m prove that .4

ANSWERS

1. (i) sin 5 – sin (ii) sin 8 – sin 2 (iii) )5cos13(cos21

10. (i) 2 cos 6 cos 3 (ii)

3

4cos

4cos2 (iii) – 2sin 8 sin 4

(iv) 2 sin 7 cos 2 36. (i) maximum = ,22 ba minimum = – 22 ba (ii) maximum = 25, minimum = – 25




Only one option is correct 1. Which defect causes decrease in the density of crystal 1. Frenkel 2. Schottky 3. Interstitial 4. F-centre

2. In a solid lattice the cation has left a lattice site and is located at an interstitial position, the lattice defect is

1. Interstitial defect 2. Valency defect 3. Frenkel defect 4. Schottky defect 3. The correct statement regarding F–centre is 1. Electron are held in the voids of crystals 2. F–centre produces colour to the crystals 3. Conductivity of the crystal increases due to F– centre 4. All of these 4. Schottky defect in crystals is observed when 1. Density of crystal is increased 2. Unequal number of cations and anions are missing from the lattice 3. An ion leaves its normal site and occupies an interstitial site 4. Equal number of cations and anions are missing from the lattice 5. Point defects are present in 1. Ionic solids 2. Molecular solids 3. Amorphous solids 4. Liquids 6. Schottky defect is found in 1. NaCl 2. KCl 3. 2MgCl 4. TlCl

7. If a electron is present in place of anion in a crystal lattice, then it is called 1. Frenkel defect 2. Schottky defect

3. Interstitial defect 4. F–centre 8. Which one of the following has Frenkel defect 1. Sodium chloride 2. Graphite 3. Silver bromide 4. Diamond

9. Absence of one cation and one anion in crystal lattice is 1. Schottky defect 2. Frenkel defect

3. Crystal defect 4. Ionic defect 10. Frenkel defect is caused due to 1. An ion missing from the normal lattice site creating a vacancy 2. An extra positive ion occupying an interstitial position in the lattice 3. An extra negative ion occupying an interstitial position in the lattice 4. The shift of a positive ion from its normal lattice site to an interstitial site

11. The flame colours of metal ions are due to 1. Frenkel defect 2. Schottky defect 3. Metal deficiency defect 4. Metal excess defect 12. Frenkel and Schottky defects are 1. Nucleus defects 2. Non-crystal defects 3. Crystal defects 4. None of these


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13. Which one of the following crystals does not exhibit Frenkel defect 1. AgBr 2. AgCl 3. KBr 4. ZnS 14. Schottky defect defines imperfection in the lattice structure of a 1. Solid 2. Liquid 3. Gas 4. Plasma 15. A binary salt AB (formula weight = 6.023 Y amu, where Y is an arbitrary number) has

rock salt structure with 1:1 ratio of A to B. The shortest A-B distance in the unit cell is Y1/3nm. Given that the measured density of the salt is 20 kg m–3, specify the type of point defect present in the crystal. 1. Frenkel defect 2. Schottky defect

3. Metal deficiency defect 4. Metal excess defect 16. Assertion (A). : In any ionic solid (MX) with Schottky defects, the number of positive

and negative ions are same. Reason (R) : Equal number of cation and anion vacancies are present

1. Both A and R are true and the R is a correct explanation of the A 2. Both A and R are true but the R is not a correct explanation of the A 3. A is true but the R is false

4. Both A and R are false 17. Which one of the following metal oxide is antiferromagnetic in nature 1. 2MnO 2. 2TiO 3. 2VO 4. 2CrO 18. The lustre of a metal is due to 1. Its high density

2. Its high polishing 3. Its chemical inertness

4. Presence of free electrons 19. Which one of the following is the most correct statement 1. Brass is an interstitial alloy, while steel is a substitutional alloy 2. Brass is a substitutional alloy, while steel is an interstitial alloy 3. Brass and steel are both substitutional alloys 4. Brass and steel are both interstitial alloys 20. Oxide of a transition metal is heated. Some of its oxygen (O2) is escaped. What is not

true about the kind of defect created in the solid ? 1. defect is of cation excess type 2. defect is of anion excess type 3. F-centers are created 4. solid acquires characteristic colour

21. What type of crystal defect is indicated in the diagram below ? Na+ Cl– Na+ Cl– Na+ Cl– Cl– ◌ Cl– Na+ ◌ Na+ Na+ Cl– ◌ Cl– Na+ Cl–

Cl– Na+ Cl– Na+ ◌ Na+ 1. Frenkel defect 2. Schottky defect 3. Interstitial defect 4. Frenkel and Schottky defect


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22. Schottky defect is observed in the crystal of, 1. NaCl 2. TiCl 3. AgCl 4. MgCl2 23. Which one of the following is correct ? 1. Schottky defect lowers the density 2. Frenkel defect increases the dielectric constant of the crystals 3. Stoichiometric defects make the crystals good electrical conductors 4. All the three 24. Frenkel defect is generally observed in, 1. AgBr 2. AgI 3. ZnS 4. All of these 25. Which of the following statements for crystals having Schottky defect is not correct? 1. Schottky defect arises due to the absence of a cation or anion from the position which it is expected to occupy 2. Schottky defect are more common in ionic compounds with high co-ordination numbers

3. The density of the crystals having Schottky defect is larger than that of the perfect crystal

4. The crystal having Schottky defect is electrical neutral as a whole 26. Which of the following statements for crystals having Frenkel defect is not correct?

1. Frenkel defects are observed where the difference in sizes of cations and anions is large

2. The density of crystals having Frenkel defect is lesser than that of a pure perfect crystal 3. In an ionic crystal having Frenkel defect may also contain Schottky defect 4. Usually alkali halides do not have Frenkel defect 27. When anion leaves the normal lattice site and electron occupies interstitial sites in its

crystal lattice, it is called 1. Schottky defect 2. Frenkel defect 3. Metal excess defect 4. Stoichiometric defect 28. NaCl shows Schottky defects and AgCl Frenkel defects. Their electrical conductivity is

due to the 1. motion of ions and not the motion of electrons 2. motion of electrons and not the motion of ions 3. lower coordination number of NaCl 4. higher coordination number of AgCl 29. Select the incorrect statement 1. Stoichiometric of crystal remains unaffected due to Schottky defect

2. Frenkel defect usually shown by ionic compounds having low coordination number

3. F-centers generation is responsible factor for imparting the colour to the crystal 4. Density of crystal always increases due to substitution impurity defect

30. If an element (at. wt. = 50) crystallizes in fcc lattice, with a = 0.50 nm. What is the density of unit cell if it contains 0.25% schottky defects (use NA = 6 × 1023)

1. 3.66g/cc 2. 2.66 g/cc 3. 1.66 g/cc 4. 1.26 g/cc


Page-4

ANSWER-DPP-5

Q.No. 1 2 3 4 5 6 7 8 9 10 Ans 2 3 4 4 1 1 4 3 1 4

Q.No. 11 12 13 14 15 16 17 18 19 20 Ans 4 3 3 1 4 1 1 4 2 2

Q.No. 21 22 23 24 25 26 27 28 29 30 Ans 2 1 4 4 3 2 3 1 4 2

PHYSICS



DPP-06 : Motion of charge particle in electric fieldONLY ONE OPTION IS CORRECT.

Take approx. 2 minutes for answering each question.1. An inclined plane making an angle of 37° with horizontal is placed in a uniform horizontal

electric field E of 100 V/m. A particle of mass 2 kg and charge 0.1 C, is allowed to slide down

from rest from a height of 1.2 m. If the co-efficient of friction 1

11 , find the time taken by the

particle to reach the bottom. (g = 10 m/s2)(A) 2 s

(B)35

s

(C)53

s

(D) 3s2. A point charge – q is revolving in a circle of radius ' r ' around a fixed infinite line charge with

positive charge per unit length. Now the point charge is shifted and it revolves in a circle ofradius ' 2 r '. Then:(A) work done by all forces is zero (B) work done by electrical force is zero(C) work done by external force is zero (D) work done by all forces cannot be zero

3. An electric field ‘E’ whose direction is radially outward varies as distance from origin ‘r’ asshown in the graph. E is taken as positive if its direction is away from the origin. Then the workdone by electric field on a 2 C charge if it is taken from (1, 1, 0) to (3, 0, 0) is :

(A) 20 (3 – 2 ) J

(B) – 60 J

(C) 60 J

(D) 20 ( 2 – 3) J

4. A light weight particle of charge Q is fixed at one end of an electrically insulated uniformelastic rod of natural length L, cross-sectional area A and Young's modulus Y. The rod isplaced in space having uniform electric field of magnitude E and directed parallel to lengthof the rod as shown. Neglecting gravity, the magnitude of extension in this rod is

(A) YA

QEL (B) YA2

QEL

(C) YA4

QEL (D) zero

370

E

PHYSICS


5. A charged particle having some mass is resting in equilibrium at a height H above the centre ofa uniformly charged non-conducting horizontal ring of radius R. The force of gravity actsdownwards. The equilibrium of the particle will be stable

(A) H (B) H > 2R

(C) if H < 2R

(D) H = 2

R

6. Two positively charged particles of charges q1 and q2 have mass m each. A uniform electric fieldhaving magnitude E exists in positive x direction as shown in figure. The given two chargedparticles are released from rest at t = 0 as shown in figure. If position of q1 at t = 2 sec. is givenby coordinate (+2a, 0) then the x-coordinate of q2 at t = 2 sec is (neglect gravitational interactionbetween the particles) -

(A) a2Em

qq 21 (B) aE

mqq 21

E

q , m2 q , m1

(–a, 0) (+a, 0)(C) a2Em

qq2 21

(D) aE

mqq2 21

7. A particle of mass m and charge Q is placed in an electric field E which varies with time t asE = E0 sint. It will undergo simple harmonic motion of amplitude

(A) 2

20

mQE

(B) 20

mQE

(C) 20

mQE

(D) m

QE0

8. A wheel having mass m has charges +q and –q on diametrically opposite points. It remains inequilibrium on a rough inclined plane in the presence of uniform vertical electric field E =

(A) qmg

(B) q2mg

(C) q2tanmg

(D) none

9. Find the force experienced by the semicircular rod charged with a charge q, placed as shown infigure. Radius of the wire is R and the line of charge with linear charge density is passingthrough its centre and perpendicular to the plane of wire.

(A) R2q

02

(B) Rq

02

(C) R4q

02

(D) R4q

0

10. Two long thin line charges having linear charge density (charge per unit length) . The separationbetween the conductors is d, with both line charges lying perpendicular to each other. The forceof electrostatic interaction between them can be given by :

(A) 0

2

2

(B) 0

2

2d

(C) d2 0

2

(D) 0

22

2d

PHYSICS


ONE OR MORE THAN ONE OPTION MAY BE CORRECTTake approx. 3 minutes for answering each question.11. A particle of charge 1C & mass 1 gm moving with a velocity of 4 m/s is subjected to a uniform

electric field of magnitude 300 V/m for 10 sec. Then it's final speed cannot be:(A) 0.5 m/s (B) 4 m/s (C) 3 m/s (D) 6 m/s

12. A charged cork of mass m suspended by a light string is placed in uniform electric filed ofstrength E = )ji( × 105 NC–1 as shown in the fig. If in equilibrium position tension in the

string is )31(mg2 then angle ‘’ with the vertical is

(A) 60°(B) 30°(C) 45°(D) 18°

13. A particle of mass m and charge q is fastened to one end of a string of length l.The other endof the string is fixed to the point O. The whole system lies on a frictionless horizontal plane.Initially, the mass is at rest at A. A uniform electric field in the direction shown is thenswitched on. Then

(A) speed of the particle when it reaches B is mqE2 l

(B) speed of the particle when it reaches B is mqEl

(C) tension in the string when particles reaches at B is qE

(D) tension in the string when the particle reaches at B is 2qE

14. A uniform electric field of strength E exists in a region. An electron (charge –e, mass m)

enters a point A with velocity V j . It moves through the electric field & exits at point B.Then:

(A) i2ed

2amv2E .

B

V

(2a,d)

A(a,0)

V

(0,0)

y

x(B) Velocity at B is jvi

dav2

.

(C) Rate of work by the electric field at A is zero .

(D) Rate of work done by the electric field at B is 3

32

dvam4 .

15. The figures below depict two situations in which two infinitely long static line charges of con-stant positive line charge density are kept parallel to each other. In their resulting electricfield, point charges q and -q are kept in equilibrium between them.The point charges are con-fined to move in the x direction only. If they are given a small displacement aobut their equi-librium positions, then the correct statement (s) is (are)

PHYSICS


(A) Both charges execute simple harmonic motion.(B) Both charges will continue moving in the direction of their displacement.(C) Charge +q eqecutes simple harmonic motion while charge –q continues moving in the direction of its displacement.(D) Charge –q executes simple harmonic motion while charge +q continues moving in thedirection of its displacement.Paragraph (Q.16 to Q.18)Electrostatic force on a charged particle is given by F qE

. If q is positive F E and if q

negative F E . In the figure mA = mB = 1kg. Block A is neutral while qB = –1C. Sizes of AA

and B are negligible. B is released from rest at a distance 1.8 m from A. Initially spring is neithercompressed nor elongated.

A B

K=18N/m

smooth x=0

E=10NC

x=1.8m x-axis

16. If collision between A and B is perfectly inelastic, what is velocity of combined mass just aftercollision ?(A) 6 m/s (B) 3 m/s (C) 9 m/s (D) 12 m/s

17. Equilibrium position of the combined mass is at x = ........m.

(A) 29

(B) 13

(C) 59

(D) 79

18. The amplitude of oscillation of the combined mass will be :–

(A) 2m

3(B) 124

m3

(C) 72m

9(D) 106

m9

Integer type questions (Q.19 to Q.22)

19. A simple pendulum is suspended in a lift which is going up with an acceleration of 5 m/s2 . An electric field of magnitude 5 N/C and directed vertically upward is also present inthe lift . The charge of the bob is 1 C and mass is 1 mg . Taking 2g and length ofthe simple pendulum 1m, find the time period of the simple pendulum (in sec).

PHYSICS


20. Find the magnitude of uniform electric field E in N/C (direction shown in figure) if anelectron entering with velocity 100m/s making 30° comes out making 60° (see figure), after

a time numerically equal to em

of electron.

21. A square loop of side ‘’ having uniform linear charge density ‘‘ is placed in ‘xy’ plane as

shown in the figure. There is a non uniform electric field )x(aE

i where a is a constant.

Find the resultant electric force in µN on the loop if = 10 cm, a = 2 N/C and charge density = 2µC/m.

A D

CB

y

x

22. Figure shows a metal ball of mass 50 kg and radius

2 m is placed on an insulating uncharged

stand. In space an upward electric field 5 × 105 N/C is switched on. A stream of light ions isincident on the ball from left side at a speed 2 × 106 m/s as shown in figure. If charge on ballat t = 0 was zero, find the time in seconds at which ball will be lifted from the stand. Thecharge density of ion beam is 5 × 10–12 coul/m3. Assume that all charge incident on the ballis absorbed.

ANSWER KEY1. A 2. A 3. A 4. B 5. B 6. C

7. B 8. B 9. B 10. A 11. A 12. AB

13. BD 14. ABD 15. C 16. B 17. C 18. D

19. 2 20. 100 21. 4 22. 25

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