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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)
(2)
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
(3)
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 %
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)
(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
Mock Test for KEAM-2017 (Paper-I) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)
(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
Mock Test for KEAM-2017 (Paper-I) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)
(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
Mock Test for KEAM-2017 (Paper-I) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)
(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
Mock Test for KEAM-2017 (Paper-I) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-I)
(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
� � �
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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
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-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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-II)
(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
Mock Test for KEAM-2017 (Paper-II) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-II)
(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
Mock Test for KEAM-2017 (Paper-II) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-II)
(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−
Mock Test for KEAM-2017 (Paper-II) Complete Syllabus Test
(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
Complete Syllabus Test Mock Test for KEAM-2017 (Paper-II)
(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
Mock Test for KEAM-2017 (Paper-II) Complete Syllabus Test
(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
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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
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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)