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FIITJEE PET – XVI (REG_1ST YEAR) MAINS_SET–A

DATE: 09.12.2017 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-XVI (1ST

YEAR)-2019-MPC-2

31. Two equal and unlike parallel forces each of magnitude 5 N act on a wheel of diameter 20 cm, as shown in the figure. Find the couple acting on the wheel.

(A) 10 Nm (B) 1.0 Nm (C) 0.5 Nm (D) 2 Nm

5F N

5F N 32. A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53° with it.

The other end rests on a rough horizontal floor. The normal force that floor exerts on the ladder is (A) 55 (B) 65 N (C) 98 N (D) none of these 33. A flywheel gains a speed of 540 rpm in 6 sec. Its angular acceleration will be

(A) 3 rad/sec2 (B) 18 rad/sec

2 (C) 54 rad/sec

2 (D) 9 rad/sec

2

34. A point mass is whirled in a circular path with a constant angular velocity and its angular momentum

is L. If the string is now halved keeping the angular velocity same, the angular momentum is: (A) L/4 (B) L (C) 2L (D) L/2 35. A uniform solid cylinder of mass M and radius R rolls down without slipping an inclined plane of height

h. The angular velocity of the cylinder when it reaches the bottom of the plane will be

(A)2

ghR

(B)2 gh

R 2 (C)

2 gh

R 3 (D)

1gh

2R

36. Suppose a body of mass M and radius R is allowed to roll on an inclined plane without slipping from its topmost point A. The velocity acquired by the body, as it reaches the bottom of the inclined plane, is given by:

(A) 2gh (B) 2gh (C)2gh

(D)

2gh

where β= 1 + 2

I

MR (I is the moment of inertia of the body about its axis of rotation).

37. A solid sphere and a solid cylinder of same mass are rolled down on two Inclined planes of heights h1

and h2 respectively. If at the bottom of the plane the two objects have same linear velocities, then the ratio of h1 : h2 is:

(A) 2 : 3 (B) 7 : 5 (C) 14 : 15 (D) 15 : 14 38. A solid cylinder of mass m = 4 kg and radius R = 10cm has two

ropes wrapped around it, one near each end. The cylinder is held horizontally by fixing the two free ends of the cords to the hooks on the ceiling such that both the cords are exactly vertical. The cylinder is released to fall under gravity. Find the linear acceleration of the cylinder.

(A) g

3 (B)

2g

3 (C)

4g

3 (D) none of these

39. Particle of mass m is projected with a velocity v0 making an angle of 45

0 with horizontal. The

magnitude of angular momentum of the projectile about the point of projection at its maximum height is

(A) Zero (B) g2mv3 (C) g24mv20

(D) 32ghm

40. A string is wrapped several times round a solid cylinder and then the end of the string is held

stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

(A) 3

mgand

3

2g (B)

2

mgandg (C)

23

mgand

g (D)

32

mgand

g



PET-XVI (1ST

YEAR)-2019-MPC-3

41. A circular ring of mass M and radius R is rotating about its axis with constant angular velocity . Two objects each of mass m get attached to the rotating ring. The ring now rotates with an angular velocity

(A) mM

M

2

(B)

2mM

m

(C)

2mM

2m)M

(D)

m

2mM

42 A rod of mass m and length fits into a hollow tube of same

length and mass. The tube is rotated with an initial angular

velocity 0 and the rod slips through the rough hollow surface. The angular velocity of the rod as it slips out of the tube is

A

B

0

(A) 2

0 (B)

4

0 (C)

16

0 (D)

7

0

43 A uniform rod of length and mass M is suspended on two

vertical inextensible strings as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.

(A) mg

2 (B) mg (C)

mg

4 (D)

mg

8

44 A uniform circular disc of radius r is placed on a rough horizontal surface

and given a linear velocity v0 and angular velocity 0 as shown. The disc comes to rest after moving some distance to the right. It follows that

v0

0

P

(A) 3 v0 = 20 r (B) 2 v0 = 0 r (C) v0 = 0 r (D) 2 v0 = 3 0 r

45. A disc is freely rotating with an angular speed on a smooth horizontal plane. It is hooked at a rigid peg P & rotates about P without bouncing. Its angular speed after the impact will be equal to.

P

(A) (B)3

(C)

2

(D) none of these

46. The moment of inertia of a uniform cylinder of length and radius R about its perpendicular bisector

is I. What is the ratio /R such that the moment of inertia is minimum ?

(A) 3

2 (B)

3

2 (C)

3

2 (D) 1

47. A slender uniform rod of mass M and length is pivoted at one

end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is .

(A) 2g

cos3

(B) 3g

sin2

(C) 2g

sin3

(D) 3g

cos2

Z

X



PET-XVI (1ST

YEAR)-2019-MPC-4

48. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CE which are placed asymmetrically (see fig), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see fig). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to

(A) turn right (B) go straight (C) turn left and right alternately (D) turn left

O

B

A C

D

49. A particle of mass m is moving along the side of a square of

side ‘a’ with a uniform speed v in the x–y plane as shown in the figure:

Which of the following statements is false for the angular

momentum L about the origin ?

(A) R ˆL mv a k2

when the particle is moving

from C to D

(B) R ˆL mv a k2


from B to C

(C) 3mv ˆL Rk

2 when the particle is moving from D to A

(D) mv ˆL Rk

2 when the particle is moving from A to B

y

O x

R

450

a C D

a a

a

A B

v v

v

v

50. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of

inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

(A) 2MR

16 2 (B)

24MR

9 3 (C)

24MR

3 3 (D)

2MR

32 2

51. The following four gases are at the same temperature. In which gas do the molecules have the

maximum root mean square speed ? (A) Hydrogen (B) Oxygen (C) Nitrogen (D) Carbon dioxide 52. Which of the following is correct for the molecules of a gas in equilibrium temperature ? (A) All have the same speed (B) Molecules have different speed distribution of which average remain constant (C) They have a certain constant average speed (D) They do not collide with one another 53. P–T diagram is shown below then choose the corresponding V–T

diagram



PET-XVI (1ST

YEAR)-2019-MPC-5

(A) (B)

(C) (D)

54. 0E and hE respectively represent the average kinetic energy of a molecule of oxygen and hydrogen.

If the two gases are at the same temperature, which of the following statements is true

(A) 0 hE E (B)

0 hE E

(C) 0 hE E

(D) Nothing can be said about the magnitude of 0E and

hE as the information given is insufficient

55. When an ideal gas is compressed isothermally then its pressure increase because (A) It potential energy increases (B) Its kinetic energy increase and molecules move apart (C) Its number of collisions per unit area with walls of container increases (D) Molecular energy increases 56. If k is the Boltzmann constant, the average translational kinetic energy of a gas molecules at absolute

temperature T is (A) k T / 2 (B) 3 k T/4 (C) k T (D) 3 k T/2 57. The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature

the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecule at the same temperature will be

(A) v/16 (B) v/4 (C) 4v (D) 16 v 58. The average kinetic energy of hydrogen molecules at 300 K is E. At the same temperature, the

average kinetic energy of oxygen molecules will be (A) E/16 (B) E/4 (C) E (D) 4 E 59. Same volumes of hydrogen and oxygen at the same temperature and pressure are mixed together so

that the volume of the mixture is same as the initial volume of the either gas. if the initial pressure be p, then the pressure of the mixture will be

(A) 4 p (B) 2p (C) p/2 (D) p/4

60. 32m of hydrogen and 32m of oxygen are at the same temperature. If the pressure of hydrogen be p, then that of oxygen will be

(A) 2 p (B) 4p (C) 8 p (D) 1 p



PET-XVI (1ST

YEAR)-2019-MPC-6

FIITJEE PET – XVI (REG_1ST YEAR)

MAINS_SET–A_ANSWERS DATE: 09.12.2017

MATHEMATICS

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

5. D 6. B 7. D 8. B

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

13. C 14. A 15. BONUS 16. B

17. C 18. D 19. C 20. C

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

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

29. B 30. B

PHYSICS

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

35. C 36. C 37. C 38. B

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

43. C 44. B 45. B 46. B

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

51. A 52. B 53. D 54. B

55. C 56. D 57. C 58. C

59. B 60. D

CHEMISTRY

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

65. C 66. B 67. B 68. A

69. BONUS 70. D 71. D 72. C

73. B OR D 74. A 75. A 76. B

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

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

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

89. B 90. D



PET-XVI (1ST

YEAR)-2019-MPC-7

FIITJEE PET – XVI (REG_1ST YEAR) MAINS_SET–B

DATE: 09.12.2017 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-XVI (1ST

YEAR)-2019-MPC-8

1. If f(x) = x 1

x 1

, then f(ax) in term of f(x) is equal to

(A) f(x) a

1 af(x)

(B)

a 1 f(x) a 1

a 1 f(x) a 1

(C)

a 1 f(x) a 1

a 1 f(x) a 1

(D) none of these

2. Let f(x) = 1 + |x|, x < –1

[x], x –1, (where [.] denotes the greatest integer function) Then f(f(–2.3)) is equal to (A) 4 (B) 3 (C) –3 (D) none of these 3. If (where [.] denotes the greatest integer function) then the domain of the real valued function

2

1x

2

log x x 2

is

(A) 3

,2

(B)

3,2 2,

2

(C)

1,2 2,

2

(D) none of these

4. Let f(x) = 2xlog 25 and g(x) = logx5, then f(x) = g(x) holds for x belonging to

(A) R (B) (0, 1) (1, +) (C) (D) none of these 5. Which of the following is an even function? Here [.] denotes the greatest integer function and f is any function. (A) [x] – x (B) f(x) – f(–x) (C) e

3 – 2x . tan

2x (D) f(x) + f(–x)

6. Let f(x) be a function whose domain is [–5, 7]. Let g(x) = |2x + 5|. Then the domain of (fog)(x) is (A) [–5, 1] (B) [–4, 0] (C) [–6, 1] (D) none of these

7. If the function f: [1, +) [1, +) is defined by f(x) = 2x(x – 1)

, then f–1

(x) is

(A)

x x 11

2

(B) 2

11 1 4log x

2 (C) 2

11 1 4log x

2 (D) not defined

8. The function f: R R defined by f(x) = 6x + 6

|x| is

(A) one-one and onto (B) many-one and onto (C) one-one and into (D) many-one and into 9. The range of the function y = log3(5 + 4x – x

2) is

(A) (0, 2] (B) (–, 2] (C) (0, 9] (D) none of these

10. The range of the function f(x) = |x – 1| + |x – 2|, –1 x 3, is (A) [1, 3] (B) [1, 5] (C) [3, 5] (D) none of these

Space for rough work



PET-XVI (1ST

YEAR)-2019-MPC-9

11. Let f(1) = 1 and f(n) = n 1

r 1

2 f(r)

. Then m

n 1

f(n)

is equal to

(A) 3m – 1 (B) 3

m (C) 3

m – 1 (D) none of these

12. The largest set of real values of x for which f(x) = 2

1x 2 5 x

x 4

is a real function is

(A) [1, 2) (2, 5] (B) (2, 5] (C) [3, 4] (D) none of these

13. The domain of the function f(x) = 2x 1 x is

(A) 1 1

1, ,12 2

(B) [–1, 1]

(C) 1 1

, ,2 2

(D) 1

,12

14. Let f: X Y, f(x) = sin x + cos x + 2 2 is invertible, then X Y is

(A) 5

, 2,3 24 4

(B)

3, 2,3 2

4 4

(C) 3 3

, 2,3 24 4

(D)

3, 2,3 2

4 4

15. The domain of the function f(x) =

1

sinx sin x , (where {.} denotes the fractional part) is

(A) [0, ] (B) 2n 1

2

(C) (0, ) (D) none of these

16. The range of the function f defined by f(x) = 1

sin x

(where [.] and {.}, respectively, denotes the

greatest integer and the fractional part functions) is (A) I, the set of integers (B) N, the set of natural numbers (C) W, the set of whole numbers (D) {2, 3, 4, ......}

17. The domain of the function f(x) = 2

1

4x x 10x 9 is

(A) 7 40,7 40 (B) 0,7 40 (C) 7 40, (D) none of these




PET-XVI (1ST

YEAR)-2019-MPC-10

18. The function f(x) =

1sec x

x x

, where [x] denotes the greatest integer less than or equal to x, is defined

for all x

(A) R (B) R – {(–1, 1) {n | n Z}}

(C) R+ – (0, 1) (D) R

+ – {n | n N}

19. If satisfies the inequation x2 – x – 2 > 0 then a value of exists for

(A) sin–1 (B) sec

–1 (C) cos

–1 (D) none of these

20. Let f(x) = sec

–1x + tan

–1x. Then f(x) is real for

(A) x [–1, 1] (B) x R (C) x (–, –1] [1, +) (D) none of these

21. The principal value of 1 1 3sin cos sin

2

is

(A) 6

(B)

3

(C)

3

(D) none of these

22. The domain of the function f(x) = log10log10(1 + x

3) is

(A) (–1, +) (B) (0, +) (C) [0, +) (D) (–1, 0)

23. If cos–1 + cos

–1 + cos

–1 = 3, then + + is equal to

(A) –3 (B) 0 (C) 3 (D) –1

24. The domain of the function f(x) = 11 x

sec2

is

(A) (–, –3] [3, +) (B) [3, +) (C) (D) R

25. Let f(x) = 2 2x xsin cos

2 2 and g(x) = sec

2x – tan

2x. The two functions are equal over the set

(A) (B) R (C) R x | x 2n 1 ,n z2

(D) none of these

26. If 10

1

ii 1

cos x 0

, then 10

ii 1

x

is

(A) 0 (B) 10 (C) 5 (D) none of these




PET-XVI (1ST

YEAR)-2019-MPC-11

27. Let f: {x, y, z} {a, b, c} be a one-one function and only one of the conditions

(i) f(x) b, (ii) f(y) = b, (iii) f(z) a is true, then the function f is given by the set (A) {(x, a), (y, b), (z, c)} (B) {(x, a), (y, c), (z, b)} (C) {(x, b), (y, a), (z, c)} (D) {(x, c), (y, b), (z, a)} 28. The domain of the real-valued function f(x) = loge|logex| is

(A) (1, +) (B) (0, +) (C) (e, +) (D) none of these

29. Let f(x) = sin (tan–1

x). Then f 3

, (where [.] denotes the greatest integer function) is

(A) 3

2 (B) 0 (C) –1 (D) none of these

30. If f(x) = cos []x + cos [x], where [y] is the greatest integer function of y then f2

is equal to

(A) cos 3 (B) 0 (C) cos 4 (D) none of these 31. The following four gases are at the same temperature. In which gas do the molecules have the

maximum root mean square speed ? (A) Hydrogen (B) Oxygen (C) Nitrogen (D) Carbon dioxide 32. Which of the following is correct for the molecules of a gas in equilibrium temperature ? (A) All have the same speed (B) Molecules have different speed distribution of which average remain constant (C) They have a certain constant average speed (D) They do not collide with one another 33. P–T diagram is shown below then choose the corresponding V–T

diagram

(A) (B)

(C) (D)




PET-XVI (1ST

YEAR)-2019-MPC-12

34. 0E and hE respectively represent the average kinetic energy of a molecule of oxygen and hydrogen.

If the two gases are at the same temperature, which of the following statements is true

(A) 0 hE E (B)

0 hE E

(C) 0 hE E

(D) Nothing can be said about the magnitude of 0E and

hE as the information given is insufficient

35. When an ideal gas is compressed isothermally then its pressure increase because (A) It potential energy increases (B) Its kinetic energy increase and molecules move apart (C) Its number of collisions per unit area with walls of container increases (D) Molecular energy increases 36. If k is the Boltzmann constant, the average translational kinetic energy of a gas molecules at absolute

temperature T is (A) k T / 2 (B) 3 k T/4 (C) k T (D) 3 k T/2 37. The mass of an oxygen molecule is about 16 times that of a hydrogen molecule. At room temperature

the rms speed of oxygen molecules is v. The rms speed of the hydrogen molecule at the same temperature will be

(A) v/16 (B) v/4 (C) 4v (D) 16 v 38. The average kinetic energy of hydrogen molecules at 300 K is E. At the same temperature, the

average kinetic energy of oxygen molecules will be (A) E/16 (B) E/4 (C) E (D) 4 E 39. Same volumes of hydrogen and oxygen at the same temperature and pressure are mixed together so

that the volume of the mixture is same as the initial volume of the either gas. if the initial pressure be p, then the pressure of the mixture will be

(A) 4 p (B) 2p (C) p/2 (D) p/4

40. 32m of hydrogen and 32m of oxygen are at the same temperature. If the pressure of hydrogen be p, then that of oxygen will be

(A) 2 p (B) 4p (C) 8 p (D) 1 p

41. Two equal and unlike parallel forces each of magnitude 5 N act on a wheel of diameter 20 cm, as shown in the figure. Find the couple acting on the wheel.

(A) 10 Nm (B) 1.0 Nm (C) 0.5 Nm (D) 2 Nm

5F N

5F N Space for rough work



PET-XVI (1ST

YEAR)-2019-MPC-13

42. A uniform ladder of mass 10 kg leans against a smooth vertical wall making an angle of 53° with it.

The other end rests on a rough horizontal floor. The normal force that floor exerts on the ladder is (A) 55 (B) 65 N (C) 98 N (D) none of these 43. A flywheel gains a speed of 540 rpm in 6 sec. Its angular acceleration will be

(A) 3 rad/sec2 (B) 18 rad/sec

2 (C) 54 rad/sec

2 (D) 9 rad/sec

2

44. A point mass is whirled in a circular path with a constant angular velocity and its angular momentum

is L. If the string is now halved keeping the angular velocity same, the angular momentum is: (A) L/4 (B) L (C) 2L (D) L/2 45. A uniform solid cylinder of mass M and radius R rolls down without slipping an inclined plane of height

h. The angular velocity of the cylinder when it reaches the bottom of the plane will be

(A)2

ghR

(B)2 gh

R 2 (C)

2 gh

R 3 (D)

1gh

2R

46. Suppose a body of mass M and radius R is allowed to roll on an inclined plane without slipping from

its topmost point A. The velocity acquired by the body, as it reaches the bottom of the inclined plane, is given by:

(A) 2gh (B) 2gh (C)2gh

(D)

2gh

where β= 1 + 2

I

MR (I is the moment of inertia of the body about its axis of rotation).

47. A solid sphere and a solid cylinder of same mass are rolled down on two Inclined planes of heights h1

and h2 respectively. If at the bottom of the plane the two objects have same linear velocities, then the ratio of h1 : h2 is:

(A) 2 : 3 (B) 7 : 5 (C) 14 : 15 (D) 15 : 14 48. A solid cylinder of mass m = 4 kg and radius R = 10cm has two

ropes wrapped around it, one near each end. The cylinder is held horizontally by fixing the two free ends of the cords to the hooks on the ceiling such that both the cords are exactly vertical. The cylinder is released to fall under gravity. Find the linear acceleration of the cylinder.

(A) g

3 (B)

2g

3 (C)

4g

3 (D) none of these




PET-XVI (1ST

YEAR)-2019-MPC-14

49. Particle of mass m is projected with a velocity v0 making an angle of 450 with horizontal. The

magnitude of angular momentum of the projectile about the point of projection at its maximum height is

(A) Zero (B) g2mv3 (C) g24mv20

(D) 32ghm

50. A string is wrapped several times round a solid cylinder and then the end of the string is held

stationary while the cylinder is released from rest with an initial motion. The acceleration of the cylinder and tension in the string will be

(A) 3

mgand

3

2g (B)

2

mgandg (C)

23

mgand

g (D)

32

mgand

g

51. A circular ring of mass M and radius R is rotating about its axis with constant angular velocity . Two objects each of mass m get attached to the rotating ring. The ring now rotates with an angular velocity

(A) mM

M

2

(B)

m

M 2m (C)

M 2m)

M 2m (D)

m

2mM

52 A rod of mass m and length fits into a hollow tube of same

length and mass. The tube is rotated with an initial angular

velocity 0 and the rod slips through the rough hollow surface. The angular velocity of the rod as it slips out of the tube is

A

B

0

(A) 2

0 (B)

4

0 (C)

16

0 (D)

7

0

53 A uniform rod of length and mass M is suspended on two

vertical inextensible strings as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.

(A) mg

2 (B) mg (C)

mg

4 (D)

mg

8

54 A uniform circular disc of radius r is placed on a rough horizontal surface

and given a linear velocity v0 and angular velocity 0 as shown. The disc comes to rest after moving some distance to the right. It follows that

v0

0

P

(A) 3 v0 = 20 r (B) 2 v0 = 0 r (C) v0 = 0 r (D) 2 v0 = 3 0 r




PET-XVI (1ST

YEAR)-2019-MPC-15

55. A disc is freely rotating with an angular speed on a smooth horizontal plane. It is hooked at a rigid peg P & rotates about P without bouncing. Its angular speed after the impact will be equal to.

P

(A) (B)3

(C)

2

(D) none of these

56. The moment of inertia of a uniform cylinder of length and radius R about its perpendicular bisector

is I. What is the ratio /R such that the moment of inertia is minimum ?

(A) 3

2 (B)

3

2 (C)

3

2 (D) 1

57. A slender uniform rod of mass M and length is pivoted at one

end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle with the vertical is .

(A) 2g

cos3

(B) 3g

sin2

(C) 2g

sin3

(D) 3g

cos2

Z

X

58. A roller is made by joining together two cones at their

vertices O. It is kept on two rails AB and CE which are placed asymmetrically (see fig), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see fig). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to

(A) turn right (B) go straight (C) turn left and right alternately (D) turn left

O

B

A C

D




PET-XVI (1ST

YEAR)-2019-MPC-16

59. A particle of mass m is moving along the side of a square of

side ‘a’ with a uniform speed v in the x–y plane as shown in the figure:

Which of the following statements is false for the angular

momentum L about the origin ?

(A) R ˆL mv a k2


from C to D

(B) R ˆL mv a k2


from B to C

(C) 3mv ˆL Rk

2 when the particle is moving from D to A

(D) mv ˆL Rk

2 when the particle is moving from A to B

y

O x

R

450

a C D

a a

a

A B

v v

v

v

60. From a solid sphere of mass M and radius R a cube of maximum possible volume is cut. Moment of

inertia of cube about an axis passing through its centre and perpendicular to one of its faces is

(A) 2MR

16 2 (B)

24MR

9 3 (C)

24MR

3 3 (D)

2MR

32 2

61. +R power of the given groups

(1) (2) - NH2 (3) - OH (4) - NHCOCH3 (A) 1 > 2 > 3 > 4 (B) 4 > 3 > 2 > 1 (C) 1 > 3 > 2 > 4 (D) 1 > 4 > 3 > 2 62. Consider the given compounds

1) CH CH NH23 2 2) CH CH CN NH23

3) CH CH Cl NH23 4) 2C H NH C H5 2 5

Arrange basicity of these compounds in decreasing order in gaseous phase: (A) 4 > 1 > 2 > 3 (B) 4 > 1 > 3 > 2 (C) 1 > 4 > 2 > 3 (D) 2 > 1 > 4 > 3




PET-XVI (1ST

YEAR)-2019-MPC-17

63. Among the following which is most stabilized cation :

(A)

(B)

(C)

(D)

64. Which of the following acids has highest Ka value ?

(A)

(B)

(C)

(D)

65. Which is the order of decreasing acidic character of the following compounds?

3 2CH CH CH CH COOH

Cl Cl

(I)

Cl Cl

3 2CH CH CH CH COOH (II)

3 2 2CH C CH CH COOH

Cl

Cl

(III) Cl

Cl

3 2 2CH CH CH C COOH

(IV)

3 2 2CH CH C CH COOH

Cl

Cl

(V)

(A) IV V III I II (B) IV I V II III

(C) I II III V IV (D) III V IV II I 66. Maximum – I effect is exerted by the group

(A)

3N H

(B) 6 5C H (C) –NO2 (D) –OCH3




PET-XVI (1ST

YEAR)-2019-MPC-18

67. The stability of following carbocations in the order

2 3 3 3 23 2

I IVIIIII

Ph CH , CH C , CH C H, CH C H

(A) I > II > III > IV (B) II > I > III > IV (C) III > II > I > IV (D) IV > I > II > III 68. The correct stability order for the following species is

O ,

(I)

,

(II)

O ,

(III)

,

(IV)

(A) II > IV > I > III (B) I > II > III > IV (C) II > I > IV > III (D) I > III > II > IV 69. Identify the correct order of stability

CH2

NO2

CH2

NO2

CH2

NO2

CH2

:

(P) (Q)(R) (S)

(A) Q > R > P > S (B) S > R > Q > P (C) S > R > P > Q (D) R > P > Q > S 70. Which one among the following is the least basic ?

(A) CH3NH2 (B) 3NH (C) CH3CH2NH2 (D) 3 2 2CH CH NO NH

71. –CN(I) –COOH (II) –F(III) Among these groups, which of the following orders is correct for the magnitude of their– I effect ? (A) I > II > III (B) III > I > II (C) II > I > III (D) III > II > I 72. –I(I), –OH(II), –Cl(III) Among these groups, which of the following orders is correct, for the magnitude of their –I effect ? (A) I > III > II (B) III > II > I (C) III > I > II (D) II > III > I 73. –OPh(I), –OCH3(II), –OH(III) Among these groups, which of the following orders is correct for their –I effect ? (A) I > II > III (B) II > III > I (C) II > I > III (D) III > I > II




PET-XVI (1ST

YEAR)-2019-MPC-19

74. Which of the following groups has +M effect ?

(A) –OCO–CH3 (B) –NH2 (C)

3N H

(D) (a) and (b)

75.

OCH3

OCH3

NH CH3

IIIIII

Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > II > III (B) I > III > II (C) III > I > II (D) II > I > III 76.

O

O

N

CH3

I II III Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > III > II (B) III > I > II (C) II > I > III (D) II > III > I 77. –OH(I), –F(II), –Cl (III) Which of the following orders is correct for the magnitude of +M effect among these groups ? (A) I > III > II (B) I > II > III (C) III > II > I (D) II > III > I 78.

NO2

NO2

OCH3

IIIIII

Which of the following orders is correct about the magnitude of –M effect among these groups ? (A) I > II > III (B) II > I > III (C) II > I > III (D) III > II > I 79. (I) CH2–O–CH=O (II) CH3–O–C(NH2)=O (III) CH3–O–C(OEt)=O In which of these cases, +M effect of –OCH3 group is operating most effectively ? (A) I (B) II (C) III (D) None of these




PET-XVI (1ST

YEAR)-2019-MPC-20

80. Which of the following statements about conformers is correct ? (A) Conformers exist in a state of dynamic equilibrium (B) At equilibrium, population of more stable conformers will be more than that of less stable

conformer (C) Conformers cannot be separated (D) all of these 81. Which of the following compounds will exhibit conformational isomerism ?

(A) 3 2 3CH CH CH (B) 3 2 2 3CH CH CH CH

(C) 3 3 3CH CH CH CH (D) all of these

82. Number of which of the following isomers is always infinite ? (A) Geometrical isomers (B) Optical isomers (C) Conformational isomers (D) Structural isomers 83.

H H

HHH

H

Translating this eclipsed Newman projection formula of ethane into sawhorse projection appears as

(A) H

HH

H

HH

(B) H

HH

H

H

H (C) Both a and b (D) None of these




PET-XVI (1ST

YEAR)-2019-MPC-21

84.

CH3

Br

H

CH3

Br

H

Translating this staggered new man projection formula of 2, 3–dibromobutane into staggered

sawhorse projection appears as

(A) CH3

BrH

CH3

Br H

(B) CH3

HBr

CH3

Br H

(C)

CH3

BrH

CH3

H Br

(D) All of these

85.

CH3

H Br

Br H

CH3 Translating this Fischer projection formula into eclipsed sawhorse projection appears as

(A) CH3

BrH

H

Br

CH3

(B) CH3

BrH

Br

H

CH3 (C) Both (a) and (b) (D) None of these




PET-XVI (1ST

YEAR)-2019-MPC-22

86. Which two fischer formulas represent a pair of enantiomers ?

HO

CH3

H

H Cl

C2H5

H

CH3

Cl

HO H

C2H5

Cl

C2H5

H

HO H

CH3

HO

CH3

H

Cl H

C2H5 (A) I & II (B) III & IV (C) I & IV (D) II & III 87. Indicate the correct relation ship In the following three pairs respectively

F

Br

H

H

CH3

H

and CH2Br

H

CH3

F(I)

Cl

H

CH3

C2H5

H

Cl

and H

Cl

H3C

H

Cl

C2H5

(II)

CH3

H Br

CH3 H

Br

and

CH3

Br Br

H CH3

Br

(III)

(A) Enantiomeric pair, Diastereomeric pair, Enantiomeric pair (B) Identical, Enantiomeric pair, enantiomeric pair (C) Enantiomeric pair, Diastereomers pair, Identical (D) Enantiomeric pair, Identical, Identical




PET-XVI (1ST

YEAR)-2019-MPC-23

88. Which of the following pairs of structures does not represent resonating structures ?

(A) CH3–CO–CH3 and CH3–C(OH)=CH2 (B) O and O

(C) CH3 C

O H

CH3CH3 C

OH

CH3and

(D) 2CH C O and

2C H C O

89. Arrange the stability of the given carbocations in decreasing order

CH2

NHCOCH3

(I)

CH2

OH

(II)

CH2

NH2

(III)

CH2

Cl

(IV)

(A) III > II > IV > I (B) III > II > I > IV (C) IV > I > II > III (D) II > III > I > IV 90. Which of the following effects of –NO2 group operates on–NH2 group in this

molecule? (A) Only –I effect (B) Only –M effect (C) both–I and –M effect (D) Only +M effect

NH2

NO2




PET-XVI (1ST

YEAR)-2019-MPC-24

FIITJEE PET – XVI (REG_1ST YEAR)

MAINS_SET–B_ANSWERS DATE: 09.12.2017

MATHEMATICS

1. C 2. B 3. Bonus 4. B

5. D 6. C 7. B 8. D

9. B 10. B 11. C 12. B

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

17. D 18. B 19. B 20. C

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

25. BONUS 26. B 27. C 28. D

29. B 30. C

PHYSICS

31. A 32. B 33. D 34. B

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

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

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

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

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

55. B 56. B 57. B 58. D

59. A OR C 60. B

CHEMISTRY

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

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

69. B 70. D 71. A 72. C

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

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

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

85. A 86. B 87. BONUS 88. A

89. B 90. C

fiitjee internal test - fiitjeehyderabad.com (champion 19) (mains...fiitjee limited. 22–97, plot...

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