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FIITJEE REVISION TEST (REG_2ND YEAR) JEEM–1_SET–A

DATE: 29.12.2017 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.:



RT-JEEM–1 (2ND

YEAR)-2018-MPC-2

1. If f(x) = 4x – 1, if x > 4;

2x 2 if 2 x 3 ’

= 3x + 4, if x < -2; then

f 3 f 5 f 0 f 1

f 2 f 1 f 5 f 3

(A) 11/3 (B) 3/11 (C) –11/3 (D) –3/11

2. If f be a function defined as 1

f x xx

when 1

xn

and f(x) = 0 when 1

xn

, n N, [x]

denotes integral part of x then when 1

xn

, f(x) is

(A) 0 (B) 1 (C) n (D) 1/n

3. If 2 2f x cos x cos x where [x] is the step function, then

(A) f(0) = 1 (B) f(/4) = 2 (C) f(/2) = -1 (D) f() = 1

4. A function f : N Z defined by n 1

f n2

when n is odd and

nf n

2

when n is even, is

(A) one-one but not onto (B) onto but not one one (C) one one onto (D) neither one one nor onto

5. If x a x b

f xx

and

f x f y f z k

x y x z y z y x z x z y xyz

then k =

(A) a (B) b (C) ab (D) 3ab

6. If f: {1, 2, 3, ....} {0, 1, 2, .... } is defined by

n/ 2 if niseven

f n n 1if nisodd

2

then 1f 100 is

(A) 100 (B) 199 (C) 201 (D) 200

7. The domain of the function 1

f xx x

is

(A) (-, 0) (B) (-,) – {0} (C) (-,) (D) (0, )

8. The domain of

2

10f x log 5x x / 4 is

(A) [0, 5] (B) [1, 4] (C) [-1, 2] (D) none

Space for rough work



RT-JEEM–1 (2ND

YEAR)-2018-MPC-3

9. The range of 2

2

x x 1

x x 1

is

(A) [1/3, 3] (B) [1/3, 1] (C) [1, 3] (D) (-, 1/3] [3, )

10. If a, b, c are the sides of a triangle then the range of 2 2 2

ab bc ca

a b c

is

(A) [1, 2) (B) (1/2, 1] (C) [1/2, 2) (D) (-1/2, 2)

11. If [x] stands for the greatest integer function, then 1 1 1 2 1 999

....2 1000 2 1000 2 1000

(A) 498 (B) 499 (C) 500 (D) 501

12. The range of 2 2sec x 4cosec x is

(A) [1, 5] (B) [5, ) (C) [9, ) (D) [4, 9]

13. If n 1

F n 1 n 1

and G n n F n n N then (GoG) (n) =

(A) 1 (B) 0 (C) -1 (D) n 14. Let f be an injective function with domain {x, y, z} and range {1, 2, 3} such that exactly one of the

following statements is correct and the remaining are false. f(x) = 1, f(y) 1, f(z) 2 . The value of

f(1) is (A) x (B) y (C) z (D) none

15. The function f: C C defined by ax b

f xcx d

for x C where bd 0 reduces to a constant function

if (A) a = c (B) b = d (C) ad = bc (D) ab = cd

16. 3x 0

tanx sinxLt

x

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

17. o o

3x 0

3sinx sin3xLt

x

(A) 0 (B) 1 (C)

3

180

(D)

3

4.180




RT-JEEM–1 (2ND

YEAR)-2018-MPC-4

18. Let and be the roots of 2ax bx c 0 , then

2

2x

1 cos ax bx cLt

x

(A) 0 (B) 21

2 (C)

22a

2 (D)

22a

2

19.

1/ 2 1/ 3

2x 0

cosx cosxLt

sin x

(A) 1

6 (B)

1

12

(C)

2

3 (D)

1

3

20. The values of constants a and b so that 2

x

x 1Lt ax b 0

x 1

is

(A) a = 0, b = 0 (B) a = 1, b = -1 (C) a = -1, b = 1 (D) a = 2, b = -1

21. n

1.1! 2.2! 3.3! .... n.n!Lt

n 1 !

(A) 0 (B) (C) 1 (D) none

22. If 4x 0

cos4x acos2x bLt

x

is finite, then the values of a, b are respectively

(A) 5, -4 (B) -5, -4 (C) -4, 3 (D) 4, 5

23.

21/ xx x

2x 0

e e 2Lt

x

(A) 1/ 2e (B) 1/ 4e (C) 1/ 3e (D) 1/12e

24. The integer n for which x

nx 0

cosx 1 cosx eLt

x

is a finite nonzero number is

(A) 1 (B) 2 (C) 3 (D) 4

25. The value of

1/ x

x 0

1 x eLt

x

is

(A) 1 (B) e/2 (C) –e/2 (D) 2/e




RT-JEEM–1 (2ND

YEAR)-2018-MPC-5

26.

x2

2x

x 5x 3Lt

x x 2

(A) e4 (B) –e (C) e (D) e

2

27.

x1/ x 1/ x 1/ x

x

a b cLt

3

, where a, b, c are real and nonzero =

(A) 0 (B) (abc)1/3

(C) (abc)-1/3

(D) abc/3

28.

2 2 2 2

3n

1 x 2 x 3 x ...... n xLt

n

(A) x/2 (B) x/3 (C) x/6 (D) 0

29. If a1 = 1 and nn 1

n

4 3aa

3 2a

, n 1 and if

nnLt a a

then the value of a is

(A) 2 (B) 2 (C) 2 (D) none of these

30. If is repeated root of 2ax bx c 0 then

2

2x

sin ax bx cLt

x

(A) 0 (B) a (C) b (D) c

31. A skier travels with a constant speed of 6 m/s along a parabolic path 2x

y20

. The acceleration of the

skier when he is at (10, 5) is given as a b

c. Then (a + b – c) is equal to

(A) 1 (B) 2 (C) 3 (D) 4 32. Width of a river is 60m. A swimmer wants to cross the river

such that he reaches from A to B directly. Point B is 45m ahead of line AC(perpendicular to river) assume speed of river and speed of swimmer as equal. Swimmer must try to swim at angle

with AC. Value of is 1 ksin

25

. Then K?

(A) 6 (B) 7 (C) 8 (D) 9

B C

A

River flow




RT-JEEM–1 (2ND

YEAR)-2018-MPC-6

33. A block of mass m is gently placed over a massive plank moving horizontally over a smooth surface

with velocity 6 m/s. The co–efficient of friction between the block and plank is 0.2. The distance travelled by the block till it slide on the plank is ……….(in m) [g = 10 m/s

2]

(A) 3 m (B) 6 m (C) 9 m (D) 12 m 34. A man moving with a velocity of 5 m/s on a

horizontal road observes that raindrops fall at

an angle of 45 with the vertical. When he moves with a velocity of 16 m/s along an

inclined plane, which is inclined at 30 with the horizontal, he observes raindrops falling vertically downward as shown in the figure. the actual velocity of the raindrops is

ˆ ˆK 3 i (K 3 5)j , then K is

30

16m/s

5 m/s

45

(A) 2 (B) 4 (C) 6 (D) 8

35. A small body was launched up an inclined plane set at an angle of 45 against the horizontal. The co–

efficient of friction is N

10 if the time of ascent of the body is = 2.0 times less than the time of its

descent. (A) 6 (B) 9 (C) 12 (D) 5 36. Three blocks A, B and C of equal mass m are placed one

over other on a frictionless surface (table) as shown in the figure co–efficient of friction between any blocks A, B and

C is . The maximum value of mass of block MD. So that the block A, B and C move without slipping over each

other is Amu

(1 ) . Then A is equal to ………..

A

MD

B

C

(A) 4 (B) 3 (C) 2 (D) 1




RT-JEEM–1 (2ND

YEAR)-2018-MPC-7

37. A locomotive accelerates a train of identical railway carts. The carts are numbered consequently with

the cart next to locomotive having the number 1. The tension in the connection between the carts with number 4 and 5 is three times bigger than the tension in the connection between the carts with numbers 14 and 15. The number of last car is given as (4K + 3), then K = ?

(A) 1 (B) 4 (C) 7 (D) 11 38. The figure shows an accelerometer, a device for

measuring the horizontal acceleration of cars and aeroplanes. A ball is free to roll on a parabolic track described by the equation y = x

2, where both x

and y are meters. A scale along the bottom is used to measure the ball’s steady position x. What is the acceleration (in m/s

2) if x = 20 cm?

–0.5m 0.5m 0m

y = x2

(A) 3 (B) 1 (C) 2 (D) 4 39. A force of 20N is acting on a block of mass 2 kg on smooth inclined plane. The direction of this force

can be any of the four as shown in figures in which case normal force can be zero.

30

F

30

F

30 F

30

F

(A) (B) (C) (D) 40. Figure shows a man pulling on a string attached to a block

kept on a rough surface. Man is heaviest than block. Coefficient of friction is same for both block and man. Subscripts R, B and M denote rope block and man respectively, taking string to be light.

R B

M

Mark the incorrect statement

(A) R/B M/RF F always

(B) block begins to move earlier than man if man continues to increase his pull from zero

(C) R/B M/RF and F can be action reaction pairs

(D) block can remain static if man walks with constant speed while letting spring to pass through his hand




RT-JEEM–1 (2ND

YEAR)-2018-MPC-8

41. In figure, two block M and m are tied together with an inextensible

and light string. The mass M is placed on a rough horizontal surface

with co–efficient of friction and the mass m is hanging vertically against a smooth vertical wall. The pulley is frictionless choose the correct statements related to the tension T in the string.

M

m

Rough()

(smooth)

(A) when m < M, T = mg (B) when m < M, T = Mg

(C) when m > M, Mg < T < Mg (D) when m > M, mg < T < Mg

42. Two men of unequal masses hold on two sections of a light rope passing over a smooth light pulley. Which of the following is not possible?

(A) the lighter man is stationary while the heavier man slides with some acceleration (B) the lighter man is stationary while the lighter man climbs with some acceleration (C) the two men slide with same acceleration in the same direction (D) the two men move with accelerations of same magnitude in opposite directions

43. If M = 3 kg, m1 = 6 kg, m2 = 4 kg

system is released from rest. Then which of the following statement is correct

M1

M

s = 0.3

M2

k = 0.2

s = 0.4

k = 0.3

(A) Friction on

1M is static (B) Friction on 2M is static

(C) M remains at rest (D) All the above

44. A block of mass 2M kg is moving with velocity 0v towards a mass-less unstretched spring of

force constant 10 /K N m .The co-efficient of friction between the

ground and the block is µs = 0.2 and µK = 0.15. Find maximum value

of 010 v where v0 is the maximum velocity such that after

pressing the spring ,the block does not return back but stops there permanently?

m

v0

K

1m (A) 4 (B) 8 (C) 12 (D) None of these




RT-JEEM–1 (2ND

YEAR)-2018-MPC-9

45. A massive horizontal platform is moving horizontally with a constant

acceleration of 10 m/s2. A particle P of mass m = 1 kg is kept at rest at

the smooth surface. It is hinged at O with the help of a massless rod OP of length 0.9m. Now P is imparted a velocity opposite to direction of acceleration so that is just able to complete full circular motion about O. If the maximum tension in the rod during the motion is 10n, then value of n?

O

P L 10m/s2

(A) 3 (B) 4 (C) 5 (D) 6 46. The mass of two blocks A and C is 1 kg and 3 kg respectively. The

block B is a very long plank of mass 1 kg. There is no friction between the block B and the surface. The coefficient of friction between A and B is 0.6. The system is released from the state of rest. What would the velocity of the block B when C has fallen by 3 m.

A

B

C

(A) 6 (B) 9 (C) 12 (D) 15 47. In the figure shown all the surfaces are frictionless, and mass of

the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 m/s

2 by

applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force(between the

block and the wedge) in ground frame on the block in 3 seconds

is 50n J. Find the value of n?

10 m/s2

m

M

(A) 7 (B) 9 (C) 3 (D) 11

48. The potential energy in joule of a particle of mass 1 kg moving in the XY plane is given

by 3 4 x y , where (x, y) are the co-ordinates of the particle in metre. If the particle is at rest at

(6, 4) at time t = 0, then which of the following is incorrect? (A) The particle has constant acceleration and the co-ordinates of the particle at time t = 4 s are (–18, –28) (B) The work done by the field force from the position of rest of the particle and the instant the particle crossing X-axis is 25 joule. (C) The speed of the particle when it crosses the Y-axis is 10 ms

–1

(D) The speed of particle when it crosses y-axis in 20 ms–1

49. The value(s) of mass m for which the 100 kg block does not remain

in static equilibrium is (A) 38 kg (B) 37 kg (C) 83 kg (D) 85 kg




RT-JEEM–1 (2ND

YEAR)-2018-MPC-10

50. In the system shown in the figure m1 > m2. System is held at rest by thread

BC. Just after the thread BC is burnt (A) acceleration of m1 will be upwards

(B) magnitude of acceleration of both blocks will be equal to 1 2

1 2

m mg

m m

(C) acceleration of m1 will be equal to zero (D) magnitude of acceleration of two blocks will be non–zero unequal For Question (51–52) As in bigger pulley a variable force F is acting in upward direction. F = at (where a = 80 and t in second). Pulleys are light and smooth.

m1m2 m3

(m1 = 2kg , m2 = 4kg , m3 = 6kg)

51. Velocity of block m2 when 3m will leave contact from horizontal surface.

(A) zero (B) 2.5 m/sec (C) 5 m/sec (D) None 52. Height attain by m2 when m3 will leave contact from horizontal surface.

(A) 5

m6

(B) 15

m3

(C) zero (D) None

For Question (53–54)

Two men A and B each of mass ‘m’ sit in light cages at the ends of a flexible light rope passing over a smooth pulley as shown in the figure. Initially both are at rest. A being higher than B by h.

Suddenly a small ball of mass 10

m is handed over to B with

negligible velocity which he instantaneously throws up with velocity v, to A such that it just reaches A.




RT-JEEM–1 (2ND

YEAR)-2018-MPC-11

53. When A catches the ball, his position is shifted up by l . Where l is

(A) 19

h (B)

3

19

h (C)

2

19

h (D)

40h

361

54. As soon as A catches the ball, its instantaneous velocity will be:

(A) Zero (B) v/20 upwards (C) v/20 downwards (D) None of the above

55. A vertical spring of force constant 100 N/m is attached with a hanging

mass of 10 kg. Now an external force is applied on the mass so that the spring Is stretched by additional 2m. The work done by the force F is :( g = 10 m/s

2)

(A) 200 J (B) 400 J (C) 450 J (D) 600 J 56. System shown in figure is released from rest with the spring un-

elongated. Pulley and spring Is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block just leaves contact with ground is : (Take force constant of spring k = 40 N/m and g = 10 m/s

2)

(A) 2 m/s (B) 2 2 m/s (C) 2 m/s (D) 4 2 m/s

57. A system consists of two cubes of masses m1 and m2 respectively connected by

a spring of force constant k. The force (F) that should be applied to the upper cube for which the lower one just lifts after the force is removed is:

(A) m1g (B) 1 2

1 2

mmg

m +m (C) (m1 + m2)g (D) m2g

58. A uniform chain of length L and mass M is held on a smooth table and one-third of its length is

hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part onto the table is: (A) MgL (B) MgL/3 (C) MgL/9 (D) MgL/18




RT-JEEM–1 (2ND

YEAR)-2018-MPC-12

59. One end of a light spring of force constant k is fixed to a wall and the other end is tied to a block

placed on a smooth horizontal surface. In a displacement, the work done by the spring is 1

2 kx

2. The

possible case(s) may be : (A) the spring was Initially stretched by a distance 2x and finally was in its natural length

(B) the spring was initially in its natural length and finally it was compressed by a distance x (C) the spring was initially compressed by a distance x and finally was in its natural length (D) the spring was initially in its natural length and finally stretched by a distance x

60. A block is suspended by an ideal spring of force constant k. If the block is pulled down by applying a

constant force F and if maximum displacement of block from its initial mean position of rest is x0 then:

(A) increase in energy stored In spring is k x2

0 (B) x0 = 3

2

F

k

(C) x0 = 2F

k (D) work done by applied force F is (1/2)Fx0

61. Consider the ground state of Cr atom (Z = 24). The numbers of electrons with the azimuthal quantum

numbers, l = 1 and 2 are respectively (A) 12 and 4 (B) 12 and 5 (C) 16 and 4 (D) 16 and 5 62. In ground state, an element has 13 electrons in its’ ‘M’ shell. The element is (A) copper (B) Iron (C) Nickel (D) chromium 63. Electromagnetic radiation with maximum wavelength is (A) radiowave (B) X–ray (C) infrared (D) ultraviolet 64. The orbital diagram in which both the pauli’s exclusion principles and Hund’s rule are violated is

(A) (B)

(C) (D)

65. The maximum number of 3d electrons having S = + ½ are (A) 10 (B) 5 (C) 14 (D) 7 66. In hydrogen atom, energy of first exicited state is –3.4 eV. The kinetic energy of the same orbit of

Hydrogen atom would be (A) +3.4 eV (B) +6.8 eV (C) –13.6 eV (D) +13.6 eV 67. The ionization energy of Hydrogen atom is 13.6 eV. What will be the ionization energy of He

+ ?

(A) 13.6 eV (B) 54.4 eV (C) 122.4 eV (D) zero




RT-JEEM–1 (2ND

YEAR)-2018-MPC-13

68. What is ratio of time periods (T1/T2) is second orbit of hydrogen atom to third orbit of He+ ion ?

(A) 8/27 (B) 32/27 (C) 27/32 (D) 27/8

69. If m = magnetic quantum number, = azimuthal quantum number then :

(A) m = + 2 (B) m = 22 + 1 (C)

m 1

2

(D) = 2m + 1

70. The photo electric current decreases if (A) The frequencies of incident radiation decreases below threshold frequency (B) The exposure time is decreased (C) The intensity of the source of light is decreased (D) none of these 71. Which of the following bond is strongest ? (A) sp–sp (B) sp

2 – sp

2 (C) s– s (D) p – p

72. The type of hybridization of sulphur atom present in SO2 and SO3 is respectively : (A) sp, sp

2 (B) sp

2, sp

2 (C) sp

2, sp

3 (D) sp, sp

3

73. In the formation of ethylene molecule, the carbon atom makes use of : (A) sp

3 hybridization (B) sp

2 hybridization

(C) sp hybridization (D) none of these 74. Which one of the following has pyramidal structure ? (A) NH3 (B) SiF4 (C) H2O (D) BF3 75. Which statement is incorrect ?

(a) sigma bond is stronger than –bond

(b) sigma bond is weaker than – bond (c) A triple bond is weaker than double bond (d) A double bond is weaker than single bond (A) a, c, d (B) b, c, d (C) Only b (D) c, d 76. In which of the following molecules the bond angle is maximum ? (A) CH4 (B) H2O (C) NH3 (D) CO2

77. Hybridization state of I in 2ICl is :

(A) dsp2 (B) sp (C) sp

2 (D) sp

3

78. The hybridization of carbon atoms in C–C single bond of HCC–CH=CH2 is : (A) sp

3 – sp

3 (B) sp

2 – sp

3 (C) sp – sp

2 (D) sp

3 – sp




RT-JEEM–1 (2ND

YEAR)-2018-MPC-14

79. The central atom assumes sp3 hybridization in :

(A) PCl3 (B) SO3 (C) BF3 (D) 3NO

80. BCl3 is a planar molecule whereas NCl3 is pyramidal because : (A) nitrogen atom is smaller than boron atom (B) BCl3 has no lone pair of electrons whereas NCl3 has a lone pair of electrons (C) N–Cl bond is more covalent than B–Cl bond (D) B–Cl bond is more polar than N–Cl bond

81. The average speed at temperature TC of CH4 (g) is 3 12810 ms

88

. What is the value of T ?

(A) 240.55C (B) –32.45C (C) 3000C (D) –24.055C 82. The compressibility of a gas is greater than unity at STP. Therefore : (A) Vm > 22.4 L (B) Vm < 22.4 L (C) Vm = 22.4 L (D) Vm = 44.8 L 83. Which gas shows real behaviour ? (A) 16g O2 at STP occupies 11.2 L (B) 1g H2 in 0.5 L flask exerts pressure of 24.63 atm at 300 K (C) 1 mole NH3 at 300 K and 1 atm occupies volume 22.4 L (D) 5.6 L of CO2 at STP is equal to 11g 84. The compressibility factor for a real gas at high pressure is :

(A) 1 (B) Pb

1RT

(C) Pb

1RT

(D) RT

1Pb

85. At 273 K temp. and 9 atm pressure, the compressibility for a gas is 0.9. The volume of 1 milli–moles

of gas at this temperature and pressure is : (A) 2.24 litre (B) 0.020 mL (C) 2.24 mL (D) 22.4 mL 86. For a gas deviation from ideal behaviour is maximum at :

(A) 0C and 1.0 atm (B) 100C and 2.0 atm (C) –13C and1.0 atm (D) –13C and 2.0 atm




RT-JEEM–1 (2ND

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87. A mixture of NH3 (g) and N2H4(g) is placed in a sealed container at 300 K. The total pressure is 0.5 atm. The container is heated to 1200 K at which time both substances decompose completely according to the equations

2NH3(g) N2(g) + 3H2(g) and N2H4(g) N2(g) + 2H2(g) After decomposition is complete, the total pressure at 1200 K is found to be 4.5 atm. Find the mole%

of N2H4 in the original mixture : (A) 20% (B) 25% (C) 50% (D) 75% 88. Two closed vessel A and B of equal volume containing air at pressure P1 and temperature T1 are

connected to each other through a narrow open tube. If the temperature of one is now maintained at T1 and other at T2 (where T1 > T2) then that what will be the final pressure ?

(A) 1

1 2

T

2P T (B) 1 2

1 2

2P T

T T (C) 1 1

1 2

2P T

T T (D) 1

1 2

2P

T T

89. The correct order of temperature of a real gas is : (I) Boyle’s temperature (II) Critical temperature (III) Inversion temperature (A) III > I > II (B) I > II > III (C) II > I > III (D) I > III > II

90. If 250 mL of N2 over water at 30C and a total pressure of 740 torr is mixed with 300 mL of Ne over

water at 25C and a total pressure of 780 torr, what will be the total pressure if the mixture is in a 500

mL vessel over water at 35C.

(Given : Vapour pressure (Aqueous tension) of H2O at 25C, 30C and 35C are 23.8, 31.8 and 42.2 torr respectively. Assume volume of H2O( ) is negligible in final vessel)

(A) 760 torr (B) 828.4 torr (C) 807.6 torr (D) 870.6 torr




RT-JEEM–1 (2ND

YEAR)-2018-MPC-16

FIITJEE REVISION TEST (REG_2ND YEAR) JEEM–1_SET–A

DATE: 29.12.2017

MATHEMATICS

1. C 2. A 3. C 4. C

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

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

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

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

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

25. C 26. A 27. B 28. B

29. A 30. B

PHYSICS

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

35. A 36. B 37. B 38. D

39. A 40. C 41. A 42. C

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

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

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

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

59. C 60. C

CHEMISTRY

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

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

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

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

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

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

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

89. A 90. D



RT-JEEM–1 (2ND

YEAR)-2018-MPC-17

FIITJEE REVISION TEST (REG_2ND YEAR) JEEM–1_SET–B

DATE: 29.12.2017 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.:



RT-JEEM–1 (2ND

YEAR)-2018-MPC-18

1. 3x 0

tanx sinxLt

x

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

2. o o

3x 0

3sinx sin3xLt

x

(A) 0 (B) 1 (C)

3

180

(D)

3

4.180

3. Let and be the roots of 2ax bx c 0 , then

2

2x

1 cos ax bx cLt

x

(A) 0 (B) 21

2 (C)

22a

2 (D)

22a

2

4.

1/ 2 1/ 3

2x 0

cosx cosxLt

sin x

(A) 1

6 (B)

1

12

(C)

2

3 (D)

1

3

5. The values of constants a and b so that 2

x

x 1Lt ax b 0

x 1

is

(A) a = 0, b = 0 (B) a = 1, b = -1 (C) a = -1, b = 1 (D) a = 2, b = -1

6. n

1.1! 2.2! 3.3! .... n.n!Lt

n 1 !

(A) 0 (B) (C) 1 (D) none

7. If 4x 0

cos4x acos2x bLt

x

is finite, then the values of a, b are respectively

(A) 5, -4 (B) -5, -4 (C) -4, 3 (D) 4, 5

8.

21/ xx x

2x 0

e e 2Lt

x

(A) 1/ 2e (B) 1/ 4e (C) 1/ 3e (D) 1/12e




RT-JEEM–1 (2ND

YEAR)-2018-MPC-19

9. The integer n for which x

nx 0

cosx 1 cosx eLt

x

is a finite nonzero number is

(A) 1 (B) 2 (C) 3 (D) 4

10. The value of

1/ x

x 0

1 x eLt

x

is

(A) 1 (B) e/2 (C) –e/2 (D) 2/e

11.

x2

2x

x 5x 3Lt

x x 2

(A) e4 (B) –e (C) e (D) e

2

12.

x1/ x 1/ x 1/ x

x

a b cLt

3

, where a, b, c are real and nonzero =

(A) 0 (B) (abc)1/3

(C) (abc)-1/3

(D) abc/3

13.

2 2 2 2

3n

1 x 2 x 3 x ...... n xLt

n

(A) x/2 (B) x/3 (C) x/6 (D) 0

14. If a1 = 1 and nn 1

n

4 3aa

3 2a

, n 1 and if

nnLt a a

then the value of a is

(A) 2 (B) 2 (C) 2 (D) none of these

15. If is repeated root of 2ax bx c 0 then

2

2x

sin ax bx cLt

x

(A) 0 (B) a (C) b (D) c 16. If f(x) = 4x – 1, if x > 4;

2x 2 if 2 x 3 ’

= 3x + 4, if x < -2; then

f 3 f 5 f 0 f 1

f 2 f 1 f 5 f 3

(A) 11/3 (B) 3/11 (C) –11/3 (D) –3/11




RT-JEEM–1 (2ND

YEAR)-2018-MPC-20

17. If f be a function defined as 1

f x xx

when 1

xn

and f(x) = 0 when 1

xn

, n N, [x]

denotes integral part of x then when 1

xn

, f(x) is

(A) 0 (B) 1 (C) n (D) 1/n

18. If 2 2f x cos x cos x where [x] is the step function, then

(A) f(0) = 1 (B) f(/4) = 2 (C) f(/2) = -1 (D) f() = 1

19. A function f : N Z defined by n 1

f n2

when n is odd and

nf n

2

when n is even, is

(A) one-one but not onto (B) onto but not one one (C) one one onto (D) neither one one nor onto

20. If x a x b

f xx

and

f x f y f z k

x y x z y z y x z x z y xyz

then k =

(A) a (B) b (C) ab (D) 3ab

21. If f: {1, 2, 3, ....} {0, 1, 2, .... } is defined by

n/ 2 if niseven

f n n 1if nisodd

2

then 1f 100 is

(A) 100 (B) 199 (C) 201 (D) 200

22. The domain of the function 1

f xx x

is

(A) (-, 0) (B) (-,) – {0} (C) (-,) (D) (0, )

23. The domain of

2

10f x log 5x x / 4 is

(A) [0, 5] (B) [1, 4] (C) [-1, 2] (D) none

24. The range of 2

2

x x 1

x x 1

is

(A) [1/3, 3] (B) [1/3, 1] (C) [1, 3] (D) (-, 1/3] [3, )




RT-JEEM–1 (2ND

YEAR)-2018-MPC-21

25. If a, b, c are the sides of a triangle then the range of 2 2 2

ab bc ca

a b c

is

(A) [1, 2) (B) (1/2, 1] (C) [1/2, 2) (D) (-1/2, 2)

26. If [x] stands for the greatest integer function, then 1 1 1 2 1 999

....2 1000 2 1000 2 1000

(A) 498 (B) 499 (C) 500 (D) 501

27. The range of 2 2sec x 4cosec x is

(A) [1, 5] (B) [5, ) (C) [9, ) (D) [4, 9]

28. If n 1

F n 1 n 1

and G n n F n n N then (GoG) (n) =

(A) 1 (B) 0 (C) -1 (D) n 29. Let f be an injective function with domain {x, y, z} and range {1, 2, 3} such that exactly one of the

following statements is correct and the remaining are false. f(x) = 1, f(y) 1, f(z) 2 . The value of

f(1) is (A) x (B) y (C) z (D) none

30. The function f: C C defined by ax b

f xcx d

for x C where bd 0 reduces to a constant function

if (A) a = c (B) b = d (C) ad = bc (D) ab = cd 31. The mass of two blocks A and C is 1 kg and 3 kg respectively. The

block B is a very long plank of mass 1 kg. There is no friction between the block B and the surface. The coefficient of friction between A and B is 0.6. The system is released from the state of rest. What would the velocity of the block B when C has fallen by 3 m.

A

B

C

(A) 6 (B) 9 (C) 12 (D) 15 32. In the figure shown all the surfaces are frictionless, and mass of

the block, m = 1 kg. The block and wedge are held initially at rest. Now wedge is given a horizontal acceleration of 10 m/s

2 by

applying a force on the wedge, so that the block does not slip on the wedge. Then work done by the normal force(between the

block and the wedge) in ground frame on the block in 3 seconds

is 50n J. Find the value of n?

10 m/s2

m

M

(A) 7 (B) 9 (C) 3 (D) 11




RT-JEEM–1 (2ND

YEAR)-2018-MPC-22

33. The potential energy in joule of a particle of mass 1 kg moving in the XY plane is given

by 3 4 x y , where (x, y) are the co-ordinates of the particle in metre. If the particle is at rest at

(6, 4) at time t = 0, then which of the following is incorrect? (A) The particle has constant acceleration and the co-ordinates of the particle at time t = 4 s are (–18, –28) (B) The work done by the field force from the position of rest of the particle and the instant the particle crossing X-axis is 25 joule. (C) The speed of the particle when it crosses the Y-axis is 10 ms

–1

(D) The speed of particle when it crosses y-axis in 20 ms–1

34. The value(s) of mass m for which the 100 kg block does not remain

in static equilibrium is (A) 38 kg (B) 37 kg (C) 83 kg (D) 85 kg 35. In the system shown in the figure m1 > m2. System is held at rest by thread

BC. Just after the thread BC is burnt (A) acceleration of m1 will be upwards

(B) magnitude of acceleration of both blocks will be equal to 1 2

1 2

m mg

m m

(C) acceleration of m1 will be equal to zero (D) magnitude of acceleration of two blocks will be non–zero unequal For Question (36–37) As in bigger pulley a variable force F is acting in upward direction. F = at (where a = 80 and t in second). Pulleys are light and smooth.

m1m2 m3

(m1 = 2kg , m2 = 4kg , m3 = 6kg)

36. Velocity of block m2 when 3m will leave contact from horizontal surface.

(A) zero (B) 2.5 m/sec (C) 5 m/sec (D) None 37. Height attain by m2 when m3 will leave contact from horizontal surface.

(A) 5

m6

(B) 15

m3

(C) zero (D) None




RT-JEEM–1 (2ND

YEAR)-2018-MPC-23

For Question (38–39)

Two men A and B each of mass ‘m’ sit in light cages at the ends of a flexible light rope passing over a smooth pulley as shown in the figure. Initially both are at rest. A being higher than B by h.

Suddenly a small ball of mass 10

m is handed over to B with

negligible velocity which he instantaneously throws up with velocity v, to A such that it just reaches A.

38. When A catches the ball, his position is shifted up by l . Where l is

(A) 19

h (B)

3

19

h (C)

2

19

h (D)

40h

361

39. As soon as A catches the ball, its instantaneous velocity will be:

(A) Zero (B) v/20 upwards (C) v/20 downwards (D) None of the above

40. A vertical spring of force constant 100 N/m is attached with a hanging

mass of 10 kg. Now an external force is applied on the mass so that the spring Is stretched by additional 2m. The work done by the force F is :( g = 10 m/s

2)

(A) 200 J (B) 400 J (C) 450 J (D) 600 J 41. System shown in figure is released from rest with the spring un-

elongated. Pulley and spring Is massless and friction is absent everywhere. The speed of 5 kg block when 2 kg block just leaves contact with ground is : (Take force constant of spring k = 40 N/m and g = 10 m/s

2)

(A) 2 m/s (B) 2 2 m/s (C) 2 m/s (D) 4 2 m/s




RT-JEEM–1 (2ND

YEAR)-2018-MPC-24

42. A system consists of two cubes of masses m1 and m2 respectively connected by

a spring of force constant k. The force (F) that should be applied to the upper cube for which the lower one just lifts after the force is removed is:

(A) m1g (B) 1 2

1 2

mmg

m +m (C) (m1 + m2)g (D) m2g

43. A uniform chain of length L and mass M is held on a smooth table and one-third of its length is

hanging vertically down over the edge of the table. If g is acceleration due to gravity, the work required to pull the hanging part onto the table is: (A) MgL (B) MgL/3 (C) MgL/9 (D) MgL/18

44. One end of a light spring of force constant k is fixed to a wall and the other end is tied to a block

placed on a smooth horizontal surface. In a displacement, the work done by the spring is 1

2 kx

2. The

possible case(s) may be : (A) the spring was Initially stretched by a distance 2x and finally was in its natural length

(B) the spring was initially in its natural length and finally it was compressed by a distance x (C) the spring was initially compressed by a distance x and finally was in its natural length (D) the spring was initially in its natural length and finally stretched by a distance x

45. A block is suspended by an ideal spring of force constant k. If the block is pulled down by applying a

constant force F and if maximum displacement of block from its initial mean position of rest is x0 then:

(A) increase in energy stored In spring is k x2

0 (B) x0 = 3

2

F

k

(C) x0 = 2F

k (D) work done by applied force F is (1/2)Fx0




RT-JEEM–1 (2ND

YEAR)-2018-MPC-25

46. A skier travels with a constant speed of 6 m/s along a parabolic path 2x

y20

. The acceleration of the

skier when he is at (10, 5) is given as a b

c. Then (a + b – c) is equal to

(A) 1 (B) 2 (C) 3 (D) 4 47. Width of a river is 60m. A swimmer wants to cross the river

such that he reaches from A to B directly. Point B is 45m ahead of line AC(perpendicular to river) assume speed of river and speed of swimmer as equal. Swimmer must try to swim at angle

with AC. Value of is 1 ksin

25

. Then K?

(A) 6 (B) 7 (C) 8 (D) 9

B C

A

River flow

48. A block of mass m is gently placed over a massive plank moving horizontally over a smooth surface

with velocity 6 m/s. The co–efficient of friction between the block and plank is 0.2. The distance travelled by the block till it slide on the plank is ……….(in m) [g = 10 m/s

2]

(A) 3 m (B) 6 m (C) 9 m (D) 12 m 49. A man moving with a velocity of 5 m/s on a

horizontal road observes that raindrops fall at

an angle of 45 with the vertical. When he moves with a velocity of 16 m/s along an

inclined plane, which is inclined at 30 with the horizontal, he observes raindrops falling vertically downward as shown in the figure. the actual velocity of the raindrops is

ˆ ˆK 3 i (K 3 5)j , then K is

30

16m/s

5 m/s

45

(A) 2 (B) 4 (C) 6 (D) 8

50. A small body was launched up an inclined plane set at an angle of 45 against the horizontal. The co–

efficient of friction is N

10 if the time of ascent of the body is = 2.0 times less than the time of its

descent. (A) 6 (B) 9 (C) 12 (D) 5




RT-JEEM–1 (2ND

YEAR)-2018-MPC-26

51. Three blocks A, B and C of equal mass m are placed one

over other on a frictionless surface (table) as shown in the figure co–efficient of friction between any blocks A, B and

C is . The maximum value of mass of block MD. So that the block A, B and C move without slipping over each

other is Amu

(1 ) . Then A is equal to ………..

A

MD

B

C

(A) 4 (B) 3 (C) 2 (D) 1 52. A locomotive accelerates a train of identical railway carts. The carts are numbered consequently with

the cart next to locomotive having the number 1. The tension in the connection between the carts with number 4 and 5 is three times bigger than the tension in the connection between the carts with numbers 14 and 15. The number of last car is given as (4K + 3), then K = ?

(A) 1 (B) 4 (C) 7 (D) 11 53. The figure shows an accelerometer, a device for

measuring the horizontal acceleration of cars and aeroplanes. A ball is free to roll on a parabolic track described by the equation y = x

2, where both x

and y are meters. A scale along the bottom is used to measure the ball’s steady position x. What is the acceleration (in m/s

2) if x = 20 cm?

–0.5m 0.5m 0m

y = x2

(A) 3 (B) 1 (C) 2 (D) 4 54. A force of 20N is acting on a block of mass 2 kg on smooth inclined plane. The direction of this force

can be any of the four as shown in figures in which case normal force can be zero.

30

F

30

F

30 F

30

F

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




RT-JEEM–1 (2ND

YEAR)-2018-MPC-27

55. Figure shows a man pulling on a string attached to a block

kept on a rough surface. Man is heaviest than block. Coefficient of friction is same for both block and man. Subscripts R, B and M denote rope block and man respectively, taking string to be light.

R B

M

Mark the incorrect statement

(A) R/B M/RF F always

(B) block begins to move earlier than man if man continues to increase his pull from zero

(C) R/B M/RF and F can be action reaction pairs

(D) block can remain static if man walks with constant speed while letting spring to pass through his hand

56. In figure, two block M and m are tied together with an inextensible

and light string. The mass M is placed on a rough horizontal surface

with co–efficient of friction and the mass m is hanging vertically against a smooth vertical wall. The pulley is frictionless choose the correct statements related to the tension T in the string.

M

m

Rough()

(smooth)

(A) when m < M, T = mg (B) when m < M, T = Mg

(C) when m > M, Mg < T < Mg (D) when m > M, mg < T < Mg 57. Two men of unequal masses hold on two sections of a light rope passing over a

smooth light pulley. Which of the following is not possible? (A) the lighter man is stationary while the heavier man slides with some acceleration (B) the lighter man is stationary while the lighter man climbs with some acceleration (C) the two men slide with same acceleration in the same direction (D) the two men move with accelerations of same magnitude in opposite directions

58. If M = 3 kg, m1 = 6 kg, m2 = 4 kg

system is released from rest. Then which of the following statement is correct

M1

M

s = 0.3

M2

k = 0.2

s = 0.4

k = 0.3

(A) Friction on

1M is static (B) Friction on 2M is static

(C) M remains at rest (D) All the above




RT-JEEM–1 (2ND

YEAR)-2018-MPC-28

59. A block of mass 2M kg is moving with velocity 0v towards a mass-less unstretched spring of

force constant 10 /K N m .The co-efficient of friction between the

ground and the block is µs = 0.2 and µK = 0.15. Find maximum value

of 010 v where v0 is the maximum velocity such that after

pressing the spring ,the block does not return back but stops there permanently?

m

v0

K

1m (A) 4 (B) 8 (C) 12 (D) None of these

60. A massive horizontal platform is moving horizontally with a constant

acceleration of 10 m/s2. A particle P of mass m = 1 kg is kept at rest at

the smooth surface. It is hinged at O with the help of a massless rod OP of length 0.9m. Now P is imparted a velocity opposite to direction of acceleration so that is just able to complete full circular motion about O. If the maximum tension in the rod during the motion is 10n, then value of n?

O

P L 10m/s2

(A) 3 (B) 4 (C) 5 (D) 6 61. In which of the following molecules the bond angle is maximum ? (A) CH4 (B) H2O (C) NH3 (D) CO2

62. Hybridization state of I in 2ICl is :

(A) dsp2 (B) sp (C) sp

2 (D) sp

3

63. The hybridization of carbon atoms in C–C single bond of HCC–CH=CH2 is : (A) sp

3 – sp

3 (B) sp

2 – sp

3 (C) sp – sp

2 (D) sp

3 – sp

64. The central atom assumes sp

3 hybridization in :

(A) PCl3 (B) SO3 (C) BF3 (D) 3NO




RT-JEEM–1 (2ND

YEAR)-2018-MPC-29

65. BCl3 is a planar molecule whereas NCl3 is pyramidal because : (A) nitrogen atom is smaller than boron atom (B) BCl3 has no lone pair of electrons whereas NCl3 has a lone pair of electrons (C) N–Cl bond is more covalent than B–Cl bond (D) B–Cl bond is more polar than N–Cl bond

66. The average speed at temperature TC of CH4 (g) is 3 12810 ms

88

. What is the value of T ?

(A) 240.55C (B) –32.45C (C) 3000C (D) –24.055C 67. The compressibility of a gas is greater than unity at STP. Therefore : (A) Vm > 22.4 L (B) Vm < 22.4 L (C) Vm = 22.4 L (D) Vm = 44.8 L 68. Which gas shows real behaviour ? (A) 16g O2 at STP occupies 11.2 L (B) 1g H2 in 0.5 L flask exerts pressure of 24.63 atm at 300 K (C) 1 mole NH3 at 300 K and 1 atm occupies volume 22.4 L (D) 5.6 L of CO2 at STP is equal to 11g 69. The compressibility factor for a real gas at high pressure is :

(A) 1 (B) Pb

1RT

(C) Pb

1RT

(D) RT

1Pb

70. At 273 K temp. and 9 atm pressure, the compressibility for a gas is 0.9. The volume of 1 milli–moles

of gas at this temperature and pressure is : (A) 2.24 litre (B) 0.020 mL (C) 2.24 mL (D) 22.4 mL 71. For a gas deviation from ideal behaviour is maximum at :

(A) 0C and 1.0 atm (B) 100C and 2.0 atm (C) –13C and1.0 atm (D) –13C and 2.0 atm 72. A mixture of NH3 (g) and N2H4(g) is placed in a sealed container at 300 K. The total pressure is 0.5

atm. The container is heated to 1200 K at which time both substances decompose completely according to the equations

2NH3(g) N2(g) + 3H2(g) and N2H4(g) N2(g) + 2H2(g) After decomposition is complete, the total pressure at 1200 K is found to be 4.5 atm. Find the mole%

of N2H4 in the original mixture : (A) 20% (B) 25% (C) 50% (D) 75%




RT-JEEM–1 (2ND

YEAR)-2018-MPC-30

73. Two closed vessel A and B of equal volume containing air at pressure P1 and temperature T1 are

connected to each other through a narrow open tube. If the temperature of one is now maintained at T1 and other at T2 (where T1 > T2) then that what will be the final pressure ?

(A) 1

1 2

T

2P T (B) 1 2

1 2

2P T

T T (C) 1 1

1 2

2P T

T T (D) 1

1 2

2P

T T

74. The correct order of temperature of a real gas is : (I) Boyle’s temperature (II) Critical temperature (III) Inversion temperature (A) III > I > II (B) I > II > III (C) II > I > III (D) I > III > II

75. If 250 mL of N2 over water at 30C and a total pressure of 740 torr is mixed with 300 mL of Ne over

water at 25C and a total pressure of 780 torr, what will be the total pressure if the mixture is in a 500

mL vessel over water at 35C.

(Given : Vapour pressure (Aqueous tension) of H2O at 25C, 30C and 35C are 23.8, 31.8 and 42.2 torr respectively. Assume volume of H2O( ) is negligible in final vessel)

(A) 760 torr (B) 828.4 torr (C) 807.6 torr (D) 870.6 torr 76. Consider the ground state of Cr atom (Z = 24). The numbers of electrons with the azimuthal quantum

numbers, l = 1 and 2 are respectively (A) 12 and 4 (B) 12 and 5 (C) 16 and 4 (D) 16 and 5 77. In ground state, an element has 13 electrons in its’ ‘M’ shell. The element is (A) copper (B) Iron (C) Nickel (D) chromium 78. Electromagnetic radiation with maximum wavelength is (A) radiowave (B) X–ray (C) infrared (D) ultraviolet 79. The orbital diagram in which both the pauli’s exclusion principles and Hund’s rule are violated is

(A) (B)

(C) (D)




RT-JEEM–1 (2ND

YEAR)-2018-MPC-31

80. The maximum number of 3d electrons having S = + ½ are (A) 10 (B) 5 (C) 14 (D) 7 81. In hydrogen atom, energy of first exicited state is –3.4 eV. The kinetic energy of the same orbit of

Hydrogen atom would be (A) +3.4 eV (B) +6.8 eV (C) –13.6 eV (D) +13.6 eV 82. The ionization energy of Hydrogen atom is 13.6 eV. What will be the ionization energy of He

+ ?

(A) 13.6 eV (B) 54.4 eV (C) 122.4 eV (D) zero 83. What is ratio of time periods (T1/T2) is second orbit of hydrogen atom to third orbit of He

+ ion ?

(A) 8/27 (B) 32/27 (C) 27/32 (D) 27/8

84. If m = magnetic quantum number, = azimuthal quantum number then :

(A) m = + 2 (B) m = 22 + 1 (C)

m 1

2

(D) = 2m + 1

85. The photo electric current decreases if (A) The frequencies of incident radiation decreases below threshold frequency (B) The exposure time is decreased (C) The intensity of the source of light is decreased (D) none of these 86. Which of the following bond is strongest ? (A) sp–sp (B) sp

2 – sp

2 (C) s– s (D) p – p

87. The type of hybridization of sulphur atom present in SO2 and SO3 is respectively : (A) sp, sp

2 (B) sp

2, sp

2 (C) sp

2, sp

3 (D) sp, sp

3

88. In the formation of ethylene molecule, the carbon atom makes use of : (A) sp

3 hybridization (B) sp

2 hybridization

(C) sp hybridization (D) none of these 89. Which one of the following has pyramidal structure ? (A) NH3 (B) SiF4 (C) H2O (D) BF3 90. Which statement is incorrect ?

(a) sigma bond is stronger than –bond

(b) sigma bond is weaker than – bond (c) A triple bond is weaker than double bond (d) A double bond is weaker than single bond (A) a, c, d (B) b, c, d (C) Only b (D) c, d




RT-JEEM–1 (2ND

YEAR)-2018-MPC-32

FIITJEE REVISION TEST (REG_2ND YEAR) JEEM–1_SET-B

DATE: 29.12.2017 MATHEMATICS

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

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

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

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

17. A 18. C 19. C 20. C

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

25. B 26. C 27. C 28. A

29. B 30. C

PHYSICS

31. A 32. C 33. D 34. D

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

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

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

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

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

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

59. D 60. C

CHEMISTRY

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

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

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

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

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

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

85. C 86. A 87. B 88. B

89. A 90. B

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