mock test for

(1)

Time : 2:30 Hrs. MM : 480

GENERAL INSTRUCTIONS :

1. Kerala Engineering Agriculture Medical Common Entrance Exam (KEAM-CEE) has two papers. Paper-I for Physics

& Chemistry and Paper-II for Mathematics.

2. For each question, five options (A/ B/ C/ D/ E) are given, of which only one have to select.

3. For each correct answer 4 marks will be awarded and for each incorrect answer 1 mark will be deducted from the

total score.

4. Read each question carefully.

5. It is mandatory to use Blue/Black Ball Point Pen to darken the appropriate circle in the answer sheet.

6. Mark should be dark and should completely fill the circle in the answer sheet.

7. Do not use white-fluid or any other rubbing material on answer sheet. No change in the answer once marked.

8. Rough work must not be done on the answer sheet.

9. Student cannot use log tables and calculators or any other material in the examination hall.

10. Before attempting the question paper, student should ensure that the test paper contains all pages and no page

is missing.

Choose the correct answer :

1. In S = a + bt + ct2. S is measured in metre and t

in second The unit of c is

(A) m2s–2

(B) m

(C) ms–1

(D) ms–2

(E) None of these

2. The dimensional formula of angular velocity is

(A) [M0L0T–1]

(B) [MLT–1]

(C) [M0L0T1]

(D) [ML0T–2]

(E) [M0L0T0]

Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005

Ph.: 011-47623456

MOCK TESTMOCK TESTMOCK TESTMOCK TESTMOCK TEST

forforforforforKEAM-2017KEAM-2017KEAM-2017KEAM-2017KEAM-2017

PAPER-I : PHYSICS & CHEMISTRYPAPER-I : PHYSICS & CHEMISTRYPAPER-I : PHYSICS & CHEMISTRYPAPER-I : PHYSICS & CHEMISTRYPAPER-I : PHYSICS & CHEMISTRY

3. Figure shows three vectors a, b and c. If RQ = 2PR,

which of the following relations is correct?

a

b

c

P

R

Q

O

(A) 2a + c = 3b

(B) a + 3c = 2b

(C) 3a + c = 2b

(D) a + 2c = 3b

(E) a + b + 2c = 0

Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)

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4. The magnitude of the resultant of ( )A B

→ →

+ and

( )A B

→ →

− .

(A) 2A (B) 2B

(C) 2 2+A B (D)

2 2–A B

(E) 2 AB

5. The magnitude of the resultant of two equal vectors is

equal to the magnitude of either vector. What is the

angle between the two vectors?

(A) 60° (B) 90°

(C) 120° (D) 150°

(E) 180°

6. The resultant of two vectors of magnitudes 3 units

and 4 units is 1 unit. What is the value of their dot

product ?

(A) 12 units (B) 7 units

(C) 1 unit (D) Zero

(E) 2 units

7. A and B are two vectors lying in a plane, C is another

vector perpendicular to the plane containing vector A

and B. Which of the following relations is possible?

(A) A + B = C

(B) A + C = B

(C) A × B = C

(D) A · C = B

(E) A – B = C – A

8. A net force F accelerates a mass m with an

acceleration a. If the net force is applied to mass

m/2, then the magnitude of the acceleration will be

(A) a/4 (B) a/2

(C) a (D) 2a

(E) a/5

9. A net force of 10 newtons accelerates an object at

5.0 m/s2. What net force would be required to

accelerate the same object at 1.0 m/s2 ?

(A) 1.0 N (B) 2.0 N

(C) 5.0 N (D) 50 N

(E) 20 N

10. A sports car with mass 1000 kg can accelerate from

rest to 27 m/s in 7.0 s. What is the average net force

on the car ?

(A) 3.9 × 103 N (B) 4.8 × 102 N

(C) 7.9 × 102 N (D) 1.7 × 103 N

(E) 4.8 × 103 N

11. A body of mass 0.1 kg moving with a velocity of

10 m/s hits a spring (fixed at the other end) of force

constant 1000 N/m and comes to rest after

compressing the spring. The compression of the spring

is

(A) 0.01 m (B) 0.1 m

(C) 0.2 m (D) 0.5 m

(E) 0.05 m

12. An engine pump is used to pump a liquid of density continuously through a pipe of cross-sectional area A.

If the speed of flow of the liquid in the pipe is v, then

the rate at which kinetic energy is being imparted to

the liquid is

(A)31

2A vρ (B)

21

2A vρ

(C)1

2A vρ (D) Av

(E)21

4A vρ

13. The amount of work done in pumping water out of a

cubical vessel of height 1 m is nearly (g = 10 ms–2)

(A) 5,000 J (B) 10,000 J

(C) 5 J (D) 10 J

(E) 1 J

14. Four identical spheres each of radius 10 cm and mass

1 kg are placed on a horizontal surface touching one

another so that their centres are located at the corners

of square of side 20 cm. What is the distance of their

centre of mass from centre of either sphere ?

(A) 5 cm (B) 10 cm

(C) 20 cm (D) 15 cm

(E) None of these

15. The position of centre of mass of a system consisting

of two particles of masses m1 and m

2 separated by a

distance L apart, from m1 will be

(A)1

1 2

m L

m m+

(B)2

1 2

m L

m m+

(C)2

1

mL

m(D)

2

L

(E)1

2

mL

m

⎛ ⎞⎜ ⎟⎝ ⎠

16 A system consists of mass M and m (<< M). The

centre of mass of the system is

(A) At the middle

(B) Nearer to M

(C) Nearer to m

(D) At the position of larger mass

(E) Nothing can be predicted

Mock Test for KEAM-2017 (Paper-I) Complete Syllabus Test

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17. The drive shaft of an automobile rotates at 3600 rpm

and transmits 80 HP up from the engine to the rear

wheels. The torque developed by the engine is

(A) 16.58 N-m (B) 0.022 N-m

(C) 158.31 N-m (D) 141.6 N-m

(E) 120.02 N-m

18. A couple consisting of two forces F1 and F

2 each equal

to 5 N is acting at the rim of a disk of mass

2 kg and radius 1 m for 5 s. Initially the disc is at rest.

The final angular momentum of the disk is

(in kg m2s–1)

F2 F

1

(A) 15 (B) 20

(C) 50 (D) 30

(E) 35

19 A disk starts rotating from rest about its axis with an

angular acceleration equal to = 10t rad/s2 where t is

time in secon(d) At t = 0 disk is at rest. The time

taken by disk to make its first complete revolution is

(A)

1/3

6

5

π⎛ ⎞⎜ ⎟⎝ ⎠ (B)

1/3

3

10

π⎛ ⎞⎜ ⎟⎝ ⎠

(C)

1/2

2

5

π⎛ ⎞⎜ ⎟⎝ ⎠ (D)

1/3

6

13

π⎛ ⎞⎜ ⎟⎝ ⎠

(E)

1

23

15

π⎛ ⎞⎜ ⎟⎝ ⎠

20. Two identical solid copper sphere of radius R placed

in contact with each other. The gravitational attraction

between them is proportional to

(A) R2 (B) R–2

(C) R4 (D) R–4

(E) R–5

21. A mass M splits into two parts m and (M – m), which

are then separated by a certain distance. What ratio

(m/M) maximises the gravitational force between the

parts?

(A) 2/3 (B) 3/4

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

(E) 1/4

22. Two bodies of mass 100 kg and 400 kg are lying one

metre apart. At what distance from 100 kg body will

the intensity of gravitational field be zero(in metres)?

(A)1

9(B)

1

3

(C)1

6(D)

10

11

(E)9

10

23. If equal quantities of ice melt completely in two

identical containers in 30 and 20 minutes respectively,

then thermal conductivities of the material of the two

containers are in the ratio

(A) 1 : 1 (B) 1 : 2

(C) 3 : 2 (D) 1 : 4

(E) 2 : 3

24. Two identical plates of metal are welded end to end

as shown in figure (A); 20 cal of heat flows through it

in 4 minutes.

(B)

If the plates are welded as shown in figure (B) the

same amount of heat will be flow through the plates

in

(A) 1 minute (B) 2 minutes

(C) 4 minutes (D) 16 minutes

(E) 18 minutes

25. If the masses of all molecules of a gas are halved and

their speeds doubled, then the ratio of initial and final

pressures would be

(A) 2 : 1 (B) 1 : 2

(C) 4 : 1 (D) 1 : 4

(E) 1 : 5

26. By what percentage should the pressure of a given

mass of a gas be increased so as to decrease its

volume by 10% at a constant temperature ?

(A) 8.1 %

(B) 9.1%

(C) 10.1%

(D) 11.1%

(E) 12.2 %


(4)

27. 70 calories of heat are required to raise the

temperature of 2 moles of an ideal gas at constant

pressure from 30°C to 35°C. The amount of heat

required to raise the temperature of the same gas

through same range (30°C to 35°C) at constant volume

is

(A) 30 cal (B) 50 cal

(C) 70 cal (D) 40 cal

(E) 120 cal

28. By opening the door of a refrigerator inside a closed

room

(A) You can cool the room to a certain degree

(B) You can cool it to the temperature inside the

refrigerator

(C) You ultimately warm the room slightly

(D) You can neither cool nor warm the room

(E) Cannot be predicted

29. An ideal gas is taken through a cyclic

thermodynamical process through four steps. The

amounts of heat involved in these steps are

Q1 = 5960 J, Q

2 = –5585 J, Q

3 = –2980 J, Q

4 = 3645 J;

respectively. The corresponding works involved are :

W1 = 2200 J, W

2 = –825 J, W

3 = –1100 J and W

4

respectively. The value of W4 is

(A) 1315 J (B) 275 J

(C) 765 J (D) 675 J

(E) 865 J

30. Time period of a simple pendulum of length l is T1 and

time period of a uniform rod of the same length l pivoted

about one end and oscillating in a vertical plane is T2.

Amplitude of oscillation in both the cases is small.

Then T1/T

2 is

(A) 1/ 3 (B) 1

(C) 4 / 3 (D) 3 / 2

(E)

4

3

31. A particle of mass 5 g is executing simple harmonic

motion with an amplitude 0.3 m and time period

/5 second. The maximum value of the force acting

on the particle is

(A) 5 N (B) 4 N

(C) 0.5 N (D) 0.15 N

(E) 0.25 N

32. A particular is executing SHM with amplitude A and

has maximum velocity v0. Its speed at displacement

A/2 will be

(A) 0

4

v(B)

0

2

v

(C) v0

(D)0

3

2

v

(E)0

2

v

33. A car with a horn of frequency 620 Hz travels towards

a large wall with a speed of 20 m/s. If the velocity of

sound is 330 m/s, the frequency of echo of sound of

horn as heard by the driver is

(A) 700 (B) 660

(C) 620 (D) 550

(E) 750

34. A man standing on a platform hears the sound of

frequency 605 Hz coming at frequency 550 Hz from a

train whistle coming towards the platform. If the velocity

of sound is 330 m/s, then what is the speed of train ?

(A) 30 m/s (B) 35 m/s

(C) 40 m/s (D) 45 m/s

(E) 50 m/s

35. A siren emitting sound of frequency 800 Hz is going

away from a static listener with a speed of 30 m/s.

Frequency of the sound to be heard by the listener is

(Take velocity of sound as 330 m/s)

(A) 733.3 Hz (B) 644.8 Hz

(C) 481.2 Hz (D) 286.5 Hz

(E) 295.8 Hz

36. A cart supports a cubic tank filled with a liquid up to

the top. The cart moves with a constant acceleration

a in the horizontal direction. The tank is tightly closed.

Assume that the lid does not exert any pressure on

the liquid when in motion with uniform acceleration.

The pressure at a point which is at a depth h and

distance l from the front wall is

(A) dgh (B) dla

(C) dgh + dla (D) dgh – dla

(E) None of these

37 The mass of a balloon with its contents is 1.5 kg. It is

descending with an acceleration equal to half that of

acceleration due to gravity. If it is to go up with the

same acceleration keeping the volume same, its mass

should be decreased by

(A) 1.2 kg (B) 1.5 kg

(C) 0.75 kg (D) 0.5 kg

(E) 1 kg


(5)

38. When at rest, a liquid stands at the same level in the

tubes shown in figure. But as indicated a height

difference h occurs when the system is given an

acceleration a towards the right. Here h is equal to

h

L

a

(A)2

aL

g(B)

2

gL

a

(C)gL

a(D)

aL

g

(E)

2aL

gh

39. A thick rope of rubber of density 1.5 × 103 kg/m3 and

Young’s modulus 5 × 106 N/m2, 8 m in length is hung

from the ceiling of a room, the increase in its length

due to its own weight is

(A) 9.6 × 10–2 m (B) 19.2 × 10–2 m

(C) 9.6 × 10–3 m (D) 9.6 m

(E) 19.2 × 10–3 m

40. A spherical ball contracts in volume by 0.01% when

subjected to a normal uniform pressure of 100

atmosphere. The bulk modulus of its material in dyne/

cm2 is

(A) 10 × 1012 (B) 100 × 102

(C) 1 × 1012 (D) 2.0 × 1011

(E) 2.5 × 1012

41. Two wires of equal length and cross-section area

suspended as shown in figure. Their Young’s modulus

are Y1 and Y

2 respectively. The equivalent Young’s

modulus will be

(A) Y1 + Y

2(B)

1 2

2

Y Y+

(C)1 2

1 2

YY

Y Y+(D) 1 2

Y Y

(E) 1 2Y Y+

42. Two equally charged identical metal spheres A and B

repel each other with a force 3 × 10–5 N. Another

identical uncharged sphere C is touched with A and

then placed at the mid-point between A and B Net

force on C is

(A) 1 × 10–5 N (B) 2 × 10–5 N

(C) 1.5 × 10–5 N (D) 3 × 10–5 N

(E) 2 × 10–4N

43. Three charges + 4q, Q and q are placed in a straight

line of length 1 at points distance 0, 1/2 and 1

respectively. What should be Q in order to make the

net force on q to be zero ?

(A) –q (B) –2q

(C) –q/2 (D) 4q

(E) –q/4

44. Two fixed insulated copper spheres A and B each

having same charge are placed at a distance (which

is very large as compared to radius of sphere), and in

this situation they repel each other with a force F.

Now another identical uncharged copper sphere C is

first touched to B, then to C and then taken far away.

The new force of interaction between A and B is

(A) 3F/8 (B) F

(C) F/4 (D) F/2

(E) F/8

45. 64 drops each having the capacitance C and potential

V are combined to form a big drop. If the charge on

the small drop is q, then the charge on the big drop

will be

(A) 2q (B) 4q

(C) 16q (D) 64q

(E) 18q

46. In a charged capacitor, the energy resides

(A) The positive charges

(B) Both the positive and negative charges

(C) The field between the plates

(D) Around the edge of the capacitor plates

(E) None of these

47. The capacity of a spherical conductor of radius R is

(A)

04

R

πε

(B)0

4

R

πε

(C) 40R (D) 4

0R2

(E) 40R–2


(6)

48. In a conductor 4 C charge flows for 2 second. The

value of electric current will be

(A) 4.2 A (B) 4 A

(C) 2 A (D) 2.2 A

(E) 0.2 A

49. The resistivity of a conducting wire

(A) Increases with the length of the wire

(B) Decreases with the length of the wire

(C) Decreases with the length and increases with the

cross-section of wire

(D) None of the above statement is correct

(E) All are correct

50. A current I flows through a uniform wire of diameter d,

when the mean drift velocity is v. The same current

will flow through a wire of diameter d/2 made of the

same material if the mean drift velocity of the electrons

is

(A) v/4 (B) v/2

(C) 4v (D) 2v

(E) v/5

51. An infinite straight current carrying conductor is bent

into a circle as shown in the figure. If the radius of the

circle is R, the magnetic field at the centre of the coil

is(i - current in the wire)

R

(A) Infinite (B) Zero

(C)02

4

i

R

μπ

π(D)

02

( 1)4

i

R

μπ +

π

(E)0

2

iµ

52. A length L of wire carries a steady current I. It is bent

first to form a circular plane coil of one turn. The same

length is now bent more sharply to give three loops of

smaller radius. The magnetic field at the centre caused

by the same current is

(A) One third of its value

(B) Unaltered

(C) Three times of its initial value

(D) Nine times of its initial value

(E) Ten times of its initial value

53. Magnetic field B on the axis of a circular coil and far

away distance x from the centre of the coil are related

as

(A) B x–3

(B) B x–2

(C) B x–1

(D) B x–4

(E) B x–5

54. As shown in figure, a metal rod makes contact and

completes the circuit. The circuit is perpendicular to

the magnetic field with B = 0.15 T. If the resistance is

3 , force needed to move the rod with a constant

speed of 2 m/s is

× × × × ×

× × × × ×

× × × × ×

× × × × ×

50 cm3 v = 2 m/s

(A) 3.75 × 10–3N (B) 3.75 × 10–2 N

(C) 3.75 × 102N (D) 3.75 × 10–4 N

(E) 3.75 × 10–5 N

55 A copper rod of length l is rotated about the end

perpendicular to the uniform magnetic field B with

constant angular velocity . The induced e.m.f.

between the two ends is

(A) 2Bl2 (B) Bl2

(C) 21

2B lω (D)

21

4B lω

(E)21

8B lω

56. The magnitude of the earth’s magnetic field at a place

is B0 and the angle of dip is δ . A horizontal conductor

of length l, lying north-south, moves eastwards with a

velocity v. The emf induced across the rod is

(A) Zero

(B) B0lv

(C) B0lv sin δ

(D) B0lv cos δ

(E) B0lv sin2

δ


(7)

57. Figure shows a series LCR circuit connected to a

variable frequency 200 V source L = 5 H, C = 80 F

and R = 40 . What is the source frequency which

drives the circuit at resonance?

L C

R

(A) 25 Hz (B)25

Hzπ

(C) 50 Hz (D)50

Hzπ

(E)5

Hz⎛ ⎞⎜ ⎟⎝ ⎠π

58. Two circuits 1 and 2 are connected to identical dc

source each of emf 12 V. Circuit 1 has a self

inductance L1 = 10 H and circuit 2 has a self

inductance L2 = 10 mH. The total resistance of each

circuit is 48 . The ratio of steady currents in circuits

1 and 2 is

(A) 1000 (B) 100

(C) 10 (D) 1

(E) 0.1

59. An alternating voltage (in volts) varies with time t

(in second) as V = 100 sin (50 π t). The peak value of

voltage, the rms value of the voltage and frequency

respectively are

(A) 100 V, 100

V2

, 50 Hz

(B) 2 100 V , 100 V, 25 Hz

(C)100

V, 2 100 V, 50 Hz2

(D) 100V, 100

V2

, 25 Hz

(E) 100 V, 10

V2

, 20 Hz

60. In a plane electromagnetic wave, the electric field

oscillates sinusoidally at a frequency of 2.0 ×

1010 Hz.

What is the wavelength of the wave ?

(A) 1.0 cm (B) 1.5 cm

(C) 2.0 cm (D) 3.0 cm

(E) 3.5 cm

61. Which of the following statement is false ?

(A) Electromagnetic waves are transverse

(B) Electromagnetic waves travel in free space at the

speed of light

(C) Electromagnetic waves travel with the same speed

in all media

(D) Electromagnetic waves are produced by an

accelerating charge

(E) All of these

62. A ray of light passes through an equilateral prism

such that the angle of incidence is equal to the angle

of emergence and the angle of incidence is equal to

3/4th of the angle of prism. The angle of deviation is

(A) 45° (B) 39°

(C) 20° (D) 30°

(E) 600

63. A thin prism P1 with angle 5° and made from glass of

refractive index 1.54 is combined with another prism

P2 made from glass of refractive index 1.92 to produce

dispersion without deviation. The angle of prism P2 is

(A) 5.33° (B) 4°

(C) 5° (D) 2.9°

(E) 5.4°

64. Two lenses of focal lengths +10 cm and –15 cm when

put in contact behave like convex lens. They will have

zero longitudinal chromatic aberration, if ratio of

dispersive powers is

(A) + 3/2 (B) + 2/3

(C) – 3/2 (D) – 2/3

(E) – 3/5

65. A beam of light of wavelength 600 nm from a distant

source falls on a single slit 1.0 mm wide and the

resulting diffraction pattern is observed on a screen 2 m

away. The distance between the first dark fringes on

either side of the central bright fringe is

(A) 1.2 cm (B) 1.2 mm

(C) 2.4 cm (D) 2.4 mm

(E) 3.2 cm

66. In a double slit experiment, instead of taking slits of

equal widths, one slit is made twice as wide as the

other, then in the interference pattern

(A) The intensities of both maxima and minima

increase

(B) The intensity of the maxima increases and the

minima have zero intensity

(C) The intensity of the maxima decreases and that

of the minima increases

(D) The intensity of the maxima decreases and the

minima have zero intensity

(E) Nothing can be predicted


(8)

67. A photon of energy 10.2 eV collide inelastically with

hydrogen atom in ground state. After few microseconds

another photon of energy 15 eV collides inelastically

with same hydrogen atom. Finally by a suitable

detector, we find

(A) Photon of energy 3.4 eV and electron of energy

1.4 eV

(B) Photon of energy 10.2 eV and electron of energy

1.4 eV

(C) Two photons of energy 3.4 eV

(D) Two photons of energy 10.2 eV

(E) Three photons of energy 10.2 eV

68. If the masses of deuterium and that of helium are

2.0140 amu and 4.0026 amu, respectively and that

22.4 MeV energy is liberated in the reaction, then the

mass of 6

3Li is

6 2 4 4

3 1 2 2Li H He He+ → +

(A) 6.015 amu (B) 4.068 amu

(C) 5.980 amu (D) 3.00 amu

(E) 2.652 amu

69. The number of neutrons released during the fission

reaction is

1 235 133 99

0 92 51 41n U Sb Nb Neutrons+ → + +

(A) 1 (B) 92

(C) 3 (D) 4

(E) 5

70. A radioactive nucleus undergoes a series of decay

according to the scheme

1 2 3 4A A A A A

If the mass number and atomic number of A are 180

and 72 respectively, then mass and atomic number of

A4 is

(A) 172,69 (B) 177,69

(C) 171,69 (D) 172,68

(E) 180,62

71. Consider the junction diode is ideal. The value of

current in the figure

–1 V–4 Vp – n

300

(A) Zero (B) 10–1A

(C) 10–2A (D) 10–3A

(E) 10–5A

72. The current gain for a common emitter amplifier is 49.

If the emitter current is 6.0 mA, then base current is

(A) 0.012 mA (B) 0.12 mA

(C) 0.24 mA (D) 1.2 mA

(E) 0.34 mA

73. In the disproportionation reaction,

3HClO3 HClO

4 + Cl

2 + 2O

2 + H

2O, the equivalent

mass of the oxidizing agent is (molar mass of HClO3

= 84.45)

(A) 16.89 (B) 32.22

(C) 84.45 (D) 28.15

(E) 29.7

74. Hyperconjugation is most useful for stabilizing which

of the following carbocations?

(A) neo-pentyl (B) tert-butyl

(C) iso-propyl (D) ethyl

(E) methyl

75. Concentrated sulphuric acid can be reduced by

(A) NaCl (B) NaF

(C) NaOH (D) NaNO3

(E) NaBr

76. A solid compound contains X, Y and Z atoms in a

cubic lattice with X atom occupying the corner.

Y atoms in the body centered positions and Z atoms

at the centers of faces of the unit cell. What is the

empirical formula of the compound?

(A) XY2Z

3(B) XYZ

3

(C) X2Y

2Z

3(D) X

8YZ

6

(E) XYZ

77. An aromatic hydrocarbon with empirical formula C5H

4

on treatment with concentrated H2SO

4 gave a

monosulphonic acid 0.104 g of the acid required

10 ml of N

NaOH20

for complete neutralization. The

molecular formula of hydrocarbon is

(A) C5H

14(B) C

10H

8

(C) C15

H12

(D) C20

H16

(E) C15

H20

78. Which one of the following has a different crystal

lattice from those of the rest?

(A) Ag (B) V

(C) Cu (D) Pt

(E) Au


(9)

79. The pH of a saturated solution of a metal hydroxide of

formula X(OH)2 is 12.0 at 298 K. What is the solubility

product of a metal hydroxide at 298 K

(in mol3L–3)?

(A) 2 × 10–6 (B) 1 × 10–7

(C) 5 × 10–5 (D) 2 × 10–1

(E) 5 × 10–7

80. In the dichromate dianion, the nature of bonds are

(A) For equivalent Cr – O bonds

(B) Six equivalent Cr – O bonds and one O-O bond

(C) Six equivalent Cr – O bonds and one Cr – Cr bond

(D) Six non-equivalent Cr – O bonds

(E) Six equivalent Cr – O bonds and one Cr – O – Cr bond

81. The enol form of acetone after treatment with D2O gives

(A) H C3 C CH

2

OD

(B) H C3 C CD

3

O

(C) H C2

C CH D2

OH

(D) H C2

C CHD2

OH

(E) D C2 C CD

3

OD

82. In Lassaigne’s test, a prussian blue colour is obtained

if the organic compound contains nitrogen. The blue

colour is due to

(A) K4[Fe(CN)

6] (B) Fe

4[Fe(CN)

6]3

(C) Na3[Fe(CN)

6] (D) Cu

2[Fe(CN)

6]

(E) Na2[Fe(CN)

5NO]

83. On addition of 1 mL solution of 10% NaCl to 10 mL

gold solution in the presence of 0.025 g of starch, the

coagulation is prevented because starch has the

following gold numbers

(A) 25 (B) 0.025

(C) 0.25 (D) 2.5

(E) 0.0025

84. Conversion of benzaldehyde to 3-phenylprop-2-en-1-oic

acid is

(A) Perkin condensation

(B) Claisen condensation

(C) Oxidative addition

(D) Aldol condensation

(E) None of these

85. Identify the mixture that shows positive deviation from

Raoult’s law

(A) CHCl3 + (CH

3)2CO (B) (CH

3)2CO + C

6H

5NH

2

(C) CHCl3 + C

6H

6(D) (CH

3)2CO + CS

2

(E) C6H

5N + CH

3COOH

86. A current strength of 9.65 A is passed through excess

fused AlCl3 for 5 h. How many liters of chlorine will be

liberated at STP? (F = 96500 C)

(A) 2.016 (B) 1.008

(C) 11.2 (D) 20.16

(E) 10.08

87. The mole fraction of methanol in 4.5 molal aqueous

solution is

(A) 0.250 (B) 0.125

(C) 0.100 (D) 0.075

(E) 0.055

88. Consider the following statements.

I. La(OH)3 is the least basic among hydroxides of

lanthanides

II. Zr4+ and Hf4+ possess almost the same ionic radii.

III. Ce4+ can act as an oxidizing agent.

Which of the above is/are true?

(A) (I) and (III) (B) (II) and (III)

(C) (II) only (D) ( I) and (II)

(E) (I) only

89. The limiting molar conductivities of HCl, CH3COONa

and NaCl are respectively 425, 90 and 125 mho cm2

mol–1 or Scm2mol–1 at the same temperature final

conductivity is 7.8 × 10–4 mho cm–1. The degree of

dissociation of 0.1M acetic acid solution at the same

temperature is

(A) 0.10 (B) 0.02

(C) 0.15 (D) 0.03

(E) 0.20

90. The temporary effect in which there is complete transfer

of a shared pair of pi-electrons to one of the atoms

joined by a multiple bond on the demand of an

attacking reagent is called

(A) Inductive effect

(B) Positive resonance effect

(C) Negative resonance effect

(D) Hyperconjugation

(E) Electromeric effect


(10)

91. The metal that produces red-violet colour in the non-

luminous flame is

(A) Ba (B) Ag

(C) Rb (D) Pb

(E) Zn

92. Halogens exist in –1, +1, +3, +5 and +7 oxidation

states. The halogen that exists only in –1 state is

(A) F (B) Cl

(C) Br (D) I

(E) At

93. According to Ellingham diagram, the oxidation

reaction of carbon to carbon monoxide may be used

to reduce which one of the following oxides at the

lowest temperature?

(A) Al2O

3(B) Cu

2O

(C) MgO (D) ZnO

(E) FeO

94. What is the overall formation equilibrium constant for

the ion [ML4]2–, given that â

4 for this complex is

2.5 × 1013?

(A) 2.5 × 1013 (B) 5 × 10–13

(C) 2.5 × 10–14 (D) 4.0 × 10–13

(E) 4.0 × 10–14

95. Select R-isomers from the following:

OHH

CHO

CH OH2

OHD

H

CH3

I II

HCl

Et

CH3

Et

OHH

III IV

H

COOH

NH2

H3C

V

CH3

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

(C) I, II and III (D) II and III

(E) I, III and V

96. The number of photons emitted per second by a

60 W source of monochromatic light of wavelength

663 nm is

(A) 4 × 10–20 (B) 1.5 × 1020

(C) 3 × 10–20 (D) 2 × 1020

(E) 1 × 10–20

97. When 0.2 g of 1-butanol was burnt in a suitable

apparatus, the heat evolved was sufficient to raise the

temperature of 200 g water by 5° C. The enthalpy of

combustion of 1-butanol in kcal mol–1 will be

(A) +37 (B) +370

(C) –370 (D) –740

(E) –14.8

98. Which of the following is a better reducing agent for

the following reduction?

RCOOHRCH2OH

(A) SnCl2/HCl (B) NaBH

4/ether

(C) H2/Pd (D) N

2H

4/C

2H

5ONa

(E) B2H

6/H

3O+

99. KCl crystallizes in the same type of lattice as does

NaCl. Given that

+ –

Na Clr /r = 0.55 and + –

K Clr /r = 0.74

What is the ratio of the side of the unit cell for KCl to

that of NaCl?

(A) 1.123 (B) 0.0891

(C) 1.414 (D) 0.414

(E) 1.732

100. Which set of terms correctly identifies the

carbohydrate shown?

H

H

HOH

HO H

O

CH2OH

HOH C2

1. Pentose 2. Hexose 3. Aldose4. Ketose 5. Pyranose 6. Furanose

(A) 1, 3 and 6 (B) 1, 3 and 5

(C) 2, 3 and 5 (D) 2, 3 and 6

(E) 1, 4 and 6

101. The percentage of an element M is 53 in its oxide of

molecular formula M2O

3. Its atomic mass is about

(A) 45 (B) 9

(C) 18 (D) 36

(E) 27


(11)

102. A 4p-orbital has

(A) One node (B) Two nodes

(C) Three nodes (D) Four nodes

(E) Five nodes

103. Streptomycin is used as

(A) Antipyretic (B) Mordant

(C) Antibiotic (D) Antihistamine

(E) Hypnotics

104. The number of isomers exhibited by [Cr(NH3)

3Cl

3] is

(A) 2 (B) 3

(C) 4 (D) 5

(E) 6

105. Which of the following molecules can act as an

oxidizing as well as a reducing agent?

(A) H2S (B) SO

3

(C) H2O

2(D) F

2

(E) H2SO

4

106. A sulphur colloid is prepared by

(A) Mechanical dispersion

(B) Oxidation

(C) Electrical dispersion

(D) Reduction

(E) Dialysis

107. Equal moles of water and urea are taken in flask. What

is the mass percentage of water in the solution?

(A) 23.077% (B) 30.77%

(C) 2.3077% (D) 0.23077%

(E) 46.154%

108. What is the half-life of 6C14, if its disintegration constant

is 2.31×10–4yr–1?

(A) 0.3 × 104yr (B) 0.3 × 103yr

(C) 0.3 × 108yr (D) 0.3 × 102yr

(E) 0.3 × 10–4yr

109. Rosenmund’s reduction of an acyl chloride gives

(A) An aldehyde (B) An alcohol

(C) An ester (D) A hydrocarbon

(E) An alkyl halide

110. Which of the following 1:1 mixture will act as buffer

solution?

(A) HCl and NaOH

(B) KOH and CH3COOH

(C) CH3COOH and NaCl

(D) CH3COONa and NH

4OH

(E) CH3COOH and CH

3COONa

111. The number of isomeric hexanes is

(A) 5 (B) 2

(C) 3 (D) 4

(E) 6

112. Which of the following statement is wrong?

(A) Using Lassaigne’s test nitrogen and sulphur

present in organic compound can be tested

(B) Using Beilstein’s test the presence of halogen in

a compound can be tested

(C) In Lassaigne’s filtrate the nitrogen present in an

organic compound is converted into NaCN

(D) Lassaigne’s test fail to identify nitrogen in diazo

compound

(E) In the estimate of carbon an organic

compound is heated with CaO in a combustion

tube

113. Cis-trans isomers generally

(A) Contains an asymmetric carbon atom

(B) Rotate the plane of polarized light

(C) Are enantiomorphs

(D) Contain a triple bond

(E) Contain double bonded carbon atoms

114. Wurtz’s reaction involves the reduction of alkyl halide

in presence of

(A) Zn/HCl (B) HI

(C) Zn/Cu couple (D) Na in ether

(E) Zn in an inert solvent

115. The compound that does not give Iodoform test is

(A) Ethanol (B) Ethanal

(C) Methanol (D) Propanone

(E) Acetophenone


(12)

116. Initial setting of cement is mainly due to

(A) Hydration and gel formation

(B) Dehydration and gel formation

(C) Hydration and hydrolysis

(D) Dehydration and dehydrolysis

(E) Hydration and oxidation

117. A certain metal will liberate hydrogen from dilute acids.

It will react with water to form hydrogen only when the

metal is heated and liberated water is in the form of

steam. The metal is probably

(A) Iron

(B) Potassium

(C) Copper

(D) Mercury

(E) Sodium

118. Hydrogen peroxide when added to a solution of

potassium permanganate acidified with sulphuric acid

(A) Forms water only

(B) Acts as a oxidizing agent

(C) Acts as a reducing agent

(D) Reduces sulphuric acid

(E) Produces hydrogen

119. Which of the following is not a thermoplastic?

(A) Polystyrene (B) Teflon

(C) Polyvinyl chloride (D) Nylon 6, 6

(E) Novalac

120. Barbituric acid and its derivatives are well known as

(A) Tranquilizers (B) Antiseptics

(C) Analgesics (D) Antipyretics

(E) Antibiotic

� � �

(13)

Time : 2:30 Hrs. MM : 480

GENERAL INSTRUCTIONS :

1. Kerala Engineering Agriculture Medical Common Entrance Exam (KEAM-CEE) has two papers. Paper-I for Physics

& Chemistry and Paper-II for Mathematics.

2. For each question, five options (A/ B/ C/ D/ E) are given, of which only one have to select.

3. For each correct answer 4 marks will be awarded and for each incorrect answer 1 mark will be deducted from the

total score.

4. Read each question carefully.

5. It is mandatory to use Blue/Black BallPoint Pen to darken the appropriate circle in the answer sheet.

6. Mark should be dark and should completely fill the circle in the answer sheet.

7. Do not use white-fluid or any other rubbing material on answer sheet. No change in the answer once marked.

8. Rough work must not be done on the answer sheet.

9. Student cannot use log tables and calculators or any other material in the examination hall.

10. Before attempting the question paper, student should ensure that the test paper contains all pages and no page

is missing.

Choose the correct answer :

1. What is the rank of the word SUCCESS as in a

dictionary?

(A) 272 (B) 270

(C) 329 (D) 331

(E) 271

2. A man has 10 formal shirts and 7 neck tie, in how

many ways can he dress?

(A) 17

(B) 16

(C) 70

(D) 69

(E) 72


Ph.: 011-47623456


forforforforforKEAM-2017KEAM-2017KEAM-2017KEAM-2017KEAM-2017

PAPER-II : MAPAPER-II : MAPAPER-II : MAPAPER-II : MAPAPER-II : MATHEMATHEMATHEMATHEMATHEMATICTICTICTICTICSSSSS

3. In an examination, there are 3 sections A, B, C

containing 5, 4, 3 questions respectively. Number of

ways to answer at least 1 question from each section.

(A) 5C1 × 4C

1 × 3C

1 × 29 (B) 5C

1 × 4C

1 × 3C

1 × 26

(C) 212 – 1 (D) 31× 15 × 7

(E) 5 × 4 × 3

4. The value of h for which 3x2 – 2hxy + 4y2 = 0 represents

a pair of coincident lines are

(A) 3 3 (B) 3

(C) 2 3 (D) 6

(E) ± 3

Complete Syllabus Test Mock Test for KEAM-2017 (Paper-II)

(14)

5. Centroid of the triangle, the equations of whose sides

are 12x2 – 20xy + 7y2 = 0 and 2x – 3y + 4 = 0 is

(A)8 8,

3 3

⎛ ⎞⎜ ⎟⎝ ⎠ (B)

4 4,

3 3

⎛ ⎞⎜ ⎟⎝ ⎠

(C) (2, 3) (D) (1, 1)

(E) (1, –1)

6. The lines lx + my + n = 0, mx + ny + l = 0 and

nx + ly + m = 0 are concurrent if

(A) l + m + n = 0

(B) l + m – n = 0

(C) l – m + n = 0

(D) l2 + m2 + n2 = lm + mn + nl

(E) l – m – n = 0

7. If the line x – y + 2 = 0 is a normal to the parabola

y2 – 6y – 4x + k = 0, then k is equal to

(A) 0 (B) 7

(C) 2 (D) –1

(E) 1

8. The equation of chord of parabola y2 = 8x having its

mid-point as (2, 3) is

(A) 3y – 4x – 1 = 0

(B) 4y – 3x – 6 = 0

(C) 3y + 4x – 17 = 0

(D) 3x – 4y + 7 = 0

(E) 3x + 4y + 1 = 0

9. A point on the curve y2 = 4x, which is nearest to the

point (2, 1) is

(A) (1, –2) (B) (–2, 1)

(C) 1, 2 2 (D) (1, 2)

(E) (0, 0)

10. For the hyperbola 3y2 – x2 = 3, the coordinates of

foci and vertices respectively are

(A) (0, ±1), (0, ±2)

(B) (±1, 0), (±2, 0)

(C) (0, ±2), (0, ±1)

(D) (±2, 0), (±1, 0)

(E) (0, 0), (0, ±1)

11. If e and e are the eccentricities of the hyperbola

2 2

2 2– 1

x y

a b and its conjugate, then

2 2

1 1

e e

is

equal to

(A) e2 + e2 (B) 2

(C)1

2(D) 1

(E) ee´

12. The centre of the hyperbola

4x2 – 9y2 – 24x + 18y – 9 = 0 is

(A) (1, 1) (B) (3, 1)

(C) (1, 3) (D) (2, 3)

(E) (0, 0)

13. The value of

2

2 2

log – 2lim

–x e

x

x e equals

(A) e (B) e2

(C)1

e(D)

2

1

e

(E) 1

14. The value of

1

lim(3 10 7 )n n n n

n is

(A) 3 (B) 1

(C) 11 (D) 7

(E) 10

15. Let f(2) = 4, f(2) = 4. Then 2

(2) – 2 ( )lim

2 –x

xf f x

x is

(A)1

–3

(B) –2

(C) 1 (D) 3

(E) 4

16. The minimum value of 2x2 + x – 1 is

(A)1

4 (B)

3

4

(C)9

8 (D)

9

4

(E)1

2

Mock Test for KEAM-2017 (Paper-II) Complete Syllabus Test

(15)

17. Let , be the roots of x2 + (3 – )x – = 0. Then the

value of for which 2 + 2 is minimum, is

(A) 0 (B) 1

(C) 2 (D) 3

(E) –1

18. The real values of ‘a’ for which the quadratic equation

2x2 – (a3 + 8a + 1) x + a2 – 4a = 0 possesses

roots of opposite signs are given by

(A) (5, ) (B) (0, 4)

(C) (0, ) (D) (7, )

(E) (1, 1)

19. The radical axis of x2 + y2 – 3x – 6y + 14 = 0,

x2 + y2 – x – 4y + 8 = 0 is

(A) x – y – 3 = 0 (B) x + y – 3 = 0

(C) x + y + 3 = 0 (D) x – y + 3 = 0

(E) x + y + 1 = 0

20. The circles

x2 + y2 – 2y – 8 = 0 and x2 + y2 – 2x – 2y = 0

(A) Touch each other

(B) One of the circles lies entirely inside the other

(C) Each of these circles lies outside the other

(D) They intersect in two points

(E) None of these

21. If the vertex of a parabola is (–3, 0) and the directrix

is the line x + 5 = 0 then its equation is

(A) y2 = 4(x + 3) (B) (y + 3)2 = 8x

(C) y2 = 8x (D) y2 = 8(x + 3)

(E) y2 = –8x

22. The sum of focal distances of any point on the ellipse

9x2 + 16y2 = 144 is

(A) 4 (B) 8

(C) 16 (D) 12

(E) 5

23. If 2x y

a b , touches the ellipse

2 2

2 21

x y

a b ,

then find the eccentric angle of the point of contact.

(A) 45° (B) 60°

(C) 30° (D) 75°

(E) 90º

24. Product of perpendiculars drawn from the foci upon

any tangent to the ellipse 5x2 + 3y2 = 45 is

(A) 3 (B) 5

(C) 8 (D) 15

(E) 9

25. Number of solution of trigonometric equation

sin + tan – sin2 = 0 in [0, 5) is

(A) 7 (B) 9

(C) 10 (D) 11

(E) 5

26. Number of solutions of the equation sin3x = sinx for

50

2x

⎡ ⎤ ⎢ ⎥⎣ ⎦

is

(A) 9 (B) 8

(C) 7 (D) 10

(E) 3

27. Number of solutions of the equation

7cos2 + 3sin2 = 4, [0, 3) is

(A) 6 (B) 12

(C) 9 (D) 3

(E) 7

28. In any ABC, 1 cos( )cos

1 cos( )cos

A B C

A C B

is equal to

(A)

2 2

2 2

a b

a c

(B)

2 2

2 2

a c

a b

(C)

2 2

2 2

a b

a c

(D)

2 2

2 2

a c

a b

(E) None of these

29. In a ABC, (s – b)(s – c) = s(s – a), then angle A is

equal to

(A) 45° (B) 90°

(C) 30° (D) 60°

(E) 180º

30. In ABC, sin( )

sin

A B

C

is equal to

(A)

2 2

2

a b

c

(B)

2

2 2

c

a b

(C)

2

2 2

c

a b(D)

2 2

2

a b

c

(E)

2 2 2

2

a b c

c


(16)

31. If 4x + 3 2x + 17 and 3x + 5 < – 2, then x

(A) (1, 7] (B) (1, 7)

(C) [1, 7) (D)

(E) None of these

32. Solve for x, |x – 1| 5

(A) x [–4, 6] (B) x [–5, 5]

(C) x (–, 6] (D) x (–, –4] [6, )

(E) x [1, 2]

33. Solve for x, 2

1| 4 |x

(A) x (–, 2) (6, ) (B) x (2, 6)

(C) x (2, 4) (4, 6) (D) x (–, 2) (4, )

(E) x (2, 6)

34. The number of ways that 5 letters can be posted in 5

envelopes such that 4 letters are in wrong envelopes.

(A) 9 (B) 10

(C) 11 (D) 45

(E) 35

35. Find the exponent of 8 in 100!

(A) 26 (B) 13

(C) 16 (D) 32

(E) 12

36. There are 3 apartments A, B and C for rent in a building.

Each apartment will accept either 3 or 4 occupants.

The number of ways of renting the apartments to 10

students is

(A) 12600 (B) 10800

(C) 13500 (D) 2100

(E) 2000

37. Find the term independent of x in the expansion of

113

2⎛ ⎞⎜ ⎟⎝ ⎠

x

x

(A) 11C62536 (B) 11C

52635

(C) 0 (D) 11C42734

(E) None of these

38. The value of

2 2 2 2

0 1 2....

nC C C C is equal to

(A) 2n+1Cn

(B) 2nCn

(C) 2n–1Cn–1

(D) 2n–1Cn+1

(E) 1

39. The value of

12C1 + 22C

2 + 32C

3 + ... + n2C

n is equal to

(A) (n + 1)2n–1 (B) n(n + 1)2n–1

(C) n(n – 1)2n–2 (D) n(n + 1)2n–2

(E) 0

40. The ratio of the sum to n terms of two distinct A.P’s is

2 3

7 1

n

n

, then the ratio of their 9th terms is

(A)21

64(B)

1

3

(C)37

120(D)

41

134

(E)1

2

41. The value of

–2

–1

1

3

5

r

r

r

∑ is equal to

(A)35

16(B)

7

4

(C)15

8(D)

5

6

(E) 1/3

42. Given that a1, a

2, a

3, ..., a

n – 1 are in H.P. Then the

value of a1a

2 + a

2a

3 + ... + a

n – 2. a

n – 1 is equal to

(A)1 –1

–1

n

n

a a(B)

1 –1

– 2

n

n

a a

(C) (n – 1)a1a

n–1(D) (n – 2)a

1a

n–1

(E) 0

43. The orthocentre of the triangle formed by the coordinate

axes and the line x + y = 4 is

(A) (0, 4) (B) (4, 0)

(C) (4, 4) (D) (0, 0)

(E) (1,1)

44. The slope of a line which passes through the origin

and the mid-point of the line segment joining the points

P(0, –4) and B(8, 0)

(A) 2 (B)1

2

(C) 0 (D)

(E) 1

45. Product of slope of two perpendicular lines is

(A) 1 (B) 0

(C) –1 (D) –2

(E) –3


(17)

46. If a set A has 3 elements then the number of proper

subsets of the power set of A is equal to

(A) 8 (B) 255

(C) 256 (D) 254

(E) 257

47. If U = {1, 3, 5, 7, 9, 11, 13, 15},

A = {3, 5, 13, 15} and B = {1, 11, 15}

then 'A B is

(A) {15} (B) {3, 5, 13}

(C) {1, 11, 15} (D) (E) None of these

48. If A and B are two sets such that n(A) = 15,

n(B) = 18 and ( ) 28n A B then n(A – B) is equal

to

(A) 10 (B) 0

(C) 5 (D) 1

(E) None of these

49. If A = {1, 2, 3, 4}, B = {2, 4, 6} then the number of

elements in (A × B) (B × A) is

(A) 12 (B) 3

(C) 4 (D) 5

(E) None of these

50. Let A = {1, 2, 3, 4, 5}, B = {1, 3, 5, 7, 9}

Which of the following is not a relation from A to B?

(A) R1 = {(1, 1), (2, 3), (3, 5), (5, 7)}

(B) R2 = {(1, 1), (2, 1), (3, 3), (4, 3), (5, 5)}

(C) R3 = {(1, 1), (1, 3), (3, 5), (3, 7), (5, 7)}

(D) R4 = {(1, 3), (2, 5), (2, 4), (7, 9)}

(E) None of these

51. Which of the following pictorial representation

represents a function?

(A)

1

2

3

1

2

f

(B)

1

2

3

4

1

2

3

f

(C)

1

2

3

4

1

2

3

f

(D)

f

1

2

3

4

1

2

3

(E) None of these

52. The value of 17

sin3

⎛ ⎞⎜ ⎟⎝ ⎠

is equal to

(A)1

2 (B)

1

2

(C)3

2(D)

3

2

(E) 0

53. If sin = 24

25 and lies in the second quadrant,

then sec + tan =

(A) –3 (B) –5

(C) –7 (D) –9

(E) 1

54.3 5 7

sin cos tan cot2 2 2 2

⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠

is equal to

(A) –sin2 (B) –cos2

(C) sincos (D) –sincos

(E) sin

55. If A + B = 4

, then (1 + tanA)(1 + tanB) is equal to

(A) 2 (B) 3

(C) 1 (D) 4

(E) –1

56. The value of sin · sin(60° + ) · sin(60° – ) is equal

to

(A)1sin3

4 (B)

1sin3

2

(C)1sin3

4 (D)

1sin2

2

(E) sin3

57. The value of 3 3

cos cos4 4

⎛ ⎞ ⎛ ⎞ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠x x is equal to

(A) 2 sinx (B) 2 sinx

(C)1

sin2

x (D)1

sin2

x

(E) 2 cosx


(18)

58. Value of

2

2

1 tan4

1 tan4

A

A

⎛ ⎞ ⎜ ⎟⎝ ⎠

⎛ ⎞ ⎜ ⎟⎝ ⎠

is equal to

(A) cos 2A (B) sin 2A

(C) tan 2A (D) cot 2A

(E) tan A

59. The value of 1 sin cos

1 sin cos

is equal to

(A) tan(/2) (B) cot(/2)

(C) cos(/2) (D) sin(/2)

(E) sec(/2)

60. The maximum value of 3sinx + 4cosx + 5 is equal

to

(A) 5 (B) 10

(C) 8 (D) 6

(E) –1

61. Let P(n) be a statement and let P(n) P(n + 1) for all

natural numbers n. Also P(1) is true, then P(n) is true

(A) For all n N

(B) For all n > m, m being a fixed positive integer

(C) For all n > 1

(D) Nothing can be said

(E) None of these

62. 9n – 8n – 1 is divisible by 64 is

(A) Always true for all n N

(B) Always false for all n N

(C) Always true for rational values of n

(D) Always true for irrational values of n

(E) None of these

63. xn – yn is divisible by x + y is true when n N is

of the form (k N)

(A) 4k + 1 (B) 4k + 3

(C) 4k + 7 (D) 2k

(E) 2k – 1

64. The square root of 3 + 4i is equal to

(A) ±(2 – i) (B) ±(2 + i)

(C) ±(3 + i) (D) ±(3 – i)

(E) 1 + i

65. The value of (3 + + 32)4 is equal to

(A) 16 (B) –16

(C) 16 (D) 162

(E) 1

66. The product of all, nth roots of unity is

(A) 0 (B) (–1)n

(C) (–1)n–1 (D) 1

(E) –1

67. Minimum value of |z – 6| + |z – 8i| is equal to

(A) 6 (B) 10

(C) 8 (D) 7

(E) 5

68. The locus of z given by 1

11

z

z

is

(A) A circle (B) An ellipse

(C) A straight line (D) Parabola

(E) None of these

69. If and are the root of the equation

4x2 + 3x + 7 = 0, then 1 1

(A)3

7 (B)

3

7

(C) 16 (D) 8

(E)1

2

70. Let R = {(n, m) | n is a factor of m} be a relation on the

set of integers then R is

(A) Reflexive and symmetric

(B) Transitive and reflexive

(C) Reflexive, transitive and symmetric

(D) Reflexive, transitive and not symmetric

(E) None of these

71. Let f : R R be a relation given by

1 1, , ( 2, 2), ( 3, 3 )

2 2f

⎡ ⎤⎛ ⎞ ⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦, then f is

(A) Reflexive only

(B) Symmetric only

(C) Transitive only

(D) Symmetric and transitive

(E) Equivalence


(19)

72. Total number of reflexive relation on a set A, where

A = {1, 2, 3, 4} are

(A) 212 (B) 210

(C) 1 (D) 64

(E) 24

73. The area enclosed by the ellipse

2 2

116 9

x y is

(A) 144sq. unit (B) 12sq. unit

(C) 36 sq. unit (D) 12 sq. unit

(E) 6 sq. unit

74. The area enclosed by the curves y = x2, y = (x – 2)2

and the x-axis is equal to

(A)2

3 sq. unit (B)

3

2 sq. unit

(C)1

3 sq. unit (D)

4

3 sq. unit

(E)1

2 sq. unit

75. The area bounded by the inverse function of

f(x) = logex, x-axis and y-axis is

(A) 1 sq. unit (B) 2 sq. unit

(C) e sq. unit (D) 2e sq. unit

(E) 3 sq. unit

76. The degree of the D.F.

32

21 0

⎛ ⎞ ⎜ ⎟⎝ ⎠

d y dy

dxdx

is

(A) 1 (B) 4

(C) 3 (D) 6

(E) 2

77. Differential equation of the family of curves

y = ex(A cos x + B sin x) is

(A)

2

2– 2 2 0 d y dy

ydxdx

(B)

2

22 2 0 d y dy

ydxdx

(C)

2

2– 2 – 2 0d y dy

ydxdx

(D)

2

22 – 2 0

d y dyy

dxdx

(E) None of these

78. The general solution of differential equation

–

dy x y

dx x y is

(A) 2 2 x y C

(B) –1 2 2

tan log⎛ ⎞ ⎜ ⎟⎝ ⎠

yC x y

x

(C)–1 2 2

tan log yx x y C

x

(D) y = x

(E) y = –x

79. Coinitial vectors in diagram are

bd

a

c

(A) ,a d

� ��

(B) ,a c

� �

(C) ,a b

� �

(D) ,b c� �

(E) None of these

80. If 26, 7a b �

�

and 35a b �

�

, then find the

value of a b� �

.

(A) 7 26 – 35 (B) 49

(C) 7 (D) 8

(E) Data is insufficient

81. If 0a b c �

� �

then

(A) a b b c � �

� �

(B) b c c a �

� � �

(C) a b c a �

� � �

(D) a c c b � � � �

(E) All of these

82. The equation of line in Cartesian form passing through

(0, 1, 2) and is parallel to a vector which has direction

ratio (3, –1, 1) is

(A)3 – 2 –1

3 –1 1

x y z

(B)1 – 2

3 –1 1

x y z

(C)–1 – 2

–3 1 1 x y z

(D)3 1 1

1 –1 2

x y z

(E) None of these


(20)

83. Angle between the lines x = 2z = 0 and x = 3z = 0

is

(A)1 7

cos50

(B)

2

(C)4

(D)

–1 –1

1 1cos – cos

3 2

(E) None of these

84. The shortest distance between the lines

–1 – 2 – 3

2 3 4

x y z and –1 – 4 – 5

3 4 5

x y z is

equal to

(A)1

6(B)

2

6

(C)3

6(D) 6

(E) None of these

85. A vertex of the linear inequalities 2x + 3y 6,

x + 4y 4, x, y 0, is

(A) (1, 0) (B) (1, 1)

(C)12 2

,5 5

⎛ ⎞⎜ ⎟⎝ ⎠ (D)

2 12,

5 5

⎛ ⎞⎜ ⎟⎝ ⎠

(E) (0, 0)

86. For the following feasible region, the linear

constraints are

X

Y

3 + 2 = 12x y

x y + 3 = 11

(A) x 0, y 0, 3x + 2y 12, x + 3y 11

(B) x 0, y 0, 3x + 2y 12, x + 3y 11

(C) x 0, y 0, 3x + 2y 12, x + 3y 11

(D) x 0, y 0, 3x + 2y 12, x + 3y 11

(E) None of these

87. Three fair coins are tossed. Find the probability that

the outcomes are all tails, if at least one of the coins

shows a tail

(A)1

7(B)

1

8

(C)7

8(D)

2

3

(E) 1

88. Let ‘*’ be the binary operation defined on a set of

integers so that 2

* ( )a b a b then ‘*’ is

(A) Commutative but not associative

(B) Associative but not commutative

(C) Both associative and commutative

(D) Neither commutative nor associative

(E) None of these

89. Let 0, 0

( )2, 0

xg x

x

⎧ ⎨ ⎩

and f(x) = sgn(–|x|) + sgn(x) +

g(x), then f(x) is

(A) Odd function

(B) Even function

(C) Neither odd nor even

(D) Both odd and even function

(E) None of these

90.

1

33( ) ( )f x x x x is

(A) An odd function

(B) An even function

(C) Both odd and even function

(D) Neither odd nor even function

(E) None of these

91.

cos cos –

sin – cos2

x x

x x

⎛ ⎞ ⎜ ⎟⎝ ⎠

is equal to

(A) –cot2x (B) cot2x

(C) tan2x (D) –tan2x

(E) cot x

92. If tan + sec = 5

3 and ‘’ is acute angle then the

value of sin is equal to

(A)3

5(B)

8

17

(C)3

10(D)

8–17

(E)1

2−


(21)

93. In any triangle ABC,

tan – tan2 2

tan tan2 2

A B

A B is equal to

(A)–a b

a b(B)

–a b

c

(C)–a b

a b c (D)

c

a b

(E)a b

ab

94. Range of f(x) = sin–1x + cos–1x + tan–1x is

(A)3

,4 4

⎡ ⎤⎢ ⎥⎣ ⎦

(B) (0, )

(C) 0, (D) (–, )

(E) ,2 2

⎡ ⎤⎢ ⎥⎣ ⎦

95. Equation of the circle passing through origin having

centre at (1, 1) is

(A) x2 + y2 – 2x – 2y = 0

(B) x2 + y2 – 2x – 2y + 1 = 0

(C) x2 + y2 + 2x + 2y = 0

(D) x2 + y2 + 2x + 2y + 1 = 0

(E) None of these

96. Combined equation of angle bisectors of the pair of

straight lines xy = 0 is

(A) x2 – y2 = 0

(B) x2 + y2 – 2xy = 0

(C) x2 – 4y2 = 0

(D) xy = 0

(E) x2 + y2 – xy = 0

97. If 1 1

sin cos,

t tx a y a

, then

dy

dx equal to

(A)y

x(B)

y

x

(C)x

y(D)

x

y

(E)

2

2

x

y

98. Let f(x) = x|x|, then f (0) is equal to

(A) 1 (B) –1

(C) 0 (D) ±1

(E) None of these

99. If f(x) is derivable and g(x) is non-derivable at x = a,

then which of the following function is necessarily non-

derivable at x = a?

(A) f(x) + g(x) (B) f(x) × g(x)

(C)( )

( )

f x

g x(D)

( )

( )

g x

f x

(E) All of these

100. If 1 2

2 3X

⎡ ⎤ ⎢ ⎥⎣ ⎦

and X2 – aX + bI = 0, then a + b is

equal to

(A) 5 (B) – 3

(C) 3 (D) – 5

(E) 2

101. If 1 1

0 1X

⎡ ⎤ ⎢ ⎥⎣ ⎦

, then Xn + 2X – I is equal to

(A)

1 3

0 1

n

n

⎡ ⎤⎢ ⎥⎣ ⎦

(B)

2 3

0 1n

⎡ ⎤⎢ ⎥⎣ ⎦

(C)

1 2

0 1

n n

n

⎡ ⎤⎢ ⎥⎣ ⎦

(D)

2 2

0 2

n ⎡ ⎤⎢ ⎥⎣ ⎦

(E)

0 1

1 0

⎡ ⎤⎢ ⎥⎣ ⎦

102. If 2 1 4

2 33 2 5

A B⎡ ⎤

⎢ ⎥⎣ ⎦

and 5 0 3

21 6 2

A B⎡ ⎤

⎢ ⎥⎣ ⎦

,

then the value of 4A + 3B is

(A)

20 5 2

9 26 13

⎡ ⎤⎢ ⎥⎣ ⎦

(B)

20 3 2

9 26 13

⎡ ⎤⎢ ⎥⎣ ⎦

(C)

20 5 18

9 26 13

⎡ ⎤⎢ ⎥⎣ ⎦

(D)

20 5 2

1 26 5

⎡ ⎤⎢ ⎥⎣ ⎦

(E) None of these

103. Let 11 12

21 22

a aA

a a

⎡ ⎤ ⎢ ⎥⎣ ⎦

, then minor of a22

is

(A) a11

(B) –a11

(C) a12

(D) a21

(E) a22


(22)

104. The value of

2

2

2

1

1

1

is equal to

(where ‘’ is the complex cube root of unity)

(A) (B) 1

(C) 1 + (D) Zero

(E) –1

105. If 2 2

1 1A

⎡ ⎤ ⎢ ⎥⎣ ⎦

, then A–1 is

(A)

1 1

1 1

2 2

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

(B)1 1

2 2

⎡ ⎤⎢ ⎥⎣ ⎦

(C)1 2

1 2

⎡ ⎤⎢ ⎥⎣ ⎦

(D) Does not exist

(E)0 1

1 0

⎡ ⎤⎢ ⎥⎣ ⎦

106.2

0

1 coslim

4x

x

x

is equal to

(A)1

4(B)

1

2

(C)1

5(D) 0

(E)1

8

107.2

0

2lim

x x

x

e e

x

is equal to

(A) –1 (B) 4

(C)1

2(D)

1

2

(E) 1

108.

1

0

lim (cos )x

x

x

is equal to

(A)1

e(B) e

(C) 0 (D) 1

(E) –1

109. The function f(x) = x + tan x has

(A) One maxima and one minima

(B) Only one maxima

(C) Only one minima

(D) Neither maxima nor minima

(E) None of these

110. If volume of a sphere is changing at a rate of

100cm3/s, then the rate of change of radius at the

instant when radius is 10 cm, is

(A)1

16(B)

1

8

(C)1

4(D)

1

2

(E)1

12

111. The function f(x) = tan–1x – x decreases in the

interval

(A) (1, ) (B) (–, )

(C) (0, ) (D) (–1, )

(E) None of these

112.

5

76

log1

K

K

x xdx a c

xx x

⎛ ⎞ ⎜ ⎟⎝ ⎠

∫ , then a and k

are

(A)2 5,

5 2(B)

1 2,

5 5

(C)5 1,

2 2(D)

2 1,

5 2

(E)1

5

113. The area bounded by the coordinate axes and normal

to the curve y = logex at the point P(1, 0) is

(A) 1 (B)1

4

(C)1

3(D)

1

2

(E)1

e


(23)

114.2

1

x

x

edx

e∫ is equal to

(A) tan–1 ex + C (B) tan–1 e2x + C

(C) 2tan–1 ex (D) 2tan–1 e–x + x + C

(E) 2tan–1 e2x + x + C

115. If f(x) = a log|x| + bx2 + x has its extremum values

at x = –1 and x = 2, then

(A)1

2,2

a b (B)1

2, –2

a b

(C)1, 2

2a b (D)

1– 2, –

2a b

(E) a = b = – 1

116. If the tangent to the curve 2y3 = ax2 + x3 at the

point (a, a) cuts intercepts and on the

coordinate axes such that 2 + 2 = 61, then a is

equal to

(A) ± 20 (B) ± 10

(C) ± 30 (D) ± 25

(E) ± 21

117. Let f(x) = 1 + 5x2 + 52x4 + ... + 510x20 be a

polynomial in real variable x, then f(x) has

(A) Neither maximum nor minimum

(B) Only one maximum

(C) Only one minimum

(D) Only one maximum and only one minimum

(E) Two extremum

118. If f(x) =

2–1

3

a⎛ ⎞⎜ ⎟⎝ ⎠

x3 + (a – 1)x2 + 2x + 1 is a

decreasing function of x in R, then the set of

possible values of a (independent of x) is

(A) [–3, 1] (B) R – [–3, 1]

(C) R – {–1, 1} (D) (–3, 1)

(E) [–1, 1]

119. Let f : R R be a function defined as

( ) 129 – 1x

x xf x is

(A) Even

(B) Odd

(C) Neither even nor odd

(D) Both even and odd

(E) None of these

120. Let g(x) be a polynomial function satisfying

g(x)g(y) = g(x) + g(y) + g(xy) – 2 for all x, y R and

g(1) 1. If g(4) = 17, then g(7) is equal to

(A) –50

(B) 50

(C) 48

(D) 8

(E) 49

� � �

(13)

1. (D)

2. (A)

3. (D)

4. (A)

5. (C)

6. (A)

7. (C)

8. (D)

9. (B)

10. (A)

11. (B)

12. (A)

13. (A)

14. (E)

15. (B)

16. (B)

17. (C)

18. (C)

19. (A)

20. (C)

21. (C)

22. (B)

23. (E)

24. (A)

ANSWERS

Time : 2:30 Hrs. MM : 480


Ph.: 011-47623456


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25. (B)

26. (D)

27. (B)

28. (C)

29. (C)

30. (D)

31. (D)

32. (D)

33. (A)

34. (A)

35. (A)

36. (C)

37. (E)

38. (D)

39. (A)

40. (C)

41. (B)

42. (D)

43. (A)

44. (A)

45. (D)

46. (C)

47. (C)

48. (C)

49. (D)

50. (C)

51. (D)

52. (D)

53. (A)

54. (A)

55. (C)

56. (C)

57. (B)

58. (D)

59. (D)

60. (B)

61. (C)

62. (D)

63. (D)

64. (B)

65. (D)

66. (A)

67. (B)

68. (A)

69. (D)

70. (A)

71. (A)

72. (B)

73. (A)

74. (B)

75. (E)

76. (B)

77. (C)

78. (B)

79. (E)

80. (E)

81. (A)

82. (B)

83. (A)

84. (A)

85. (D)

86. (D)

87. (D)

88. (B)

89. (B)

90. (E)

91. (C)

92. (A)

93. (B)

94. (A)

95. (C)

96. (D)

97. (C)

98. (E)

99. (A)

100. (A)

101. (E)

102. (B)

103. (C)

104. (A)

105. (C)

106. (B)

107. (A)

108. (A)

109. (A)

110. (E)

111. (A)

112. (E)

113. (E)

114. (D)

115. (C)

116. (A)

117. (A)

118. (C)

119. (E)

120. (A)

(24)

1. (D)

2. (C)

3. (D)

4. (C)

5. (A)

6. (A)

7. (E)

8. (A)

9. (D)

10. (C)

11. (D)

12. (B)

13. (D)

14. (E)

15. (E)

16. (C)

17. (C)

18. (B)

19. (B)

20. (B)

21. (D)

22. (B)

23. (A)

24. (E)

25. (C)

26. (B)

27. (A)

28. (C)

29. (B)

30. (D)

31. (D)

32. (A)

33. (C)

34. (D)

35. (D)

36. (A)

37. (C)

38. (B)

39. (D)

40. (C)

41. (D)

42. (D)

43. (D)

44. (B)

45. (C)

46. (B)

47. (B)

48. (A)

49. (C)

50. (D)

51. (C)

52. (D)

53. (C)

54. (C)

55. (A)

56. (A)

57. (A)

58. (B)

59. (A)

60. (B)

61. (A)

62. (A)

63. (D)

64. (B)

65. (C)

66. (C)

67. (B)

68. (C)

69. (A)

70. (B)

71. (D)

72. (A)

ANSWERS

Time : 2:30 Hrs. MM : 480


Ph.: 011-47623456


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73. (B)

74. (A)

75. (A)

76. (E)

77. (A)

78. (B)

79. (A)

80. (C)

81. (E)

82. (B)

83. (A)

84. (B)

85. (C)

86. (A)

87. (A)

88. (A)

89. (D)

90. (B)

91. (B)

92. (B)

93. (B)

94. (A)

95. (A)

96. (A)

97. (B)

98. (C)

99. (A)

100. (C)

101. (D)

102. (A)

103. (A)

104. (D)

105. (D)

106. (E)

107. (E)

108. (D)

109. (D)

110. (C)

111. (B)

112. (A)

113. (D)

114. (A)

115. (B)

116. (C)

117. (C)

118. (B)

119. (A)

120. (B)

mock test for

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