MOCK PRACTICE PAPER FOR - JEE -Advance- 2020

Faridabad (Delhi NCR)-FIITJEE Ltd., Sector-15A Market, Near Vidya Mandir Public School, Ajrounda Chowk, Faridabad Ph-0129-4174582

Website: www.fiitjee.com

Time: 3 hours Maximum marks: 225

INSTRUCTIONS

Caution: Question Paper CODE as given above MUST be correctly marked in the answer OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.

2. This question paper contains Three Parts.

3. Part-1 is Mathematics, Part-2 is Chemistry and Part-3 is Physics.

4. Rough spaces are provided for rough work inside the question paper. No additional sheets will be provided for rough

work.

5. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed.

B. Filling of OMR Sheet 1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on OMR sheet. 2. On the OMR sheet, darken the appropriate bubble with HB pencil for each character of your Enrolment No. and write

in ink your Name, Test Centre and other details at the designated places.

3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Sections. (i) Section-A (01 – 5) contains 5 multiple choice questions which have only one correct

answer. Each question carries +3 marks for correct answer and -1 for incorrect answer.

(ii) Section-A (06 – 10) contains 5 multiple choice questions which have one or more than one correct

answers. Each question carries +4 marks for correct answer and -2 for incorrect answer. (iii) Section-C (01 – 10) contains 10 questions. The answer to each question is a single –digit integer, ranging from 0 to

9 (both inclusive). Each question you will be awarded +4 marks for correct answer and No negative marking in this

section.

Name of the Candidate :_____________________________________________________________

Batch :____________________ Date of Examination :____________________________________

Enrolment Number :________________________________________________________________

FIITJEE FARIDABAD

JEE -Advance- 2020

MOCK PRACTICE PAPER FOR

MOCK PRACTICE PAPER-19

MATHAMETICS

SECTION – I (SINGLE CORRECT ANSWER TYPE)

3 4 2008

1! 2! 3! 2! 3! 4! 2006! 2007! 2008!

in equal to

A) 1 12 2006! B)

1 12 2010! C)

12006! 2008!

D)1 1

2007! 2008!

2. General solution of the equation

cos 2sin sin 1 sin 2cos cos 04 4x xx x x x

is

A) 4 1 ,n n z B) 4 1 2 ,n n z

C) 2 1 2 ,n n z D) 2 1 ,n n z

3. In ,ABC E is the mid point of AB and D is a point on the side BC such that : 2 :1BD DC

the line AD and CE intersect in Q. Then ratio AQ: QD is

A) 2:1 B) 2:3 C) 3:1 D) 3:2

4. A pair of dice is rolled together till the sum of the faces is either 5 or 7. The probability that 5

comes before 7 is

A) 15

B) 25

C) 35

D)45

5. If 1 tan1 1 tan 2 1 tan 3 1 tan 45 2n then n is equal to

A) 22 B) 23 C) 21 D) 24

FIITJEE FARIDABAD

This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE option can be correct.

1. The sum

SECTION – II (MULTIPLE CORRECT ANSWER TYPE)

This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer,

6. If

2

4 3 2 4 3 24 2

1 1 1

1 1

x dxx x

x x x x x xx x

1sec f x c and f(1) = 2 0x then which of the following is / are true

A) Maximum value of 2f x B) minimum value of 2f x

C) 3 132 6

f

D) f f e

7. If 2 ( 1) ( ) ( ) ( 1)f x f f x f f x f x and (1) 1f then

A) (1), (3), (5),.....f f f are is A.P

B) (1), (4), (16), (64),.....f f f f are is G.P

C) 1 2013

10

2013r

f r dx

D) 1 2013

10

20131007r

r f rdx

8. A straight line through the vertex P of a triangle PQR intersect the side QR at the point S and

the circle of the triangle PQR at the point T. If S is not the centre of the circum-circle,then

A) 1 1 2PS PT QS SR

B) 1 1 2PS ST QS SR

C) 1 1 4

PS ST QR D)

1 1 4PS ST QR

FIITJEE FARIDABAD

out of which ONE OR MORE than ONE option can be correct.

9. If

2 2

2 2 3 2

2 2 3 2 4 2 2 4

3 3 3 2( ) 3 3 2 3 6

3 2 3 6 3 12 2

x x af x x x a x a x

x a x a x x a x a

then ( a is a fixed non – zero

real number) A) 1( ) 0f x B) ( )y f x is a straight line parallel to x-axis

C) 2

4

0

( ) 32f x dx a

D) 1

6

0

4f x dx a

10. If 1 1 21( ) cos cos 3 3 ,2 2xf x x x

then

A) 23 3

f

B) 12 22cos3 3 3

f

C) 13 3

f

D) 11 12cos3 3 3

f

SECTION - III (INTEGER ANSWER TYPE)

2 2

14 1x y

and the circle 2 2 3x y then

2m is equal to

FIITJEE FARIDABAD

This section contains 10 questions. The answer is a single digit integer ranging from 0 to 9 (both inclusive).

1. The no.of solutions of the equation sin x sin 2x sin3x sin 4x 4 in the interval [0,10]

is _______

2. If Z is a complex number satisfying Z 3 2i 2, then the minimum value of 2Z 6 5i is

3. If m is the slope of common tangent of the ellipse

circle is pq

then p q

2sec cos tan cotdxIf

x ecx x x

2 cos

cos24x

x x da b c

Then a b c is

, then the value of the expression 2 22 4 , is

21 3

x c xy c e c e is ------

2 251 19 represents the sum of K consecutive odd integer then the value of 8k

20

1 2x

p xlt

x

Then the value of 2P

FIITJEE FARIDABAD

4. In a triangle ABC, a:b:c=4:5:6. The ratio of the radius of the circum circle to that of the in

5.

6. If the equation x2 2x 2 1 0and x2 2x 2 1 0 have a common root

7. The order of the differential equation obtained by eliminating arbitrary constants from

8.

9. Let P x be a polynomial of degree 4 having extremum at x 1,2 and

10. The shortest distance between z-axis and the line x y 2z 3 0, 2x 3y 4z 4 0 is


1 1 1, ,A Ea KA B

2 2 2, ,A Ea KA C

If 51

2

A eA

and 1 22 30Ea Ea kcal/mol, then the temperature at which equimolar amounts of

products will form, is

A) 3750K B) 1500K C) 3000K D) 750K

2H in presence of

Lindlar’s catalyst?

A) B) C) D)

HCN (Q) 4LiAlH (R) 2NaNO HCl

O

(S)

Relationship between (P) & (S).

A) Identical compound B) Homologues compound

C) Position isomers D) Chain isomers

61.0 10spK

A) 21.0 10 B) 31.0 10 C) 21.26 10 D) 36.3 10

FIITJEE FARIDABAD

CHEMISTRY


1. A substance ‘A’ undergoes two parallel first order reactions as

2. Which of the following produce chiral molecule after treatment with

3. (P)

4. What is the molarity of F ions in a saturated solution of BaF2 ?

A) Using KCN solution 2Cu and 2Cd ion cannot be distinguished

B) 2 2SO Cl on hydrolysis produces two molecules of HCl and Caro’s acid.

C) The oxidation state of boron in sodium perborate is +2.

D) No indicator is required in the estimation of 4KMnO using standard oxalic acid solution

SECTION – II

(MULTIPLE CORRECT ANSWER TYPE) This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer, out of which ONE OR MORE than ONE option can be correct.

62 10 . Which of the following

is/are correct regarding this acid?

log 2 0.3

A) 2A H O ;HA OH 95 10eqK

B) The equilibrium constant for the reaction of HA with a very strong base in water is

82 10

C) The pH of 0.1M-HA solution is 3.35

D) The pH of 0.1M-NaA solution is 9.35

A) 4AuCl (B) 24CuCl (C) 2

3 4Cu NH

(D) 2

Co dmg

FIITJEE FARIDABAD

5. Which of the following statement is correct.

6. For weak monobasic acid, HA, the dissociation constant is

7. Which of following complex is/are square planar as well as paramagnetic.

2CH OH3CH

OH

and are functional isomers

B)

C)

Me CH CH CH Me

ClClCl

has four optically active stereoisomers

D)

Me

Me

3CH3CH

H

His meso compound

do not have geometrical isomers

2 sH O 2 lH O equilibrium mixture at its melting point

273K. Select correct statement(s), assuming temperature remain constant:

A) Reaction will move in forward direction

B) Equilibrium will remain unaffected

C) Reaction will move in backward direction

D) Ice melts completely.

FIITJEE FARIDABAD

8. Select correct statement: A)

9. A non volatile solute is added to

1 24 2 3

HKMnO HCN CO NO Mn . This 2CO when passed through slaked lime gives

10g of white ppt. A) Volume of 4KMnO needed for titration is 40ml. B) Volume of 4KMnO needed for titration is 4ml C) Normality of HCN is 1N. D) Normality of HCN is 10N.


the initial pressure at same temperature is 0.5 atm the half-life is 50 sec. the order of reaction is

x. What is the value of x

HP of 0.01M aq. solution of HA is 4. Find the value of apK of HA at 25o C .

3CrCl . 26H O , displays an osmotic pressure of 3RT. 0.5 L of

the same solution on treatment with excess of 3AgNO solution will yield (assume 1 ) x moles of

AgCl. What is the value of x

2, NaOH,

KOH, RbOH, CsOH, 2( )Ca OH , 3( )Sr OH , 2( )Ba OH .

3HNO when dissolved in water (cold or hot)

2 2 3 2 2 4 2 5, , , , ,N O NO N O NO N O N O .

2 6B H .

FIITJEE FARIDABAD

10. 100 ml of HCN requires 5M KMnO4 in acidic medium for complete titration.


1. At 300 K the half-life of a sample of a gaseous compound initially at 1 atm is 100 sec. When

2.

3. 1.0 molar solution of the complex salt,

4. Out of given hydroxide find no. of hydroxide(s) which can form salt with CO

5. No. of oxides of nitrogen which produce

6. The maximum number of atoms are lying in the same plane for

4HIO is required to break down the given molecule here ?

HHH

OHOH

CH 3OCHO

2CH OH

R C 2NH

O

2Br NaOH

or NaOBrR 2 2 3NH NaBr Na CO

OH2 4.Conc H SO

2 44 8 2

Br CCl C H Br

FIITJEE FARIDABAD

7. How many moles of

8. Number of moles of NaOH consumed in reaction:

9. How many alkenes, from following are more stable than

, , , ,

10. How many structure of final products are possible?

PHYSICS Max.Marks:80


20cm with speed of 5 /m s at an angle of 1tan 2 with principle axis as shown in fig. Choose the correct option [Consider the moment just after projection]

f=20cm

30cm

A) The magnitude of longitudinal magnification is 1 B) Image speed is 5 2 /m s C) Image velocity makes an angle 30with principal axis

cross-section A & B as shown. A' v ' and B' v ' represents average speed of electrons at two cross-

sections

ee

A B

A) A Bi i B) A Bv v C) A Bi i D) A Bv v

FIITJEE FARIDABAD


1. A point object is projected from a point on the principal axis of a concave mirror of focal length

D) Relative speed of image with respect to object is 61m / s 2. In a photo electric experiment under condition of saturation current, we consider two different

aCT

where a is constant.

,CpCv

the work done by one mole of gas during heating from 0T to 0T through the same

process will be

A) 1 loga

B) 01log1

a RT

C) 0log 1a RT D) 011

RT

A B

xR4 8

205

Six resistances are connected between A & B as shown in fig. The Equivalent resistance

appliances is 1% less than that in second appliances then the power of first appliance will be

less by

A) 5% B) 4% C) 2% D) 1%

SECTION – II

(MULTIPLE CORRECT ANSWER TYPE) This section contains 5 multiple choice questions. Each question has 4 options (A), (B), (C) and (D) for its answer,

1q is placed at a distance ‘b’ from center of sphere outside the sphere as shown in fig. now

select the correct statement

FIITJEE FARIDABAD

3. The molar heat capacity C of an ideal gas in a process is given by ,

4.

between A and B of this network does not depends on the value of R if x is equal to

A) 5(0hm) B) 10(ohm) C) 15(ohm) D) 20(ohm)

5. Two electrical appliance are connected in parallel to a constant voltage supply. If current in one

out of which ONE OR MORE than ONE option can be correct.

6. A very thin Metallic spherical shell contain a charge Q over it. A point charge +q is placed

inside the shell at a point “T” separated from center by a distance “a”. Another point charge

qT

cR

q1

A) Electric field at center due to charge over outer surface of shell is zero

B) Electric field at the centre due to charge over outer surface of shell is 12

04q

b

C) Electric potential at the centre due to all charge in the space is 114

q q Q qo a R R b

D) Electric potential at the center due to all charges in space is 114

q Q qo a R b

0

A

B CS

t

AB Straight line

A) work done by all force in region OA is positive

B) Work done by all forces in the region AB is zero

C) work done by all force in the region BC is negative

D) work done by all force in region OA is negative

FIITJEE FARIDABAD

7. Displacement-time graph of a particle moving on a straight line is shown. Select the correct

Option(s).

P(m)

u A(m)

B(m)

which of the following statements are correct

A) , ,a b c

and d

must be a null vector

B) the magnitude of a c

equals the magnitude b d

C) the magnitude of a

can never be greater than the sum of magnitude of ,b c

and d

D) a c b d

Therefore

A) A particle keeps on moving away from origin for 2sect

B) the particle momentarily comes to rest at 1sect

C) the particle performs SHM

D) The given equation represent uniformly accelerated motion

FIITJEE FARIDABAD

8. Two particles A and B, of mass m each, are joined by a rigid massless rod of length l. A particle P of mass m, moving with a speed u normal to AB, strikes A and sticks to it. The centre of mass of the ‘A + B + P’ system is C.

A) The velocity of C before impact is u/3

B) The velocity of C after impact is u/3

C) The velocity of ‘A + P’ immediately after impact is u/2.

D) The velocity of B immediately after impact is zero.

9. Given a b c d 0

10. A particle moves along x-axis Its equation of motion is x 2t t 2where t is in second


duration between releasing mass m and breaking off of mass 2m is t, then average force(in Newton)

exerted by wall on mass 2m is given as mkt

x

n. Find the value of n.

2m m

2use 10

4

9 cm

O

and perpendicular to its length. The other end of rod slides without friction on a circular

conducting rail (negligible resistance). Point “O” is the center of circular rail. A resistance R

connected to the rod and rail as shown in fig. whose set up lies in horizontal plane with uniform

magnetic field B directed in to plane of ring. The rod is given angular speed 0 and released.

The total heat generate in R is 27 joule. Find value of 0 in rad/sec

FIITJEE FARIDABAD


1. Two blocks of mass m and 2m connected by a weightless spring of stiffness k rest on a smooth

horizontal plane. Block of mass m is shifted to a small distance x to the left and then released. If the

2. A point object O is kept at a distance of 9cm from thin prism of refracting angle 4 & refractive

index 3 / 2 as shown in figure. Find distance (in cm) of point image formed by this prism from O?

3. A rod of mass m 2kg and length l 3m rotates about an axis passing through one end “O”

0 rod

1S and 2S emit light of wavelength 400 nm in same phase. The

separation between the sources is 3 . Consider a line passing through 2S and perpendicular to the line

1 2S S . If the smallest distance from 2S where a minimum intensity is observed is 7k 10 m , what is the

5MeV and 3MeV respectively and from a nucleus C in the exited stats with excitation energy

10MeV. The kinetic energy of C is just after formation is 5.3MeV

p take mass of nuclear A,B

and C as 25 amu, 10amu & 34.995 amu respectively. 1amu=930MeV/C2. Find the value of p.

E

2E

C

C B+Q-Q

3Q+ 3Q-A

of 2A with its plane in X-Y plane. A uniform magnetic field B=2T is directed along y-axis. Find initial angular acceleration of frame in rad/sec2

FIITJEE FARIDABAD

4. Two coherent point sources

value of k to the nearest integer? 5. Consider a nuclear reaction A B C . Nucleus A and B are moving with kinetic energy of

6. Initially when batteries are not connected capacitor A & B are charged as shown with Q=CE. Find the ratio of final charge in capacitor A to the final charge in capacity B when cells are connected as shown.

7. A square wire frame of linear mass density 1kg / m , side length L 1m carrying current

3l m is suspended about one end is surrounded by liquid of

density 2 as shown. The rod is released from rest in horizontal position. Find the angular speed in (rad/sec) of rod. When it becomes vertical 210 /g m s

L

2

final temperature is 15 times its initial temperature. The work done by the gas is kRT. What is the value of k?

k 10 T . What is the value of k?

A

i

B

3 1 m

030

060

P

FIITJEE FARIDABAD

108. A rod of density and length

9. One mole of an ideal gas at a temperature T expands slowly according to the law P / V = constant. Its

10. A finite straight wire is carrying a current of 100 A, as shown in figure. The magnitude of magnetic field at point P which is at perpendicular distance ( 3 1) m from the wire is 6

Faridabad (Delhi NCR)-FIITJEE Ltd., Sector-15A Market, Near Vidya Mandir Public School, Ajrounda Chowk, Faridabad Ph-0129-4174582

Website: www.fiitjee.com

MATHEMATICS CHEMISTRY PHYSICS

1 B 1 B 1 D

2 B 2 C 2 C

3 C 3 B 3 B

4 B 4 C 4 D

5 B 5 D 5 D

6 BC 6 ABCD 6 BD

7 ABCD 7 BCD 7 A

8 BD 8 AD 8 ABCD

9 ABD 9 AD 9 BC

10 AD 10 AD 10 BD

1 0 1 0 1 1

2 5 2 6 2 1

3 2 3 1 3 3

4 9 4 7 4 2

5 4 5 4 5 2

6 6 6 6 6 1

7 1 7 1 7 6

8 4 8 4 8 3

9 0 9 4 9 7

10 2 10 5 10 5

ANSWER KEY

MATHEMATICS 1.

2008

1

2! 1 ! 2 !k

kk k k

2008

21

2! 2k

kk k

2008 2008

1 1

1 1! 2 2 !k k

kk k k

2008 2008

1 1

2 1 1 12 ! 1 ! 2 !k k

kk k k

Putting k=1,2,3-----------------2008

1 1 1 1 1 12! 3! 3! 4! 4! 5!

1 1 1 12008! 2009! 2009! 2010!

1 12 2010!

2. given equation can be written as 2 2sin cos cos ,sin 2 sin cos cos 04 4x xx x x x x

5sin cos 2 04x x

5sin cos 24x x

It is possible when 5sin 14x and cos 1x

5 24 2x n 2x k k z

8 2

5 5nx n z

8 2 4 125 5 5n nk k

k is an integer So 4 1n should be the multiple of 5 so 5 1n m

4 5 1 1 20 5

5 5m mk

4 1k m

2 4 1x m 4 1 2x m

3. Consider the point A as origin and let the position vector of point B as b and position vector of point C as c

cb

A

B C

Q

D

E

2b

1

1

Let Q divides AD as :1 : :1AQ QD Q divides CE as :1 : :1CQ QE

FIITJEE FARIDABAD

2 1 03 2 1

1 1

b c b c

Since b and c are non collinear vectors so compare the coff of b and c on both the sides of eq (1)

2

3 1 2 1

2 1 3

3 1 1

On solving eq (2) and eq (3) 3 & 1 So : 3:1AQ QD

4. Let A be the event that the sum is 5 and B the event that the sum is 5 or 7 A and B are respectively, their complements

1,4 , 2,3 , 3,2 , 4,1A

4 16 6 9

n AP A

n S

1,4 , 2,3 , 3,2 , 4,1 , 1,6 , 2,5 , 3,4 , 4,3 , 5,2 , 6,1B

10 5( ) 6 6 18

5 137 ( ) 1 118 1

58

n BP B

n s

the probabilityof getting neither no pr B P B

The event of getting 5 before 7 . . .P A P B P A P B P B P A

21 13 1 13 1.

9 18 9 18 9

11 18 29

13 9 5 5118

5. If 45A B

Then 1 tan 1 tan 2A B

Or 1 tan 1 tan 45 2 1A A

1 tan1 1 tan 2 1 tan 43 1 tan 44 1 tan 45 2n

From eq (1)

FIITJEE FARIDABAD

1 tan1 1 tan 44 2 1 tan 2 1 tan 43

2 1 tan1 1 tan 44 1 tan 2 1 tan 43 1 tan 22 1 tan 23n 1 tan 45

22 232 2 .2 2 2n n 23n 6. (a,b,c)

2

4 3 2 4 3 24 2

1 1 1

1 1

x dxx x

x x x x x xx x

2

2

3 23 2

1

1 1 11

x dxx

x x xx x x

2

1

2

111sec

1 1 1

x x cx

x xx x

12

1 11f x x f xx x

For max/min 1 0f x 1x

11 11 113

2 1 2 0 & 1 2 0f f fx

max 1 2f f (a) is correct min 1 2f f (b) is correct

0f is undefined c is correct 1f

1f e ee

Clearly f f e d is incorrect

7. (a,b,c,d) we have ( 1) 2 ( ) 1 ( )f x f f x f f x

( )( 1)

2 ( ) 1f f x

f xf f x

Putting 1x

( )(2)

2 (1) 11f f

ff f

11

2 1 1f

f

Putting 2x then (3) 1f

1 2 (3) ......... 1f f f (1), (3), (5),.....f f f are is A.P………………………………. (a)

FIITJEE FARIDABAD

(1), (4), (16), (64),.....f f f f are is G.P………………… (b)

1 12013

10 0

1 2 ..... 2013r

f r dx f f f dx

1

0

2013 2013dx …………………………… (c)

1 12013

10 0

1 1 1 2 2 .....2013 20131007 1007r

r f rdx f f f dx

1

0

1 1 2 3.....2013 20131007

dx ………….(d)

8. As S is not the centre of the circum-circle, PS ST and QS SR Also . .PS ST QS SR ………….(1) Since . .A M G M

1 1 1 12 .PS ST PS ST

1 1 2.PS ST QS SR

form eq (1) option b

As & . .QS SR QR A M G M

Then 1 2. .

2 2 .QS SR QRQS SR QS SR

QRQS SR

1 1 2

.PS ST QS SR

1 1 4

PS ST QR

So (b,d) are correct option

9. (a,b)

2 2

2 2 3 2

2 2 3 2 4 2 2 4

3 3 3 2( ) 3 3 2 3 6

3 2 3 6 3 12 2

x x af x x x a x a x

x a x a x x a x a

2 3 4 2 2

2 3 2 4 2 23

2 2 3 2 4 2 2 4

3 3 3 21 3 3 2 3 6

3 2 3 6 3 12 2

x x x a xx x a x x a x

xx a x a x x a x a

On applying 1 1 2R R R and 2 2 3R R R ,we get

2 2 2

2 2 2 2 43

2 2 3 2 4 2 2 4

0 2 41 2 4 6 2

3 2 3 6 3 12 2

a x a xa a x a x a

xx a x a x x a x a

FIITJEE FARIDABAD

2 2 2 2

2 2 2 2 2 44

2 2 4 2 2 4 2 2 4

0 4 41 2 8 6 2

23 2 6 12 3 12 2

a x a xa a x a x a

xx a x a x x a x a

On applying 2 2 3C C C ,we get

2 2

2 2 2 4 2 2 44

2 2 4 4 4 2 2 4

0 0 41 2 2 2 6 2

23 2 3 2 3 12 2

a xa a x a a x a

xx a x a x a x a

2 2 2 4 6 2 4 2 4 64

1 4 6 4 6 2 42

a x a x a a x x a ax

6 1( ) 4 ( ) 0f x a f x Since 1( ) 0f x ( )f x is a straight line parallel to x-axis

10. 1 1 21 3( ) cos cos 12 2

f x x x x

1 1 11cos cos cos2

x x

[according as 1 11cos cos2

or x ]= 1 1cos2

[when 1 11cos cos2

x ,which holds for 23

x ]= 1 1 12cos cos2

x

[when 1 11cos cos2

x ,which holds for 13

x ]

11. It is possible only if sin sin 2 sin3 sin 4x x x x which do not occur simultaneously.

12. 52 6 5 2 32

Z i Z i

=2 distance between Z and the point53,

2

But 3 2 2Z i (3 2 ) 2Z i Z is a point on or inside circle whose radius is 2 & the centre is (3,2)

Minimum value of 2 6 5Z i 52 52

X

Y

1X

1Y

(3,2)

53,2

13. Let m be the slope of the common tangent then 24 1m 2 23 3 4 1m m 2 2m 2m

FIITJEE FARIDABAD

14. 4 , 5 , 6a k b k c k 15 7 5 3, , ,2 2 2 2

s k s a k s b k s c k

4

2 15 7 5 32k

2

15 72k

2 1515 7 7

2 2 2k k kr

s

3

2

4.56. 84 4.15 7 / 4 7abc kR k

k

8 7 16

2 77Rr

15.

2 2

2sin cos

sin cos 1x xI dx

x x

2

2

sin cos 114 sin cos 1

x x

x x

21 sin cos 1

4x x dx

On simplifying 4a b c

16. Subtracting the two equations, we get the common root as 12

x substituting this in

any equation, we get 2 4 i.e 2

Now, 2 22 4 22 22 4 2 2 2 2 2.4 2 8 2 6

17. 2 21 3 1 3. c cx x x xy c e e c e c e c e ce There is only one arbitrary constant

18. sum of n odd consecutive integers beginning with 1 is 2n So 2

nS n 2 251 19 51 19S S So remaining terms are 20 21 22 50 51T T T T T 32 consecutive odd integer So K=32

48k

19. Let 4 3 20 1 2 3 4p x a x a x a x a x a

1 3 20 1 2 34 3 2p x a x a x a x a

Now 1 1 0p and 2 1 0p implies

0 1 2 34 3 2 0a a a a ---------(1)

0 1 2 332 12 4 0a a a a ------(2)

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2 20 0

1 2, 1x x

p x p xlt lt

x x

4 3 20 1 2 3 4

201

x

a x a x a x a x altx

For limited to be finite 3 4 0a a

4 3 2

0 1 220

1x

a x a x a xltx

20 1 20

1xlt a x a x a

2 1a Put the value of 2a 3a and 4a in eq(1) & eq(2)

0 14 3 2a a 0 132 12 4a a Solving above two equation simultaneously

0 11 14

a a So 4 3 214

p x x x x 162 8 4 04

p

20. The equation of given line is 2 3 0,2 3 4 4 0x y z x y z The equation of the plane passing through the given line is 2 3 2 3 4 4 0x y z x y z -----(1)

1 2 1 3 2 4 3 4 0x y z

If this plane parallel to the z-axis

Whose D.C are <0, 0, 1> then normal of plane perpendicular to z-axis

1 2 0 1 3 0 2 4 1 0

12

Putting this value is eq(1)

Then equation of plane passing through the given line and parallel to z-axis is

12 3 2 3 4 4 02

x y z x y z

2 0 2y

Now the shortest distance is the distance of any point on the z-axis from the plane-2 let us take (0,0,0) as a point on z-axis

shortest distance=length of ar from (0,0,0) on plane 22 21

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CHEMISTRY

21.

A

B

C

1K

2K

1

2

B KC K

B C 1 2K K

1 21 2

Ea RT Ea RTA e A e 2

1

1

2

Ea RT

Ea RTA eA e

2 11

2

Ea RT Ea RTA eA

1 25 Ea Ea RTe e

1 25 Ea EaRT

30 155

kcalRT

15 100052 T

3 1000 15002

T K

22.

2

4

H PdBaSO ]

23.

O

HCN 4LiAlH

OHCN

OH2 2CH NH

2NaNO HCl

P Q R S

O

(B) Homologues compound ] 24. 2

2 2 .BaF s Ba aq F aq

S 2S 3 24 ; 0.63 10spK S S

Molarity of 22 2 0.63 10F S 21.26 10 25. (A)

KCN

2cu

2cd

2( )Cu CN

2( )Cd CN

yellow ppt.

white ppt. (B) 22

2 2 2 4 2H OSO Cl H SO HCl (C) In sodium perborate oxidation state of boron is +3 (D) 4KMnO acts as self indicator. 26. 62 10aK 2log 0.3

(A) 12A H O 1 AH OH 95 10w

ha

KKK

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(B) HA OH 2A H O 89

1 1 2 105 10eq

h

KK

(C) pH axK

C x

62 10 0.1ax K C

44.47 10x pH =3.349=3.5 (D) pH =0.1M=NaA

2

hxK

C x

2hx K C

52.23 10x pOH = 4.65 pH = 14-4.65=9.35 27. A) Square planar & diamagnetic

B) Square planar paramagnetic

C) Square planar & paramagnetic

D) Square planar & paramagnetic

28.

2CH OH3CH

OH

( )A

Alchol & phenols are functioned group isomer of each other.

B)

C)

Me CH CH CH Me

ClClCl

2 optical Acetic = 2 Meso

Me

Me

3CH3CH

H

HNo chiral carbon so can't be meso ]

D) don’t exibit geometrical isomerism 29. 30. 10 products are formed 31. 1/2t a 1/2t partial pressure So n= 0

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32. 4HP 410H

210C aH K C

4 210 .10aK

610aK 6kaP 33. ; 3 1 1 ;iCRT i n For the salt 1 , hence n = 3 2 2 2 35

. 2Cr H O Cl Cl H O AgNO

2

2 52Cr H O Cl AgCl s

0.5 L of 1m salt = 0.5 2 1.0 mole of AgCl 34. They form salt with acidic 2CO 2 2 3 22NaOH CO Na CO H O 35. 2 2 3 3

2 4 2 3 2

2NO H O HNO HNON O H O HNO HNO

2 5 2 3

2 3 2 2 3

22 (Produce ondisproportion)

N O H O HNON O H O HNO HNO

36. Ans.(6) atom – are is same plane

B

H

H

H

H

B

H

H

All terminal H- atoms are in same plane.

37. only one linkage C C

OH OH

38.

R C NH

O

H2

OHH O R C

O

NH Br Br R C N Br

O

H

2H O OH

BrNCR

O

RNC

O

2H O2 2 3NH Na COR

2 moles of NaOH will be consumed here

SlowStep

39. More alkylated alkenes are more stable 40. Trans Alkene on anti addition gives mesoform.

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PHYSICS 41. ans: d

30 . ? 20u cm v f cm So 1 1 1 60vv u f

2vmu

Now 15 cos tan 2 1 / 1nv m s i 15 sin tan 2 2 / 2yv m s j

2 4 4 / 4x

x

IIx

o

Vm V m s j

V

2 4 / 4y

y

IIy

o

VV m s j

V

Velocity of image 2 2 4 2 /y xI I IV V V m s

Relative speed of image with respect to object 2 25 6 / 5 6i j m s 61 /m s

42. Ans: b Current at any cross –section same as number of electrons coming out of cathode =no. of

electron entering units time Also dB dAv v rift speed equal 43. Ans: b

9 logTo

To

dQ nCdT aT

1 11v

Rdv nCvdT C To Tor

1log1

dw dQ dv a RTor

44. Ans: d

If 20 8 5 10

20 4xx

then 20x

For 20x the effective resistance between A and B is independent of R 45. Ans: d 1 20.99i i given 1 1 2 2 1 1 2 2v i R and V i R i R i R , Or 2 1 2 2 1 20.99 0.99i R i R R R Power 2i R so for first appliance power will be less by

221

2 2 1 1 12 2 1 1

222 2 1

1

.99.99100

0.99.99

i R i Ri R i R

i R i R

1 .99 100 .99

.99

1%

46. Ans: b,d

E-field inside the shell sue to inner charges (induced t real) only. Total electric field due to

outer charges is zero. Let E be electric field due to charge over outer surface then

1 12 2

1 104 0 4 0

q qE Eb b

Potential inside charges at can the becomes zero

1104 0

Q q qR b

1Q q qR b R

put in --------(1)

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Then 11 .4

q Q qva R b

47. Ans: b,c From the graph, rate of change of velocity is zero in region AB and rate change of velocity is

negative in region BC

48. (Before collision)

cm(m m m)u mu

cmuu3

No external force working on system so cmu will be constant .

Initial angular momentum = mul No external torque working on system so final = (m m)u ' l

mu 2mu 'l l

uu '2

Final linear momentum = 'B B

mu mu m u mu2 2

'Bu 0

49. Ans: b,c Conceptual 50. Ans: a,b,d

22 4x t t 4 4dx tdt

2

2 4d xdt

51. As impulse exerted by wall is equal to change in momentum of the system.

mkxmVmtF cmav 3

.3.3.

kmt

xFav nkm

tx .

(given)

n = 1 52.

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O A n 1 OI 9

34 1 9

180 2

1cm 53. Ans: 3 / secwo rad

Heat generated 212

Iow

2

2 27 3 / sec6

ml wo wo rad

54.

P x

1S

2S

3

1 25S P S P2

2 2 53 x x2

2

2 2 2259 x x 5 x4

8 711 11x 40 10 2 1020 20

K 2 55. Ans: P=2 Use the equation 2 2 2

A B C CM C KA M C KB M C K excited energy 2.65CK MeV 56. Ans: 1

-Q QA

QQB

2EE

2 0A BQ QEC C

0BQEC

AQ CE BQ CE 1A

B

QQ

57. Ans: 6 MB

2I IL B

2

22 212 2

LL LI L

3 3 32 2 2

12 4 3L L L

23 6 /

2BI rad s

L

58. Ans: 3

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2

20 32 2

2

l l MlF w w 2 2

22 2 2 6l l l v l wvg v g v g

2 33

lw gg wl

59. xPV Constant, n=1 x x 1dPV PxV dV 0 dP V x PdV PV nRT dP V PdV nRdT

PdV 1 x nRdT

nRdTdw1 x

nR 15T Tw

2

w 7RT K = 7 60.

o30

o160

o o2 360 30

3 1 0

1 2B sin sin4 r

710 100 3 1B

2 23 1

6B 5 10 J K = 5

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MOCK PRACTICE PAPER FOR - JEE -Advance- 2020

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