fiitjee pet – vii (reg_1st year)

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FIITJEE PET – VII (REG_1ST YEAR) MAINS_SET–A

DATE: 17.08.2019 Time: 3 hours Maximum Marks: 360

INSTRUCTIONS:

Instructions to the Candidates 1. This Test Booklet consists of 90 questions.

Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.

2. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted.

3. Attempt all questions.

4. In case you have not darkened any bubble you will be awarded 0 mark for that question.

5. Use of calculator/logarithmic table is not permitted.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:



PET-VII (1ST

YEAR)-SET-B-2021-MPC-2

1. If A and B are square matrices of size n n such that A2 – B

2 = (A – B)(A + B), then which of the

following will be always true (A) either of A or B is a zero matrix (B) either of A or B is an identity matrix (C) A = B (D) AB = BA 2. Let A and B be two symmetric matrices of same order. Then the matrix AB – BA is (A) a symmetric matrix (B) a skew-symmetric matrix (C) a null matrix (D) the identity matrix 3. If A = [aij] is a scalar matrix, then trace of A is

(A) i j aij (B)

i aij (C)

j aij (D)

i aii

4. The minors of 1 and –1 in the matrix

1 4 2

2 1 4

3 7 6

are

(A) –22, 0 (B) 0, 9 (C) 0, –9 (D) –1, –1

5. The product of the cofactors of 3 and –2 in

1 0 2

3 1 2

4 5 6

is

(A) –190 (B) –6 (C) 1 (D) 19

6. If the matrix A =

8 6 2

6 7 4

2 4

is singular one, then is

(A) 3 (B) 4 (C) 2 (D) 5

7. If the matrix

cos sin 0

sin cos 0

0 0 1

is singular, then =

(A) (B) 2

(C)

3

(D)

4

Space for rough work



PET-VII (1ST


8. If =

1 sin 1

sin 1 sin

1 sin 1

, then lies in the interval

(A) [2, 3] (B) [3, 4] (C) [2, 4] (D) (2, 4)

9. A = 2 3

2 1

8A

–1 =

(A) 1 3

2 2

(B) 1 3

2 2

(C) 1 3

2 2

(D) 1 3

2 2

10. If A is a matrix such that 2 1

3 2

A(1 1) = 1 1

0 0

, then A =

(A) 1 1

0 1

(B) (2, 1) (C) 1 0

1 1

(D) 2

3

11. If A = 2 2

3 2

, B = 0 1

1 0

, then (B–1

A–1

)–1

=

(A) 2 2

2 3

(B) 3 2

2 2

(C) 2 21

2 310

(D) 3 21

2 210

12. If A =

1 2 2

2 1 2

2 2 1

, Adj A = xAT, then x =

(A) 0 (B) 1 (C) 2 (D) 3




PET-VII (1ST


13. The matrix having the same matrix as its inverse is

(A)

1 1 1

1 1 1

1 1 1

(B)

1 0 0

0 1 0

0 0 1

(C)

1 0 1

0 0 0

1 0 1

(D)

0 1 0

1 1 1

0 1 0

14. The inverse of

3 5 7

2 3 1

1 1 2

is

(A)

7 3 5

3 1 2

26 11 19

(B)

7 3 26

3 1 11

5 2 19

(C)

3 2 1

5 3 1

7 1 2

(D) none of these

15. The inverse of

cos sin 0

sin cos 0

0 0 1

is

(A)

cos sin 0

sin cos 0

0 0 1

(B)

cos sin 0

sin cos 0

0 0 1

(C)

cos sin 0

sin cos 0

0 0 1

(D)

cos sin 0

sin cos 0

0 0 1

16. If A =

1 0 2

2 1 0

3 2 1

, then 3A–1

=

(A)

1 4 2

2 5 4

1 2 1

(B)

1 4 2

2 5 4

1 2 1

(C)

1 4 2

2 5 4

1 2 1

(D)

1 4 2

2 5 4

1 2 1




PET-VII (1ST


17. A =

1 0 1

0 1 1

0 1 0

A2 – 2A =

(A) A–1

(B) –A–1

(C) I (D) –I

18. Let P and Q be 3 3 matrices with P Q. If P3 = Q

3 and P

2Q = Q

2P, then determinant of (P

2 + Q

2) is

equal to (A) 0 (B) –1 (C) –2 (D) 1 19. Let A be a square matrix all of whose entries are integers. Then which of the following is true

(A) If det A 1, then A–1

exists and all its entries are non-integers

(B) If det A = 1, then A–1

exists and all its entries are integers

(C) If det A = 1, then A–1

need not exist

(D) If det A = 1, then A–1

exists but all its entries are not necessarily integers

20. If A =

0 1 2

1 2 3

3 x 1

and A–1

=

1/ 2 1/ 2 1/ 2

4 3 y

5 / 2 3 / 2 1/ 2

, then

(A) x = 1, y = –1 (B) x = –1, y = 1 (C) x = 2, y = 1

2 (D) x =

1

2, y =

1

2

21. If A =

0 1 1

2 1 3

3 2 1

, then [A (adj A) A–1

] A =

(A)

3 0 0

2 0 3 0

0 0 3

(B)

6 0 0

0 6 0

0 0 6

(C)

0 1/ 6 1/ 6

1/ 3 1/ 6 1/ 2

1/ 2 1/ 3 1/ 6

(D) none of these

22. If A is non zero square matrix of order n with det (I + A) 0 and A3 = O, where I, O are unit and null

matrices of order n n respectively, then (I + A)–1

= (A) I – A + A

2 (B) I + A + A

2 (C) I + A

–1 (D) I + A




PET-VII (1ST


23. If A is an invertible matrix of order n, then the determinant of adj A is equal to (A) |A|

n (B) |A|

n + 1 (C) |A|

n – 1 (D) |A|

n + 2

24. If A is a 3 3 matrix and det A = 5, then det (adj A) = (A) 100 (B) 25 (C) 10 (D) 0 25. Which of the following statements is false (A) If |A| = 0, then |adj A| = 0

(B) adjoint of a diagonal matrix of order 3 3 is a diagonal matrix (C) product of two upper triangular matrices is an upper triangular matrix (D) adj (AB) = adj (A) adj (B) 26. If A and B are two square matrices such that B = –A

–1 BA, then (A + B)

2 =

(A) O (B) A2 + B

2 (C) A

2 + 2AB + B

2 (D) A + B

27. A square non-singular matrix satisfies A

2 – A + 2I = O, then A

–1 =

(A) I – A (B) I A

2

(C) I + A (D)

I A

2

28. A is a square matrix satisfying the equation A

2 – 4A – 5I = O. Then A

–1 =

(A) A – 4I (B) 1

3(A – 4I) (C)

1

4(A – 4I) (D)

1

5(A – 4I)

29. If A =

2 1 1

1 2 1

1 1 2

, then A–1

=

(A) A2 – 6A + 9I (B)

1

4(A

2 – 6A + 9I) (C)

1

4 (A

2 – 6A + 9I) (D) none of these

30. If A =

2 2 1

1 3 1

1 2 2

, then A–1

+ (A – 5I)(A – I)2 =

(A)

4 2 11

1 3 15

1 2 4

(B)

4 2 11

1 3 15

1 2 4

(C)

4 2 1

1 3 1

1 2 4

(D)

4 2 11

1 3 15

1 2 4




PET-VII (1ST


31. A block of mass 2 kg slides down the face of

a smooth 045 wedge of mass 9 kg as

shown in fig. The wedge is placed on a

frictionless horizontal surface. Determine the

acceleration of the wedge

(A) 22m/ s (B) 211m/ s

2 (C) 21m/ s (D) None of these

32. In the given figure direction of the acceleration of A

(A) towards right (B) towards left

(C) downward (D) upward

3m/s2

37o

B

A

33. A block of mass 10 kg is suspended through two light spring balance as shown below.

(A) Both the scales will read 5 kg (B) The upper scale will read 10 kg and the lower zero (C) Both the scales will read 10 kg (D) The readings may be anything but their sum will be 10kg




PET-VII (1ST


34. A 50 kg person stands on a 25kg platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the fig. The platform moves upward at a steady rate if the force with which the person pulls the rope is _______

(A) 500 N (B) 250 N (C) 25 N (D) 50 N

35. In the shown mass pulley system, pulley and string are massless. The one end of the string is pulled by the force F= 2mg. The acceleration of the block will be

(A) g/2 (B) 0 (C) g (D) 3 g

36. A block of mass 10 kg splits in two blocks of masses m1 and m2. Now they are connected through a massless string as shown in figure. For the maximum tension in the string, the ratio of m1 and m2 is

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

37. Blocks A and C starts from rest & moves to

the right with acceleration 2

Aa 24t m/s

and 2

ca 3m/ s . Here ‘t’ is in seconds. The

time when block B again comes to res is :

(A) 1 s (B) 3

s2

(C) 1

4s (D)

1s

2




PET-VII (1ST


38. Two blocks A and B each of mass m are placed on

a smooth horizontal surface. Two horizontal force F

and 2F are applied on blocks A and B, respectively,

as shown in fig. Block A does not slide on block B.

Then the normal reaction acting between the two

blocks is (assume no friction between the blocks)

(A) F (B) F/2

(C) F

3 (D) 3F

39. If the acceleration of block A is 5 m/s

2, then, acceleration of block B is

(A) 5 m/s2

(B) 10 m/s2

(C) zero (D) 6.67 m/s

2

40. The end A of rod OA is in touch of triangular block B. Its other end O is hinged at the point O. The speed of end A of rod at the instant shown in the figure is

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

41. For the situation shown in the figure, find the speed of

cylinder at the instant shown in figure.

(A) 21 cm/s (B) 17 cm/s

(C) 7 cm/s (D) 2 7 cm/s




PET-VII (1ST


42. A wedge of mass M is free to move on smooth horizontal surface.

Two blocks of mass m1 and m2 are free to move on smooth inclined surfaces of the wedge.

If 1 2

2 1

m sin2

m sin2

, the wedge

(A) remains stationary (B) may accelerate left ward (C) may accelerate rightward (D) None of these

43. For the given arrangement, pulleys and string are light and

smooth. All surfaces are smooth. Find the magnitude of acceleration of block A of mass M.

(A) F(1 cos )

M

(B)

Fcos

m M

(C) Fcos

m

(D) none of these

44. The figure shows the position–time (x – t) graph of one–

dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

(A) 0.4 N–s (B) 0.8 N–s (C) 1.6 N–s (D) 0.2 N–s

45. A 3–kg steel ball strikes a wall with a speed of 10.0

ms–1

at angle of 60.00 with the surface of the wall. The

ball bounces off The same speed and same angle fig.

If the ball was in contact with the wall for 0.2s, find the

average force exerted by the wall on the ball is

(A) 130 3 N (B) 150 3 N (C) 170 3 N (D) None




PET-VII (1ST


46. fig shows a light platform on which a man of mass M is

standing and holding a string passes over a system of

ideal pulley. Another mass m is hanging as shown in fig.

Also find the ratio of M/m to keep system in equilibrium

(A) 5 (B) 7 (C) 9 (D) None

47. A man is raising himself and the crate on which he stands

with an acceleration of 5 2ms by a massless rope and

pulley arrangement. Mass of the man is 100 kg and that of

the crate is 50 kg. if 2g 10ms , then the tension in the

rope is

(A) 2250 N (B) 1125 N

(C) 750 N (D) 375 N

48. Three blocks A,B, and C are suspended as

shown in fig. Mass of each of blocks A and

B is m. If the system is in equilibrium, and

mass of C is M, then

(A) M> 2m (B) M=2m

(C) M<2m (D) None of these




PET-VII (1ST


49. The pulleys and strings shown in fig are

smooth and of negligible mass. For the

system to remain equilibrium, the angle

should be

(A) 00 (B) 030

(C) 045 (D) 060

50. A string of negligible mass going over a clamped pulley of mass

m supports a block of M as shown in the fig. The force on the

pulley by the clamp is given by

(A) 2 Mg

(B) 2mg

(C) 2 2M m m g

(D) 2 2M m M g

51. A boy of mass 40 kg is hanging from the horizontal branch of a tree. The tension in his arms is

minimum when the angle between the arms is (A) 0

o (B) 90

o (C) 120

o (D) 180

o




PET-VII (1ST


52. A force vector applied on a mass is represented a k10j8i6F and accelerates with 1 m/s2.

What will be the mass of the body?

(A) 10 2 kg (B) 2 10 kg (C) 10 kg (D) 20 kg

53. A riffle bullet loses 1

20of its velocity in passing through a plank. The least number of such planks

required to just stop the bullet is (A) 5 (B) 10 (C) 11 (D) 20

54. A light string fixed at one end to a clamp on ground passes over a fixed

pulley and hangs at the other side. It makes an angle of 30o with the

ground. A monkey of mass 5 kg climbs up the rope. The clamp can tolerate a vertical force of 40 N only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take g = 10 m/s

2)

(A) 2 m/s2 (B) 4 m/s

2 (C) 6 m/s

2 (D) 8 m/s

2

a

55. In a figure a block of mass 10kg is in equilibrium. Identify the string in

which the tension is zero. (A) B (B) C (C) A (D) None of these

56. The figure represents a light inextensible string ABCDE in which AB = BC = CD

= DE and to which are attached masses M, m and M at the points B, C and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line shown in figure. It is given that

3 12tan and tan

4 5 . Then the tension in the string BC is

(A) 2mg (B) 13

mg10

(C) 3

mg10

(D) 20

mg11




PET-VII (1ST


57. Two masses m and M are attached with strings as shown. For

the system to be in equilibrium we have

(A) 2M

tan 1m

(B) 2m

tan 1M

(C) M

tan 12m

(D) m

tan 12M

58. An object is in equilibrium under four concurrent forces in the

directions shown in figure. The magnitude of 1F is

(A) 2

3N (B)

20N

3

(C) 4

N3

(D) None of these

59. A ball of mass 1 kg hangs in equilibrium form two strings OA

and OB as shown in figure. What are the tensions in strings

OA and OB? Take g = 10 ms2.

(A) 5N, 5 3 N (B) 5N, 5N

(C) 5 3N.5 3N (D) 5

N,5N3

60. In the figure a rope of mass m and length

is such that its one end is fixed to a rigid wall and the other is applied with a horizontal force F as shown below, then tension at the middle of the string is

(A) F (B) 2F (C) zero (D) F/2




PET-VII (1ST


61. Chlorine is prepared in the laboratory by treating manganese dioxide (MnO2) with aqueous hydrochloric acid according to the reaction.

4HCl(aq) + MnO2(s) 2H2O(l) + MnCl2 (aq) + Cl2(g). How many grams of HCl will react with 5g of MnO2. [ At. wt of Mn = 55] (A) 6.4g (B) 4.8g (C) 8.4g (D) 7.2 g 62. The percentage of an element M is 53 in its oxide of molecular formula M2O3. Its atomic mass is about (A) 45 (B) 9 (C) 18 (D) 27 63. A metal M of equivalent mass E forms on oxide of molecular formula MxOy. The atomic mass of the

metal is given by the correct equation (A) 2 E (y/x) (B) xy/E (C) E/y (D) y/ E 64. A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is (A) 168 (B) 192 (C) 188 (D) 182 65. 0.32g of a metal on treatment with an acid gave 112 mL of hydrogen at NTP. Calculate the equivalent

weight of the metal (A) 58 (B) 32 (C) 11.2 (D) 24 66. In an experiment, 4g of M2Ox oxide was reduced to 2.8 g of the metal. If the atomic mass of the metal

is 56g mol–1

, the number of O atoms in the oxide is (A) 1 (B) 2 (C) 3 (D) 4 67. Sucrose solution which is 40% by mass is heated till it becomes 50% by mass. Water lost form 100g

of the solution is (A) 10g (B) 15g (C) 20g (D) 25g 68. How many moles of lead (II) chloride will be formed from a reaction between 6.5g of PbO and 3.2g of

HCl ? (At mass of Pb = 207) (A) 0.044 (B) 0.333 (C) 0.011 (D) 0.029 69. 50 mL solution of BaCl2 (20.8% w/v) and 100 mL solution of H2SO4 (9.8% w/v) are mixed (Ba = 137,

Cl = 35.5 , S = 32). BaSO4 formed will be (A) 11.65g (B) 23.3g (C) 29.8g (D) 46.6g

70. IN the reaction , 4 NH3(g) + 5O2 (g) 4 NO(g) + 6 H2O(l) , when 1 mole of ammonia and 1 mole of O2 are made to react to completion

(A) 1.0 mole of H2O is produced (B) 1.0 mole of NO will be produced (C) all the oxygen will be consumed (D) all the ammonia will be consumed.




PET-VII (1ST


71. A mixture of CaCl2 and NaCl weighing 4.44g is treated with sodium carbonate solution to precipitate all the Ca

2+ ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get

0.56 g of CaO. The percentage of NaCl in the mixture (atomic mass of Ca = 40) is (A) 75 (B) 30.6 (C) 25 (D) 69.4 72. An organic compound made of C, H and N contains 20% nitrogen. Its minimum molecular weight is (A) 70 (B) 140 (C) 100 (D) 65 73. The crystalline salt Na2SO4 . x H2O on heating loses 55.9% of its weight. The formula of the crystalline

salt is (A) Na2SO4. 5H2O (B) Na2SO4. 7H2O (C) Na2SO4. 2H2O (D) Na2SO4.10H2O 74. 3.28 g of a sample of pure copper when heated in presence of oxygen for some time forms black

copper oxide (CuO) which weighs 3.92 g. What approximate percent of copper remains unoxidized ? (A) 4.6% (B) 5.6% (C) 6.6% (D) 7.6% 75. Hydroxylamine (NH2OH) reduces ferric sulphate to ferrous sulphate getting oxidized to N2O. In what

mole ratio does NH2OH and Fe2(SO4)3 react. (A) 2 : 1 (B) 1 : 2 (C) 2 : 3 (D) 1 : 1 76. Calculate the volume in mL of 0.1 M KMnO4 in acidic medium needed to oxidize one gram of FeC2O4

[At. wt. of Fe = 56 ; M = 55) (A) 41.7 mL (B) 23.6 mL (C) 20.85 mL (D) 47.2 mL 77. A solution KIO3 is boiled with excess of oxalic acid. The products are K2C2O4, CO2, H2O and I2.

Calculate the quantity of oxalic acid in grams used up in the formation of one mole of Iodine. (A) 450g (B) 540g (C) 590g (D) 420 g 78. The hydrated salt of Na2SO4.nH2O, undergoes 56% loss in weight on heating and becomes

anhydrous. The value of n will be (A) 5 (B) 3 (C) 7 (D) 10




PET-VII (1ST


79. One mole of Fe reacts completely with 0.65 moles of O2 to give a mixture of only FeO and Fe2O3. The

mole ratio of FeO and Fe2O3 is : (A) 2 : 3 (B) 4 : 3 (C) 1 : 2 (D) 2 : 7 80 In an organic compound, C and O are in the ratio 3 : 2 (by wt) and C and H are in the ratio 4 : 1. The

compound(s) may be (A) CH3COOH (B) CH3OCH3 (C) HCHO (D) CH3CHO 81. The empirical formula of an organic compound containing carbon and hydrogen is CH2. The mass of

one litre. of this organic gas is exactly equal to that of one lit of N2. There fore, the molecular formula of the compound is

(A) C2H4 (B) C3H8 (C) C6H12 (D) C4H8

82. 2 moles of 2CO is required to prepare:

(A) 336g of 3NaHCO (B) 84g of 3NaHCO

(C) 462g of 3 2Ca HCO (D) 162g of 3 2

Ca HCO

83. 11g of a sample of Zn with a purity of 87% is dissolved by V mL of hydrochloric acid with density of

1.18 g/mL containing 35% of HCl by mass. Calculate V ml. [Atomic weight of Zn = 66g]

(A) 26 mL (B) 30 mL (C) 15 mL (D) 13 mL 84. The amount of KClO3 (80% pure) needed to produce 48g O2 is ?

(KClO3 KCl + O2) (A) 122.5 (B) 24.5 (C) 98 (D) 153.12g 85. The reaction

3ClO ClO Cl is an example of

(A) oxidation (B) disproportionation (C) reduction (D) decomposition




PET-VII (1ST


86. In the reaction Zn3As2 + 6H2O 3Zn (OH)2 + 2AsH3 indicate the element which suffers a change of oxidation state

(A) Zn (B) Sb (C) Both (D) None 87. If 4.2 gm of NaHCO3 is added to 10 gms of CH3COOH solution. The weight of aqueous solution is 12

gm. The mass of CO2 released in the reaction

( 3 3 3 2 2CH COOH NaHCO CH COONa H O CO ) is

(A) 12 gm (B) 2.2 gm (C) 14.2 gm (D) 3.3 gm 88. 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 (A) 50% (B) 49% (C) 55% (D) 47%

89. The molality of 40% w

W

aqueous NaOH solution is

(A) 15.66 (B) 16.66 (C) 17.66 (D) 10 90. Equivalent weight of the double salt KCl. MgCl2. 6H2O is (If M.wt of this salt is M)

(A) M

6 (B)

M

3 (C)

M

4 (D)

M

2




PET-VII (1ST


FIITJEE PET – VII (REG_1ST YEAR)

MAINS_SET–A_ANSWERS DATE: 17.08.2019

MATHEMATICS

1. D 2. B 3. D 4. A

5. A 6. A 7. D 8. C

9. D 10. D 11. A 12. D

13. B 14. B 15. B 16. A

17. B 18. A 19. B 20. A

21. A 22. A 23. C 24. B

25. D 26. B 27. B 28. D

29. B 30. A

PHYSICS

31. C 32. C 33. C 34. B

35. D 36. A 37. C 38. D

39. D 40. B 41. C 42. A

43. A 44. B 45. B 46. B

47. B 48. C 49. C 50. D

51. A 52. A 53. C 54. C

55. D 56. B 57. A 58. C

59. A 60. A

CHEMISTRY

61. C 62. D 63. A 64. C

65. B 66. C 67. C 68. D

69. A 70. C 71. Bonus 72. A

73. D 74. A 75. D 76. Bonus

77. Bonus 78. D 79. B 80. B

81. A 82. D 83. A 84. D

85. B 86. D 87. B 88. D

89. B 90. B



PET-VII (1ST


FIITJEE PET – VII (REG_1ST YEAR) MAINS_SET–B

DATE: 17.08.2019 Time: 3 hours Maximum Marks: 360

INSTRUCTIONS:

Instructions to the Candidates 1. This Test Booklet consists of 90 questions.

Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.

2. For each correct answer 4 Marks will awarded and for each wrong answer 1 Mark will be deducted.

3. Attempt all questions.

4. In case you have not darkened any bubble you will be awarded 0 mark for that question.

5. Use of calculator/logarithmic table is not permitted.

Don’t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam.

NAME:

ENROLLMENT NO.:



PET-VII (1ST


1. If A =

1 0 2

2 1 0

3 2 1

, then 3A–1

=

(A)

1 4 2

2 5 4

1 2 1

(B)

1 4 2

2 5 4

1 2 1

(C)

1 4 2

2 5 4

1 2 1

(D)

1 4 2

2 5 4

1 2 1

2. A =

1 0 1

0 1 1

0 1 0

A2 – 2A =

(A) A–1

(B) –A–1

(C) I (D) –I

3. Let P and Q be 3 3 matrices with P Q. If P3 = Q

3 and P

2Q = Q

2P, then determinant of (P

2 + Q

2) is

equal to (A) 0 (B) –1 (C) –2 (D) 1 4. Let A be a square matrix all of whose entries are integers. Then which of the following is true

(A) If det A 1, then A–1

exists and all its entries are non-integers

(B) If det A = 1, then A–1

exists and all its entries are integers

(C) If det A = 1, then A–1

need not exist

(D) If det A = 1, then A–1

exists but all its entries are not necessarily integers

5. If A =

0 1 2

1 2 3

3 x 1

and A–1

=

1/ 2 1/ 2 1/ 2

4 3 y

5 / 2 3 / 2 1/ 2

, then

(A) x = 1, y = –1 (B) x = –1, y = 1 (C) x = 2, y = 1

2 (D) x =

1

2, y =

1

2




PET-VII (1ST


6. If A =

0 1 1

2 1 3

3 2 1

, then [A (adj A) A–1

] A =

(A)

3 0 0

2 0 3 0

0 0 3

(B)

6 0 0

0 6 0

0 0 6

(C)

0 1/ 6 1/ 6

1/ 3 1/ 6 1/ 2

1/ 2 1/ 3 1/ 6

(D) none of these

7. If A is non zero square matrix of order n with det (I + A) 0 and A3 = O, where I, O are unit and null

matrices of order n n respectively, then (I + A)–1

= (A) I – A + A

2 (B) I + A + A

2 (C) I + A

–1 (D) I + A

8. If A is an invertible matrix of order n, then the determinant of adj A is equal to (A) |A|

n (B) |A|

n + 1 (C) |A|

n – 1 (D) |A|

n + 2

9. If A is a 3 3 matrix and det A = 5, then det (adj A) = (A) 100 (B) 25 (C) 10 (D) 0 10. Which of the following statements is false (A) If |A| = 0, then |adj A| = 0

(B) adjoint of a diagonal matrix of order 3 3 is a diagonal matrix (C) product of two upper triangular matrices is an upper triangular matrix (D) adj (AB) = adj (A) adj (B) 11. If A and B are two square matrices such that B = –A

–1 BA, then (A + B)

2 =

(A) O (B) A2 + B

2 (C) A

2 + 2AB + B

2 (D) A + B

12. A square non-singular matrix satisfies A

2 – A + 2I = O, then A

–1 =

(A) I – A (B) I A

2

(C) I + A (D)

I A

2

13. A is a square matrix satisfying the equation A

2 – 4A – 5I = O. Then A

–1 =

(A) A – 4I (B) 1

3(A – 4I) (C)

1

4(A – 4I) (D)

1

5(A – 4I)




PET-VII (1ST


14. If A =

2 1 1

1 2 1

1 1 2

, then A–1

=

(A) A2 – 6A + 9I (B)

1

4(A

2 – 6A + 9I) (C)

1

4 (A

2 – 6A + 9I) (D) none of these

15. If A =

2 2 1

1 3 1

1 2 2

, then A–1

+ (A – 5I)(A – I)2 =

(A)

4 2 11

1 3 15

1 2 4

(B)

4 2 11

1 3 15

1 2 4

(C)

4 2 1

1 3 1

1 2 4

(D)

4 2 11

1 3 15

1 2 4

16. If A and B are square matrices of size n n such that A2 – B

2 = (A – B)(A + B), then which of the

following will be always true (A) either of A or B is a zero matrix (B) either of A or B is an identity matrix (C) A = B (D) AB = BA 17. Let A and B be two symmetric matrices of same order. Then the matrix AB – BA is (A) a symmetric matrix (B) a skew-symmetric matrix (C) a null matrix (D) the identity matrix 18. If A = [aij] is a scalar matrix, then trace of A is

(A) i j aij (B)

i aij (C)

j aij (D)

i aii

19. The minors of 1 and –1 in the matrix

1 4 2

2 1 4

3 7 6

are

(A) –22, 0 (B) 0, 9 (C) 0, –9 (D) –1, –1

20. The product of the cofactors of 3 and –2 in

1 0 2

3 1 2

4 5 6

is

(A) –190 (B) –6 (C) 1 (D) 19




PET-VII (1ST


21. If the matrix A =

8 6 2

6 7 4

2 4

is singular one, then is

(A) 3 (B) 4 (C) 2 (D) 5

22. If the matrix

cos sin 0

sin cos 0

0 0 1

is singular, then =

(A) (B) 2

(C)

3

(D)

4

23. If =

1 sin 1

sin 1 sin

1 sin 1

, then lies in the interval

(A) [2, 3] (B) [3, 4] (C) [2, 4] (D) (2, 4)

24. A = 2 3

2 1

8A

–1 =

(A) 1 3

2 2

(B) 1 3

2 2

(C) 1 3

2 2

(D) 1 3

2 2

25. If A is a matrix such that 2 1

3 2

A(1 1) = 1 1

0 0

, then A =

(A) 1 1

0 1

(B) (2, 1) (C) 1 0

1 1

(D) 2

3

26. If A = 2 2

3 2

, B = 0 1

1 0

, then (B–1

A–1

)–1

=

(A) 2 2

2 3

(B) 3 2

2 2

(C) 2 21

2 310

(D) 3 21

2 210




PET-VII (1ST


27. If A =

1 2 2

2 1 2

2 2 1

, Adj A = xAT, then x =

(A) 0 (B) 1 (C) 2 (D) 3 28. The matrix having the same matrix as its inverse is

(A)

1 1 1

1 1 1

1 1 1

(B)

1 0 0

0 1 0

0 0 1

(C)

1 0 1

0 0 0

1 0 1

(D)

0 1 0

1 1 1

0 1 0

29. The inverse of

3 5 7

2 3 1

1 1 2

is

(A)

7 3 5

3 1 2

26 11 19

(B)

7 3 26

3 1 11

5 2 19

(C)

3 2 1

5 3 1

7 1 2

(D) none of these

30. The inverse of

cos sin 0

sin cos 0

0 0 1

is

(A)

cos sin 0

sin cos 0

0 0 1

(B)

cos sin 0

sin cos 0

0 0 1

(C)

cos sin 0

sin cos 0

0 0 1

(D)

cos sin 0

sin cos 0

0 0 1




PET-VII (1ST


31. fig shows a light platform on which a man of mass M is

standing and holding a string passes over a system of

ideal pulley. Another mass m is hanging as shown in fig.

Also find the ratio of M/m to keep system in equilibrium

(A) 5 (B) 7 (C) 9 (D) None

32. A man is raising himself and the crate on which he stands

with an acceleration of 5 2ms by a massless rope and

pulley arrangement. Mass of the man is 100 kg and that of

the crate is 50 kg. if 2g 10ms , then the tension in the

rope is

(A) 2250 N (B) 1125 N

(C) 750 N (D) 375 N

33. Three blocks A,B, and C are suspended as

shown in fig. Mass of each of blocks A and

B is m. If the system is in equilibrium, and

mass of C is M, then

(A) M> 2m (B) M=2m

(C) M<2m (D) None of these




PET-VII (1ST


34. The pulleys and strings shown in fig are

smooth and of negligible mass. For the

system to remain equilibrium, the angle

should be

(A) 00 (B) 030

(C) 045 (D) 060

35. A string of negligible mass going over a clamped pulley of mass

m supports a block of M as shown in the fig. The force on the

pulley by the clamp is given by

(A) 2 Mg

(B) 2mg

(C) 2 2M m m g

(D) 2 2M m M g

36. A boy of mass 40 kg is hanging from the horizontal branch of a tree. The tension in his arms is

minimum when the angle between the arms is (A) 0

o (B) 90

o (C) 120

o (D) 180

o

37. A force vector applied on a mass is represented a k10j8i6F and accelerates with 1 m/s2.

What will be the mass of the body?

(A) 10 2 kg (B) 2 10 kg (C) 10 kg (D) 20 kg




PET-VII (1ST


38. A riffle bullet loses 1

20of its velocity in passing through a plank. The least number of such planks

required to just stop the bullet is (A) 5 (B) 10 (C) 11 (D) 20

39. A light string fixed at one end to a clamp on ground passes over a fixed

pulley and hangs at the other side. It makes an angle of 30o with the

ground. A monkey of mass 5 kg climbs up the rope. The clamp can tolerate a vertical force of 40 N only. The maximum acceleration in upward direction with which the monkey can climb safely is (neglect friction and take g = 10 m/s

2)

(A) 2 m/s2 (B) 4 m/s

2 (C) 6 m/s

2 (D) 8 m/s

2

a

40. In a figure a block of mass 10kg is in equilibrium. Identify the string in

which the tension is zero. (A) B (B) C (C) A (D) None of these

41. The figure represents a light inextensible string ABCDE in which AB = BC = CD

= DE and to which are attached masses M, m and M at the points B, C and D, respectively. The system hangs freely in equilibrium with ends A and E of the string fixed in the same horizontal line shown in figure. It is given that

3 12tan and tan

4 5 . Then the tension in the string BC is

(A) 2mg (B) 13

mg10

(C) 3

mg10

(D) 20

mg11

42. Two masses m and M are attached with strings as shown. For

the system to be in equilibrium we have

(A) 2M

tan 1m

(B) 2m

tan 1M

(C) M

tan 12m

(D) m

tan 12M




PET-VII (1ST


43. An object is in equilibrium under four concurrent forces in the

directions shown in figure. The magnitude of 1F is

(A) 2

3N (B)

20N

3

(C) 4

N3

(D) None of these

44. A ball of mass 1 kg hangs in equilibrium form two strings OA

and OB as shown in figure. What are the tensions in strings

OA and OB? Take g = 10 ms2.

(A) 5N, 5 3 N (B) 5N, 5N

(C) 5 3N.5 3N (D) 5

N,5N3

45. In the figure a rope of mass m and length

is such that its one end is fixed to a rigid wall and the other is applied with a horizontal force F as shown below, then tension at the middle of the string is

(A) F (B) 2F (C) zero (D) F/2 46. A block of mass 2 kg slides down the face of

a smooth 045 wedge of mass 9 kg as

shown in fig. The wedge is placed on a

frictionless horizontal surface. Determine the

acceleration of the wedge

(A) 22m/ s (B) 211m/ s

2 (C) 21m/ s (D) None of these




PET-VII (1ST


47. In the given figure direction of the acceleration of A

(A) towards right (B) towards left

(C) downward (D) upward

3m/s2

37o

B

A

48. A block of mass 10 kg is suspended through two light spring balance as shown below.

(A) Both the scales will read 5 kg (B) The upper scale will read 10 kg and the lower zero (C) Both the scales will read 10 kg (D) The readings may be anything but their sum will be 10kg

49. A 50 kg person stands on a 25kg platform. He pulls on the rope which is attached to the platform via the frictionless pulleys as shown in the fig. The platform moves upward at a steady rate if the force with which the person pulls the rope is _______

(A) 500 N (B) 250 N (C) 25 N (D) 50 N




PET-VII (1ST


50. In the shown mass pulley system, pulley and string are massless. The one end of the string is pulled by the force F= 2mg. The acceleration of the block will be

(A) g/2 (B) 0 (C) g (D) 3 g

51. A block of mass 10 kg splits in two blocks of masses m1 and m2. Now they are connected through a massless string as shown in figure. For the maximum tension in the string, the ratio of m1 and m2 is

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

52. Blocks A and C starts from rest & moves to

the right with acceleration 2

Aa 24t m/s

and 2

ca 3m/ s . Here ‘t’ is in seconds. The

time when block B again comes to res is :

(A) 1 s (B) 3

s2

(C) 1

4s (D)

1s

2

53. Two blocks A and B each of mass m are placed on

a smooth horizontal surface. Two horizontal force F

and 2F are applied on blocks A and B, respectively,

as shown in fig. Block A does not slide on block B.

Then the normal reaction acting between the two

blocks is (assume no friction between the blocks)

(A) F (B) F/2

(C) F

3 (D) 3F




PET-VII (1ST


54. If the acceleration of block A is 5 m/s

2, then, acceleration of block B is

(A) 5 m/s2

(B) 10 m/s2

(C) zero (D) 6.67 m/s

2

55. The end A of rod OA is in touch of triangular block B. Its other end O is hinged at the point O. The speed of end A of rod at the instant shown in the figure is

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

56. For the situation shown in the figure, find the speed of

cylinder at the instant shown in figure.

(A) 21 cm/s (B) 17 cm/s

(C) 7 cm/s (D) 2 7 cm/s

57. A wedge of mass M is free to move on smooth horizontal surface.

Two blocks of mass m1 and m2 are free to move on smooth inclined surfaces of the wedge.

If 1 2

2 1

m sin2

m sin2

, the wedge

(A) remains stationary (B) may accelerate left ward (C) may accelerate rightward (D) None of these

58. For the given arrangement, pulleys and string are light and

smooth. All surfaces are smooth. Find the magnitude of acceleration of block A of mass M.

(A) F(1 cos )

M

(B)

Fcos

m M

(C) Fcos

m

(D) none of these




PET-VII (1ST


59. The figure shows the position–time (x – t) graph of one–

dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is

(A) 0.4 N–s (B) 0.8 N–s (C) 1.6 N–s (D) 0.2 N–s

60. A 3–kg steel ball strikes a wall with a speed of 10.0

ms–1

at angle of 60.00 with the surface of the wall. The

ball bounces off The same speed and same angle fig.

If the ball was in contact with the wall for 0.2s, find the

average force exerted by the wall on the ball is

(A) 130 3 N (B) 150 3 N (C) 170 3 N (D) None

61. Calculate the volume in mL of 0.1 M KMnO4 in acidic medium needed to oxidize one gram of FeC2O4 [At. wt. of Fe = 56 ; M = 55)

(A) 41.7 mL (B) 23.6 mL (C) 20.85 mL (D) 47.2 mL 62. A solution KIO3 is boiled with excess of oxalic acid. The products are K2C2O4, CO2, H2O and I2.

Calculate the quantity of oxalic acid in grams used up in the formation of one mole of Iodine. (A) 450g (B) 540g (C) 590g (D) 420 g 63. The hydrated salt of Na2SO4.nH2O, undergoes 56% loss in weight on heating and becomes

anhydrous. The value of n will be (A) 5 (B) 3 (C) 7 (D) 10 64. One mole of Fe reacts completely with 0.65 moles of O2 to give a mixture of only FeO and Fe2O3. The

mole ratio of FeO and Fe2O3 is : (A) 2 : 3 (B) 4 : 3 (C) 1 : 2 (D) 2 : 7




PET-VII (1ST


65 In an organic compound, C and O are in the ratio 3 : 2 (by wt) and C and H are in the ratio 4 : 1. The compound(s) may be

(A) CH3COOH (B) CH3OCH3 (C) HCHO (D) CH3CHO 66. The empirical formula of an organic compound containing carbon and hydrogen is CH2. The mass of

one litre. of this organic gas is exactly equal to that of one lit of N2. There fore, the molecular formula of the compound is

(A) C2H4 (B) C3H8 (C) C6H12 (D) C4H8

67. 2 moles of 2CO is required to prepare:

(A) 336g of 3NaHCO (B) 84g of 3NaHCO

(C) 462g of 3 2Ca HCO (D) 162g of 3 2

Ca HCO

68. 11g of a sample of Zn with a purity of 87% is dissolved by V mL of hydrochloric acid with density of

1.18 g/mL containing 35% of HCl by mass. Calculate V ml. [Atomic weight of Zn = 66g]

(A) 26 mL (B) 30 mL (C) 15 mL (D) 13 mL 69. The amount of KClO3 (80% pure) needed to produce 48g O2 is ?

(KClO3 KCl + O2) (A) 122.5 (B) 24.5 (C) 98 (D) 153.12g 70. The reaction

3ClO ClO Cl is an example of

(A) oxidation (B) disproportionation (C) reduction (D) decomposition

71. In the reaction Zn3As2 + 6H2O 3Zn (OH)2 + 2AsH3 indicate the element which suffers a change of oxidation state

(A) Zn (B) Sb (C) Both (D) None




PET-VII (1ST


72. If 4.2 gm of NaHCO3 is added to 10 gms of CH3COOH solution. The weight of aqueous solution is 12 gm. The mass of CO2 released in the reaction

( 3 3 3 2 2CH COOH NaHCO CH COONa H O CO ) is

(A) 12 gm (B) 2.2 gm (C) 14.2 gm (D) 3.3 gm 73. 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 (A) 50% (B) 49% (C) 55% (D) 47%

74. The molality of 40% w

W

aqueous NaOH solution is

(A) 15.66 (B) 16.66 (C) 17.66 (D) 10 75. Equivalent weight of the double salt KCl. MgCl2. 6H2O is (If M.wt of this salt is M)

(A) M

6 (B)

M

3 (C)

M

4 (D)

M

2

76. Chlorine is prepared in the laboratory by treating manganese dioxide (MnO2) with aqueous

hydrochloric acid according to the reaction.

4HCl(aq) + MnO2(s) 2H2O(l) + MnCl2 (aq) + Cl2(g). How many grams of HCl will react with 5g of MnO2. [ At. wt of Mn = 55] (A) 6.4g (B) 4.8g (C) 8.4g (D) 7.2 g 77. The percentage of an element M is 53 in its oxide of molecular formula M2O3. Its atomic mass is about (A) 45 (B) 9 (C) 18 (D) 27 78. A metal M of equivalent mass E forms on oxide of molecular formula MxOy. The atomic mass of the

metal is given by the correct equation (A) 2 E (y/x) (B) xy/E (C) E/y (D) y/ E




PET-VII (1ST


79. A bivalent metal has an equivalent mass of 32. The molecular mass of the metal nitrate is (A) 168 (B) 192 (C) 188 (D) 182 80. 0.32g of a metal on treatment with an acid gave 112 mL of hydrogen at NTP. Calculate the equivalent

weight of the metal (A) 58 (B) 32 (C) 11.2 (D) 24 81. In an experiment, 4g of M2Ox oxide was reduced to 2.8 g of the metal. If the atomic mass of the metal

is 56g mol–1

, the number of O atoms in the oxide is (A) 1 (B) 2 (C) 3 (D) 4 82. Sucrose solution which is 40% by mass is heated till it becomes 50% by mass. Water lost form 100g

of the solution is (A) 10g (B) 15g (C) 20g (D) 25g 83. How many moles of lead (II) chloride will be formed from a reaction between 6.5g of PbO and 3.2g of

HCl ? (At mass of Pb = 207) (A) 0.044 (B) 0.333 (C) 0.011 (D) 0.029 84. 50 mL solution of BaCl2 (20.8% w/v) and 100 mL solution of H2SO4 (9.8% w/v) are mixed (Ba = 137,

Cl = 35.5 , S = 32). BaSO4 formed will be (A) 11.65g (B) 23.3g (C) 29.8g (D) 46.6g

85. IN the reaction , 4 NH3(g) + 5O2 (g) 4 NO(g) + 6 H2O(l) , when 1 mole of ammonia and 1 mole of O2 are made to react to completion

(A) 1.0 mole of H2O is produced (B) 1.0 mole of NO will be produced (C) all the oxygen will be consumed (D) all the ammonia will be consumed.




PET-VII (1ST


86. A mixture of CaCl2 and NaCl weighing 4.44g is treated with sodium carbonate solution to precipitate all the Ca

2+ ions as calcium carbonate. The calcium carbonate so obtained is heated strongly to get

0.56 g of CaO. The percentage of NaCl in the mixture (atomic mass of Ca = 40) is (A) 75 (B) 30.6 (C) 25 (D) 69.4 87. An organic compound made of C, H and N contains 20% nitrogen. Its minimum molecular weight is (A) 70 (B) 140 (C) 100 (D) 65 88. The crystalline salt Na2SO4 . x H2O on heating loses 55.9% of its weight. The formula of the crystalline

salt is (A) Na2SO4. 5H2O (B) Na2SO4. 7H2O (C) Na2SO4. 2H2O (D) Na2SO4.10H2O 89. 3.28 g of a sample of pure copper when heated in presence of oxygen for some time forms black

copper oxide (CuO) which weighs 3.92 g. What approximate percent of copper remains unoxidized ? (A) 4.6% (B) 5.6% (C) 6.6% (D) 7.6% 90. Hydroxylamine (NH2OH) reduces ferric sulphate to ferrous sulphate getting oxidized to N2O. In what

mole ratio does NH2OH and Fe2(SO4)3 react. (A) 2 : 1 (B) 1 : 2 (C) 2 : 3 (D) 1 : 1




PET-VII (1ST


FIITJEE PET – VII (REG_1ST YEAR) MAINS_SET–B_ANSWERS

DATE: 17.08.2019

MATHEMATICS

1. A 2. B 3. A 4. B

5. A 6. A 7. A 8. C

9. B 10. D 11. B 12. B

13. D 14. B 15. A 16. D

17. B 18. D 19. A 20. A

21. A 22. D 23. C 24. D

25. D 26. A 27. D 28. B

29. B 30. B

PHYSICS

31. B 32. B 33. C 34. C

35. D 36. A 37. A 38. C

39. C 40. D 41. B 42. A

43. C 44. A 45. A 46. C

47. C 48. C 49. B 50. D

51. A 52. C 53. D 54. D

55. B 56. C 57. A 58. A

59. B 60. B

CHEMISTRY

61. Bonus 62. Bonus 63. D 64. B

65. B 66. A 67. D 68. A

69. D 70. B 71. D 72. B

73. D 74. B 75. B 76. C

77. D 78. A 79. C 80. B

81. C 82. C 83. D 84. A

85. C 86. Bonus 87. A 88. D

89. A 90. D

fiitjee pet – vii (reg_1st year)

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