Manipal MET 2027 Sample Paper

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

Manipal MET 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

150 600 150 Min +4 / −1

GENERAL INSTRUCTIONS

1. This paper contains 150 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 4 marks; 1 mark is deducted for each wrong answer.

4. Total time allowed is 150 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

Manipal MET 2027
SAMPLE QUESTION PAPER

Questions 150 Max Marks 600 Time 150 Min Marking +4 / −1

Attempt all questions. Choose the one correct option for each.

PHYSICS

1. The temperatures of two bodies A and B are 2. A thin walled glass sphere of radius 2.5 cm is filled
respectively 727°C and 327°C. The ratio Ha:Hb of the with water. An object (O) is placed at 7.5 cm from the
rates of heat radiated by them is surface of the sphere. Neglecting the effect of glass wall,
at what distance the image (I) of the object, measured
(A) 727 : 327
from the centre of sphere is formed?
(B) 5:3
(A) 20 cm
(C) 25:9,
(B) 15 cm
(D) 625 : 81
(C) 10 cm

(D) 7.5 cm

3. A stone is projected from the ground with velocity 50 4. Two coils X and Y are placed in a circuit such that a
m/s at an angle 30° with horizontal. It crosses a wall after current changes by 3 A in coil X and magnetic flux
3 s. How far beyond the wall the stone will strike the changes of 1.2 Wb occurs in Y. The value of mutual
ground? (g = 10 m/s) inductance of the coils is

(A) 90.2 m (A) 0.2 H

(B) 12.5 m (B) 0.4 H

(C) 86.5 m (C) 0.6 H

(D) 125√3 m (D) 3.6 H

5. An artificial satellite moving in a circular orbit around 6.  In Young's experiment, using red light (λ= 6600 Å), 60
the earth has a total (kinetic + potential) energy En, its fringes are seen in the field of view. How many fringes
potential energy is will be seen by using violet light (λ= 4400 Å)?

(A) -Eₒ (A) 10

(B) 1.5 Eₒ (B) 20

(C) 2 Eₒ (C) 45

(D) Eₒ (D) 90

7. A short solenoid of length 4 cm, radius 2 cm and 100 8. The plane faces of two identical plano-convex lenses
turns is placed inside and on the axis of a long solenoid each having a focal length of 50 cm are placed against
of length 80 cm and 1500 turns. A current of 3 A flows each other to form a usual biconvex lens. The distance
through the short solenoid. The mutual inductance of two from this lens combination at which an object must be
solenoids is placed to obtain a real, inverted image which has the
same size as the object is
(A) 2.96x10⁻⁴ H

(B) 5.3x 10⁻⁵ H (A) 50 cm

(C) 3.52x10⁻³ H (B) 25 cm

(D) 8.3 x 10⁻⁵ H (C) 100 cm

(D) 40 cm

9. In the arrangement, the minimum value of tension in 10. Three blocks of masses m₁ m₂ and m₃ are connected
the string to prevent it from sliding down is by mass less string as shown kept on a friction less table.
They are pulled with a force T₃=40 N . If m₁=10 kg , m₂=6
(A) 6 N
kg and m₃=4 kg, the tension T₂ will be
(B) 8 N

(C) 10.8N

(D) zero
(A) 20N

(B) 40 N

(C) 10N

(D) 32 N

11. Two identical cells whether connected in parallel or in 12. The angle of a prism is 60° and its refractive index is
series gives the same current when connected to an √2 . The angle of minimum deviation suffered by a ray of
external resistance 1.5 Ω. Find the value of internal light in passing through it is
resistance of each cell.
(A) about 20°
(A) 1Ω (B) 30°
(B) 0.5Ω (C) 60°
(C) zero (D) 45°
(D) 1.5Ω

13. In photoelectric effect, the photo current 14. What is the Boolean equation for the figure?

(A) increases with increase of frequency of incident photon

(B) decreases with increase of frequency of incident photon

(C) does not depend on the frequency of photon but
depends only on intensity of incident light

(D) depends both on intensity and frequency of incident
beam

(A)

(B)

(C)

(D)

15. The momentum of a body is increased by 25%. The 16. A 2 kg copper block is heated to 500°C and then it is
kinetic energy is increased by about placed on a large block of ice at 0°C. If the specific heat
capacity of copper is 400 J/kg/C and latent heat of fusion
(A) 25%
of water is 3.5 x 105 J/Kg, the amount of ice that can melt
(B) 5 %
is
(C) 56 %
(A) 7/8 kg
(D) 38 %
(B) 7/5 kg

(C) 8/7 kg

(D) 5/7 kg

17. First diffraction minima due to a single slit of width 1 18. A string of density 7.5 g cm⁻³ and area of cross-
x 10-5cm is at θ = 30°. Then wavelength of the light used section 0.2 mm² is stretched under a tension of 20N.
is When it is plucked at the mid-point, the speed of the
transverse wave on the wire is
(A) 400 Å

(B) 500 Å (A) 116 ms⁻¹

(C) 600 Å (B) 40 ms⁻¹

(D) 625 Å (C) 200 ms⁻¹

(D) 80 ms⁻¹

19. The ratio of the wavelength of first line of Balmer 20. A long wire carries a steady current. It is bent into a
series to the first line of Lyman series is circle of one turn and the magnetic field at the centre of
the coil is B. It is then bent into a circular loop of n turns.
(A) 3:1
The magnetic field at the centre of the coil will be
(B) 17:5
(A) n B
(C) 27:5
(B) n² B
(D) 27:3
(C) 2n B

(D) 2n² B

21. Two blocks A and B are placed one over the other on 22. Water rises in a capillary tube to a height h. Choose
a smooth horizontal surface. The maximum horizontal false statement regarding capillary rise from the
force that can be applied on the upper block B, so that A following.
and B move without separation is 49N. The coefficient of
(A) On the surface of Jupiter, height will be less than h
friction between A and B is
(B) In a lift moving up with constant acceleration height is
(A) 0.2 less than h
(B) 0.3 (C) On the surface of moon the height is more than h
(C) 0.5 (D) In a lift moving down with constant acceleration height
(D) 0.8 is less than h

23. Two junction diodes one of germanium (Ge) and other 24. The wavelength of incident light falling on a
of silicon (Si) are connected as shown in figure to a photosensitive surface is changed from 2000 Å to 2100 Å.
battery of emf 12 V and a load resistance 10 k 12. The The corresponding change in stopping potential is
germanium diode conducts at 0.3 V and silicon diode at
(A) 0.03 V
0.7 V. When a current flows in the circuit, then the
(B) 0.3 V

(C) 0

(D) 3.3v

potential of terminal Y will be

(A) 12 V

(B) 11 V

(C) 11.3 V

(D) 11.7 V

25. A thin rod of length f/3 is placed along the optic axis 26. A sinusoidal voltage of peak value 300 V and an
of a concave mirror of focal length f, such that its image angular frequency ɷ = 400 rad/s is applied to a series L-C-
which is real and elongated just touches the rod, the R circuit, in which R= 312, L = 20 mH and C =625 ��F. The
magnification is peak current in the circuit is

(A) 1.5 (A) 30 √( 2 ) A

(B) 2.5 (B) 60 A

(C) 3.5 (C) 100 A

(D) 4.5 (D) 60 √( 2 ) A

27. The half-life of radioactive element is 100 μs. The 28. Two coherent sources of intensity ratio 9:4 produce
time taken for the radioactivity of a sample of this interference. What is the ratio between maxima and
nucleus to decay by 93.75 % of its initial value is minima in the interference pattern produced ?

(A) 6.3 μs (A) 3:2

(B) 40 μs (B) 25: 1

(C) 300 μs (C) 13:5

(D) 400 μs (D) 5:1

29. A voltmeter of resistance 998 Ω is connected across a 30. The electric potential is + 100 V at a distance of 10
cell of emf 2 V and internal resistance 2Ω. The potential cm from a point charge q. Then, q is equal to
difference across the voltmeter is
(A) + 1.1 × 10 ^ - 9 C
(A) 1:99 V (B) + 1.1 × 10 ^ - 3 C
(B) 3.5 V (C) 3 C
(C) 5 V (D) 3 × 10 ^ - 5 C
(D) 6 V

31. When an equilateral prism of refractive index 32. Force between two identical charges placed at a
produces minimum deviation the angle of incidence at distance of r in vacuum is F. Now a slab of dielectric of
the first face must be dielectric constant 4 is inserted between these two
charges. If the thickness of the slab is r/2, then the force
(A) 30°
between the charges will become
(B) 42°
(A) F
(C) 60°
(B) 3F/5
(D) 75°
(C) 4F/9

(D) F/4

33. In a potentiometer experiment for measuring the emf 34. How does the energy difference between the
of a cell, the null point is at 240 cm when we have a 500 consecutive energy level vary as the quantum number n
ohm resistor in series with the cell and galvanometer. If increases?
the series resistance reduced to half, then the null point
(A) Increases
will be at
(B) Decreases
(A) 480 cm
(C) Remains unchanged
(B) 240 cm
(D) First increases and then decreases
(C) 120 cm

(D) 60 cm

35. The ionisation potential of hydrogen atom is 16 eV. 36. What will be the kinetic energy of an electron having
How much energy need to be supplied to ionise the de-Broglie wavelength 2Å?
hydrogen atom in the first excited state?
(A) 37.5 eV
(A) 16 eV (B) 75 eV
(B) 27.2 eV (C) 150 eV
(C) 4 eV (D) 300 eV
(D) 6.8 eV

37. If a wave travelling in positive x-direction with A = 38. White light reflected at normal incidence from a soap
0.2 m/s, velocity = 360 m/s and λ = 60 m, then correct film has minima at 6500 Å and maxima at 7500 Å in the
expression for the wave is visible region with not minimum in between. If μ is 3/4 for
the, thin film, the thickness of film is
(A) y = 0.2 [ 2 π ( 6 t + ( x )/( 60 ) ) ]

(B) y = 0.2 [ π ( 6 t + ( x )/( 60 ) ) ] (A) 40 x 10⁻⁷ cm

(C) y = 0.2 [ 2 π ( 6 t - ( x )/( 60 ) ) ] (B) 9.75 x 10⁻⁵ mm

(D) y = 0.2 [ π ( 6 t - ( x )/( 60 ) ) ] (C) 9.70 x 10⁻⁷ cm

(D) 9.75 x 10⁻⁴ mm

39. A thin dielectric rod of length l lies along X-axis. One 40. The apparent frequency of the whistle of an engine
end of the rod is placed at the origin and the other end of changes in the ratio 9:8 as the engine passes a stationary
the rod is placed at (l,0). A total charge Q is distributed observer. If the velocity of the sound is 340 , then the
uniformly along the length of the rod. What is the velocity of the engine is
potential at a point (x, 0) when x > l ?
(A) 40 ms⁻¹
(A) Q 4 π ε _ 0 · _ e ( ( x )/( x - 1 ) ) (B) 20 ms ⁻¹
(B) Q 4 π ε _ 0 l · _ e ( ( x )/( l ) ) (C) 340 ms ⁻¹
(C) Q 4 π ε _ 0 l · _ e ( ( x - l )/( x ) ) (D) 180 ms ⁻¹
(D) Q 4 π ε _ 0 l

41. A mixture of two gases is contained in a vessel. The 42. The width of a single slit if the first minimum is
gas 1 is monoatomic and gas 2 is diatomic and the ratio observed at an angle 2° with a light of wavelength 6980
of their molecular masses M₁/M₂ = 1/4.What is the ratio of A°
root mean square speeds of the molecules of two gases?
(A) 0.2 mm
(A) 2 (B) 2x 10⁻⁵ mm
(B) 4 (C) 2x 10⁵ mm
(C) 8 (D) 2 mm
(D) 16

43. A voltmeter has resistance of G ohms and range V 44. A sphere of mass m moving with a constant velocity u
volts. The value of resistance used in series to convert it hits another stationary sphere of the same mass. If e is
into a voltmeter of range nV volts is the coefficient of restitution, then the ratio of velocities
of the two spheres after collision will be
(A) nG

(B) (n - 1)G (A) ( 1 - e )/( 1 + e )

(C) G/n (B) ( 1 + e )/( 1 - e )

(D) G/(n-1) (C) ( e + 1 )/( 1 - e )

(D) ( e - 1 )/( e + 1 )

45. When the inputs of a two input logic gate are 0 and 0,
the output is 1. When the inputs are 1 and 0 the output is
0. The logic gate is of the type

(A) AND

(B) NAND

(C) NOR

(D) OR

CHEMISTRY

46. Which of the following anions is present in the chain 47. Match the Column I and Column II and pick the correct
structure of silicates? matching from the codes given below.

(A) (Si₂O₅²⁻)ₙ

(B) (Si₂O₃²⁻)ₙ

(C) Si₂O₄⁴⁻

(D) Si₂O₇⁶⁻
AB

CDE

(A) 3 4 1 5 2

(B) 1 2 3 4 5

(C) 3 5 1 2 4

(D) 5 3 1 2 4

48. Which one of the following is aromatic? 49. Which one of the following complexes is an 9 outer
orbital complex ?
(A) Cycloheptatrienyl cation

(B) Cycloheptrariene (A) [Fe(CN)₆]⁴⁻

(C) Cyclooctateraene (B) [Mn(CN)₆]⁴⁻

(D) Cyclopentadienyl cation (C) [Co (NH₃)₆]³⁺

(D) [Ni (NH₃)₆ ]²⁺

50. The molecule (ion) having one unpaired electron is 51. The effective atomic number of central Cu (at. no. 29)
metal in [Cu(NH₃)₄] SO₄ is
(A) NO

(B) CO (A) 29

(C) CN⁻ (B) 30

(D) O₂ (C) 35

(D) 36

53. A man writes his biodata with carbon pencil on the

52. plane paper having mass 150 mg. After writing his
biodata, he weighs the written paper and find its mass is
Intermediate in the above reaction is
152 mg. What is the number of carbon atoms present in
the paper?

(A) 1.0036 x 10²⁰

(B) 5.02 x 10²⁰
(A)
(C) 1.0036 x 10²³

(D) 0.502 x 10²⁰

(B)

(C)

(D)

54. The conjugate base of the acid H₂S is 55. The mass of CaCO₃ required to react with 25 mL of
0.75 M HCl is
(A) HS⁻

(B) S²⁻ (A) 0.94 g

(C) S (B) 9.4 g

(D) None of these (C) 0.094 g

(D) 0.49 g

56. Which of the following compounds has zero dipole 57. Cₚ/cᵥ for noble gases is
moment?
(A) 1.66
(A) CH₂Cl₂ (B) 1.43
(B) NH₃ (C) 1.80
(C) CH₄ (D) 1.33
(D) PH₃

58. Calculate the energy of photons having wavelength, 5 59. What is the kinetic energy of 1 g of O₂ at 47°C ?
x 10⁻⁷ m falls on a metal surface of work function, 3.4 x
(A) 2.17 x 10² J
10⁻¹⁹ J.
(B) 2.24 x 10² J
(A) 3.97 x 10⁻¹⁹ J.
(C) 1.24 x 10² J
(B) 3.55 x 10⁻¹⁹ J.
(D) None of these
(C) 2.97 x 10⁻¹⁹ J.

(D) 2.57 x 10⁻¹⁹ J.

60. Which of the following has the highest electron 61. Dry distillation of calcium benzoate gives
affinity?
(A) benzaldehyde
(A) K (B) acetophenone
(B) O⁻ (C) benzoic acid
(C) F⁻ (D) benzophenone
(D) O

62. The compound which reacts fastest with Lucas 63. A silicon chip used in an integrated circuit of
reagent at room temperature is computer has a mass of 5.68 mg. The number of Si atoms
present in this chip are
(A) butan-1-ol

(B) butan-2-ol (A) 1.44 x 10²⁰ atoms

(C) 2-methyl propan-1-ol (B) 1.8 x 10²⁰ atoms

(D) 2-methyl propan-2-ol (C) 1 x 10²⁰ atoms

(D) None of these

64. Anti-Markownikoff's rule addition reaction is not 65. 1 C electricity deposits
observed in the following compound.
(A) half of electrochemical equivalent of Ag
(A) propene (B) electrochemical equivalent of Ag
(B) 1-butene (C) 96500 g of Ag
(C) but-2-ene (D) 10.8 g of Ag
(D) pent-2-ene

66. For the chemical equilibrium, 67. K₂Cr₂O₇ on heating with aqueous caustic

(A) CrO₄²⁻

(B) Cr(OH)₂
increase in temperature
(C) Cr(OH)₃
(A) favours the formation of N₂O₄
(D) Cr₂O₇²⁻
(B) favours the decomposition of N₂O₄

(C) does not affect equilibrium

(D) stop the reaction

68. Enthalpy of formation of HF and HCl are -161 kJ and - 69. Which of the following element has maximum
92 kJ, respectively. Select the incorrect statement on the photoelectric effect?
basis of the above fact.
(A) Li
(A) HF is more stable than HCI (B) Na
(B) HCl is more stable than HF (C) K
(C) Affinity of fluorine to hydrogen is greater than affinity of (D) Cs
chlorine to hydrogen

(D) HF and HCl are exothermic compound

70. Formic acid reacts with PCl₅ to form 71. The most reactive towards electrophilic reagent is

(A) methyl chloride

(B) acetyl chloride

(C) formyl chloride

(D) carbon monoxide and hydrogen chloride

(A)

(B)

(C)

(D)

72. The following compound which cannot be prepared by 73. Among the following species, the most stable
Wurtz reaction? carbonium ion is

(A) Methane (A) C₆H₅C⁺HC₆H₅

(B) Ethane (B) C₆H₅C⁺H₂

(C) Butane (C) CH₃C⁺H₂

(D) Propane (D) C₆H₅CH₂C⁺H₂

74. Keto-enol tautomerism is not observed in 75. The concentration of a solution can be expressed in
molarity, normality, formality and molality. Among them,
(A) CH₃COCH₂COCH₃
which mode of expression is the most accurate for the all
(B) C₆H₅COCH₂COCH₃
conditions?
(C) C₆H₅COCH₂=CH₂
(A) Molarity
(D) C₆H₅COC₆H₅
(B) Formality

(C) Normality

(D) Molality

76. A reaction is spontaneous at low temperature, but 77. Metals are usually used as catalysts belong to
non-spontaneous at high temperature. Which of the
(A) s-block
following condition is true for the chemical reaction?
(B) p-block
(A) ΔH 0, ΔS 0
(C) d-block
(B) ΔH > 0, ΔS = 0
(D) f-block
(C) ΔH 0, ΔS > 0

(D) ΔH > 0, ΔS > 0

78. Glycine can be obtained from formaldehyde 79. The process of 'eutrophication' is due to

(A) Streker synthesis (A) increase in concentration of radioactive substances in

(B) Williamson's synthesis water

(C) Phthalimide synthesis (B) the reduction in concentration of the dissolved oxygen in
water due to phosphate pollution in water
(D) Coupling reaction
(C) increase in concentration of fluoride ion in water

(D) increase in concentration of insecticide in water

80. Carbylamine test is performed in alcoholic KOH by 81. Wurtz reaction involves the reduction of alkyl halide
heating a mixture of with

(A) chloroform and silver powder (A) Zn/HCI

(B) trihalogenated methane and a primary amine (B) HI

(C) an alkyl halide and a primary amine (C) Zn/Cu Couple

(D) an alkyl cyanide and a primary amine (D) Na in ether

82.  A gaseous compounds having carbon, hydrogen and 83. The ionisation energy of nitrogen is larger than that
oxygen was burnt in the presence of oxygen. After of oxygen because
combustion, 1 volume of the gaseous compound
(A) the size of nitrogen atom is smaller
produces 2 volumes of CO₂ and 2 volumes of steam.
(B) there is greater attraction of electrons towards the
Determines the molecular formula of the compound, if all
nucleus
the volumes were measured under the same conditions of
pressure and temperature. (C) half-filled p-orbitals of nitrogen have extra stability

(D) None of the above
(A) C₂H₄O₂

(B) C₃H₆O₃

(C) C₄H₈O₂

(D) C₅H₁ₒO₃

84. van't Hoff factor, when benzoic acid is dissolved in 85. In which of the following the pyrophosphate bond of
benzene, will be ATP is broken down and linkage takes place between two
molecules?
(A) 2

(B) 1 (A) I some rases

(C) 0.5 (B) Lyases

(D) 1.5 (C) Transferases

(D) Ligases

86. Which of the following option best describes the 87. Decarboxylation of sodium propionate leads to the
'hydrogen economy? formation of

(A) Using dihydrogen in an efficient manner (A) methane

(B) Dihydrogen is carried and stored in the form of liquid or (B) ethene
gas (C) propanone
(C) Addition of dihydrogen to the reactant (D) ethane
(D) Both a and b

88. Which of the following is the most sweetest sugar? 89. Myosin(s) is/are

(A) Sucrose (A) fibrous proteins

(B) Fructose (B) globular proteins

(C) Glucose (C) enzyme

(D) Lactose (D) Both a and b

90. Which of the following statements are true with
respect to electronic displacement in a covalent bond? I.
Inductive effect operates through π-bond. II. Resonance
effect operates through σ-bond. III. Inductive effect
operates through σ-bond. IV. Resonance effect operates
through π-bond. V. Resonance and inductive effects
operates through σ-bond.

(A) III and I

(B) I and II

(C) II and IV

(D) I and V

MATHEMATICS

91. If the position vectors of A, B, C are respectively 1 - 2 92. All the chords of the hyperbola 3 x ^ 2 - y ^ 2 - 2 x +
j + k , 2 1 + 3 j and 2 i - k then the projection of AB on BC 4 y = 0 subtending a right angle at the origin pass
is equal to through the fixed point

(A) - 14 √( 10 ) (A) (1, -2)

(B) √( 5 ) (B) (-1,2)

(C) √( 7 ) (C) (1,2)

(D) 2 (D) None of these

93. If x = ^ - 1 ( β t - 4 t ^ 3 ) and y = ^ - 1 ( √ 1 - t ^ 2 ) 94. Let A and B be two 'events such that P ( A B ) = ( 1 )/(
then dy/dx is equal to 6 ) , P ( A B ) = ( 1 )/( 4 ) and P ( A ) = ( 1 )/( 4 ) where A
stands for complement of event A. Then, the events A
(A) 1/3
and B are
(B) 2/5
(A) mutually exclusive and independent
(C) 3/2
(B) independent but not equally likely
(D) 2/3
(C) equally likely but not independent

(D) equally likely and mutually exclusive

95. The differential equation of the family of lines 96. The sum of the series ( 3 )/( 4 · 8 ) - ( 3 · 5 )/( 4 · 8 ·
passing through the origin is 12 ) + ( 3 · 5 · 7 )/( 4 · 8 · 12 · 16 ) - … is

(A) x ( d y )/( d x ) + y = 0 (A) √( ( 3 )/( 2 ) ) - ( 3 )/( 4 )

(B) x + ( d y )/( d x ) = 0 (B) √( ( 2 )/( 3 ) ) - ( 3 )/( 4 )

(C) x ( d y )/( d x ) - y = 0 (C) √( ( 3 )/( 2 ) ) - ( 1 )/( 4 )

(D) ( d y )/( d x ) = x (D) √( ( 2 )/( 3 ) ) - ( 1 )/( 4 )

97. If 77x = 88 (mod 5) , then x is equal to 98. In triangle ABC equal to a ( b ^ 2 + c ^ 2 ) A + b ( c ^
2 + a ^ 2 ) B+ c ( a ^ 2 + b ^ 2 ) C
(A) 4

(B) 61 (A) abc

(C) 59 (B) 2 abc

(D) 48 (C) 3abc

(D) 4abc

99. If t _ n = Σ _ r = 0 ^ n 1 ( ^ n C _ r ) ^ k and S _ n = Σ _ 100. If sin A + cos B =a and sin B + cos A=b then sin
r = 0 ^ n r ( ^ n c _ r ) ^ k where k Z ^ + then ^ - 1 ( S _ n (A+B) is equal
n t _ n ) is
(A) a ^ 2 + b ^ 2 2
(A) ( π )/( 6 ) (B) a ^ 2 - b ^ 2 + 2 2
(B) ( π )/( 3 ) (C) a ^ 2 + b ^ 2 - 2 2
(C) ( π )/( 4 ) (D) None of these
(D) ( π )/( 2 )

101. ∫ _ 0 ^ 1 ( d )/( d x ) [ ^ - 1 ( 2 x 1 + x ^ 2 ) ] d x is 102. The direction cosines l, m, n of two lines are
equal to are in connected by the relations l + m + n=0 , Im = 0, then the
angle between them is
(A) 0

(B) π (A) π/3

(C) π/2 (B) π/4

(D) π/4 (C) π/2

(D) 0

103. The equation of the circle passing through the point 104. The function y = a(1- cos x) is maximum when x is
(2a, 0) and whose radical axis is x=a/2 with respect to the equal to
circle x ^ 2 + y ^ 2 = a ^ 2 will be
(A) π
(A) x ^ 2 + y ^ 2 - 2 a x = 0 (B) π/2
(B) x ^ 2 + y ^ 2 + 2 a x = 0 (C) -π/2
(C) x ^ 2 + y ^ 2 + 2 a y = 0 (D) -π/6
(D) x ^ 2 + y ^ 2 - 2 a y = 0

105. Total number of polynomials of the form x ^ 3 + a x 106. The area bounded by the parabolas y ^ 2 = 4 a ( x +
^ 2 + b x + c that are divisible by x ^ 2 + 1 , where a,b,c a ) and y ^ 2 = - 4 a ( x - a ) is
∈ 1, 2, 3, ..., 10 is equal to
(A) ( 16 )/( 3 ) a ^ 2
(A) 90 (B) ( 8 )/( 3 ) a ^ 2
(B) 45 (C) ( 4 )/( 3 ) a ^ 2
(C) 5 (D) None of these
(D) 10

107. A letter lock contains 5 rings each marked with four 108. The degree of the differential equation x = 1 + ( ( d
different letters. The number of all possible unsuccessful y )/( d x ) ) + ( 1 )/( 2 ! ) ( ( d y )/( d x ) ) ^ 2 + ( 1 )/( 3 ! ) (
attempts to open the lock is ( d y )/( d x ) ) ^ 3 + …

(A) 625 (A) 3

(B) 1024 (B) 2

(C) 624 (C) 1

(D) 1023 (D) Not defined

109. If f ( x + y ) = f ( x ) · f ( y ) , f ( β ) = 3 , f ^ ′ ( 0 ) = 110. The condition that the straight line c x - b y + b ^ 2
11 then f ^ ′ ( 3 ) is equal to = 0 may touch the circle x ^ 2 + y ^ 2 = a x + b y is

(A) 11 · e ^ 33 (A) abc = 1

(B) 33 (B) a=c

(C) 11 (C) b = ac

(D) log 33 (D) None of these

111. The locus of the point of intersection of two 112. _ n arrow ∞ ( 1 √ 4 n ^ 2 - 1 + 1 √ 4 n ^ 2 - 2 ^ 2 + …
perpendicular tangents to a circle is called + 1 √ 3 n ^ 2 ) is

(A) point circle (A) 0

(B) circumcircle (B) 1

(C) director circle (C) π/3

(D) auxiliary circle (D) π/6

113. The coefficient of the term independent of x in the 114. If θ = ^ - 1 x + ^ - 1 x - ^ - 1 x , 1 ≤ x ∞ then the
expansion of ( x + 1 x ^ 2 / 3 - x ^ 1 / 3 + 1 - x - 1 x - x ^ 1 smallest interval in which θ lies is
/ 2 ) ^ 10
(A) ( π )/( 2 ) ≤ θ ≤ ( 3 π )/( 4 )
(A) 210 (B) 0 ≤ θ ≤ ( π )/( 4 )
(B) 105 (C) - ( π )/( 4 ) ≤ θ ≤ 0
(C) 70 (D) ( π )/( 4 ) ≤ θ ≤ ( π )/( 2 )
(D) 112

115. Area bounded by the curves y = x ^ 2 and y = 2 - x 116. If f(x) is a non-negative continuous function for all x
^ 2 is 21 such that f'(x) pf (x), where p>0 and f(1) = 0, then
[f(√e) + f(√π)] is equal to
(A) 8/3 sq units

(B) ⅜ sq unit (A) o

(C) 3/2 sq unit (B) negative

(D) None of these (C) positive

(D) none of these

117. If the product of roots of the equation m x ^ 2 + 6 x 118. _ x arrow 0 ( 3 x - x )/( x )
+ ( 2 m - 1 ) = 0 is - 1 , then the value of m is
(A) -2
(A) 1 (B) 2
(B) -1 (C) 0
(C) 1/3 (D) None of these
(D) -1/3

119. If x - 2y = 4, then the minimum value of xy is 120. Total number of regions in which 'n' coplanar lines
can divide the plane, it is known that no two lines are
(A) – 2
parallel and no three of them are concurrent, is equal to
(B) 0
(A) ( 1 )/( 2 ) ( n ^ 2 + n + 2 )
(C) 1
(B) ( 1 )/( 2 ) ( n + 3 n ^ 2 )
(D) -3
(C) ( 1 )/( 2 ) ( 3 n + n ^ 2 )

(D) ( n ^ 2 - n + 2 )

121. 1 + 2 ^ 3 2 ! + 3 ^ 3 3 ! + 4 ^ 3 4 ! + … ∞ equals 122. The value of ∫ ( x + x )/( 3 + 2 x ) d x

(A) 5e (A) ( 1 )/( 4 ) ( ( 2 - x + x )/( 2 + x - x ) ) + C

(B) 4e (B) ( 1 )/( 2 ) ( ( 2 + x )/( 2 - x ) ) + C

(C) 3e (C) ( 1 )/( 4 ) ( ( 1 + x )/( 1 - x ) ) + C

(D) 2e (D) None of these

123. The domain of definition of the function f ( x ) = 1 √( 124. A vector perpendicular to the plane containing the
| | | | x | | - 1 | | - 5 ) is points A (1, - 1, 2), B (2,0,-1), C (0, 2, 1) is

(A) ( - ∞ , - 7 ] [ 7 , ∞ ) (A) 4 i + 8 j - 4 k

(B) ( - ∞ , ∞ ) (B) 8 i + 4 j + 4 k

(C) ( 7 , ∞ ) . (C) 3 i + j + 2 k

(D) ( - 7 , ∞ ) (D) i + j - k

125. Consider the hyperbola the area x ^ 2 a ^ 2 - y ^ 2 b 126. ( p q ) ( p q ) is
^ 2 = 1 the area of the triangle formed by the
(A) a contradiction
asymptotes and the tangent drawn to it at (a,0) is
(B) a tautology
(A) ½ ab
(C) either a or b
(B) ab
(D) neither a nor b
(C) 2ab

(D) 4ab

127.  If the roots x ^ 2 + a x + 9 = 0 are complex, then 128. If Δ = | array l l l 1 & a & a ^ 2 \ 1 & b & b ^ 2 \ 1 & c
& c ^ 2 array | = k ( a - b ) ( b - c ) ( c - a ) then k is equal
(A) a 6
to
(B) a-6
(A) -2
(C) | a | 6
(B) 1
(D) | a | > 6
(C) 2

(D) abc

129. The GCD of 364 and 462 is 130. ∫ √( x ) x x d x is equal to

(A) 3 (A) 2 tan x +c

(B) 11 (B) √( x ) + c

(C) 14 (C) 2 √( x ) + c

(D) 7 (D) ^ 2 x + c

131. The equation of the circle circumscribing the 132. _ n arrow ∞ [ ( 1 )/( n + 1 ) + ( 1 )/( n + 2 ) + … + ( 1
triangle formed by the lines x + y=6, 2x + y = 4 and x + )/( 6 n ) ]
2y = 5 is
(A) log 2
(A) x ^ 2 + y ^ 2 + 17 x + 19 y - 50 = 0 (B) ( 1 + √( 5 ) )
(B) x ^ 2 + y ^ 2 - 17 x - 19 y - 50 = 0 (C) log 6
(C) x ^ 2 + y ^ 2 + 17 x - 19 y - 50 = 0 (D) 0
(D) x ^ 2 + y ^ 2 - 17 x - 19 y + 50 = 0

133. The derivative of ^ - 1 ( 2 x √ 1 - x ^ 2 ) with respect 134. The number of ways in which a team of 11 player
to ^ - 1 ( 3 x - 4 x ^ 3 ) is can be selected from 22 players including 2 of them and
excluding 4 of them is
(A) ⅔

(B) 3/2 (A) ^ 16 C _ 11

(C) ½ (B) ^ 16 C _ 5

(D) 1 (C) ^ 16 C _ 9

(D) 20 _ C _ 8

135. The intercepts on the straight line y = mx by the
line y = 2 and y = 6 is less than 5, then m belongs to

(A) ] - ( 4 )/( 3 ) , ( 4 )/( 3 ) [

(B) ] ( 4 )/( 3 ) , ( 3 )/( 8 ) [

(C) ] - ∞ , - ( 4 )/( 3 ) [ ] ( 4 )/( 3 ) , ∞ [

(D) ] ( 4 )/( 3 ) · ∞

ENGLISH & GENERAL APTITUDE

136. Each of the following items consists of a sentence 137. In the following questions,choose the option which
followed by four words or group of words. Select the shows common feature in the relationship given in each
opposite of the word occurring in the sentence as per the question. Jaipur : Bengaluru : Mumbai
context. His family severed ties with him for marrying
(A) They are the cities in Rajasthan Minister
inter-caste.
(B) They are the famous business cities of India
(A) joined
(C) They are the three biggest villages of India
(B) included
(D) They are the capitals of Indian states
(C) detached

(D) disrupted

138. Directions : In each of the following questions, 139. In the following questions,choose the option which
choose the most suitable alternative to fill in the blank. shows common feature in the relationship given in each
True happiness consists ......... giving pleasure question. Squeak : Hiss : Howl

(A) for (A) They are names of animals

(B) by (B) They are currencies

(C) in (C) They are biggest animals on earth

(D) of (D) They are sound produced by animals

140. Directions : In each of the following questions, 141. 1, 4, 2, 3, 2, ?
choose the alternative which best expresses the meaning
(A) 2
of the word given in capital letters. ADJUNCT
(B) 5
(A) Adaptation
(C) 3
(B) Addition
(D) 4
(C) Decree

(D) Oath

142. In each of the following sentences, find out the part
which has an error. If there is no error, your answer is
(d).

(A) I've been to a few of his lectures,

(B) /but understood little of

(C) /what he has said

(D) . /No error

143. Directions : Read the following passage carefully and answer the questions given below it. Most employees
decide their own working hours, set production quotas, improving product and processes, are responsible for their
own quality and for approval of leadership appointments. Everyone votes on major corporate decisions and on how to
split the profits. As confidence in its novel approach has grown,Semco has happily abolished a lot more of the
conventions by which businesses are usually run No secretaries, receptionists or personal assistants. Reserved
parking spaces and dining rooms, dress codes and almost all rules have gone, including hose for travel and expenses.
The employees referred to are

(A) employees of a public sector undertaking

(B) employees of a private company

(C) employees of essential services

(D) government employees

144. Directions : In each of the following questions, 145. John, in the morning, started walking towards North
choose the alternative which best expresses the meaning and then turn towards opposite side of the Sun. He then
of the word given in capital letters. COMPETENCE turn left again and stops. Which direction is he facing

(A) Efficiency (A) North

(B) Competition (B) West

(C) Ability (C) South

(D) Compensation (D) East

146. Directions Four words are given in question below, 147. In each of the following sentences, find out the part
out of which only one word is correctly spelt. find the which has an error. If there is no error, your answer is
correctly spelt word and mark your answer. (d).

(A) arcitecture (A) The Prime Minister has said that India would not have

(B) architectere spent so much on defence

(C) architecetur (B) /if some of the neighbouring countries

(D) architecture (C) /adopted the policy of restricting defence expenditure

(D) ./No error

148. If 64 + 7 = 460 and 25 + 8 = 212 then 43 + 8 = ? 149. In these questions, look at the underlined part of
the given sentence. Below the sentence are given three
(A) 360
possible substitutions for the underlined part. If any of
(B) 376
substitutions; a), b) or c) is better than the underlined
(C) 332 part, choose that substitution as your response. If none
(D) 356 of the substitution improves the sentence, choose d) as
your response. Thus, a 'No improvement” response will
be signified by the letter d). He has been working off and
on for several years to compile a dictionary.

(A) on or off

(B) on and off

(C) regularly

(D) No improvement.

150. Fill in the blank with correct preposition.
The poor have to work ......... morning to evening.

(A) in

(B) to

(C) from

(D) before

ANSWER KEY

1. (D) 2. (C) 3. (C) 4. (B) 5. (C) 6. (B) 7. (A)

8. (A) 9. (D) 10. (D) 11. (D) 12. (B) 13. (C) 14. (D)

15. (C) 16. (C) 17. (B) 18. (A) 19. (A) 20. (B) 21. (C)

22. (D) 23. (D) 24. (B) 25. (A) 26. (B) 27. (D) 28. (D)

29. (A) 30. (A) 31. (B) 32. (D) 33. (B) 34. (B) 35. (C)

36. (A) 37. (A) 38. (A) 39. (C) 40. (A) 41. (A) 42. (B)

43. (B) 44. (A) 45. (C) 46. (B) 47. (A) 48. (A) 49. (D)

50. (A) 51. (C) 52. (D) 53. (A) 54. (A) 55. (A) 56. (C)

57. (A) 58. (A) 59. (C) 60. (D) 61. (D) 62. (D) 63. (D)

64. (C) 65. (B) 66. (B) 67. (A) 68. (B) 69. (D) 70. (D)

71. (C) 72. (A)Get Free Sample73. (A) 74. (D) 75. (D)
Papers, Question Papers, Mock Tests & Study Material at
76. (A) 77. (C)

78. (A) 79. (B) 80. (B) 81. (D) 82. (A) 83. (C) 84. (C)

85. (D) 86. (D) 87. (D) 88. (B) 89. (A) 90. (C) 91. (A)

92. (A) 93. (A) 94. (A) 95. (C) 96. (A) 97. (A) 98. (C)

99. (A) 100. (A) 101. (C) 102. (A) 103. (A) 104. (A) 105. (A)

106. (A) 107. (A) 108. (A) 109. (A) 110. (A) 111. (C) 112. (D)

113. (A) 114. (A) 115. (A) 116. (A) 117. (C) 118. (B) 119. (A)

120. (A) 121. (A) 122. (A) 123. (A) 124. (A) 125. (B) 126. (A)

127. (C) 128. (B) 129. (C) 130. (C) 131. (D) 132. (C) 133. (A)

134. (C) 135. (A) 136. (A) 137. (D) 138. (C) 139. (D) 140. (B)

141. (D) 142. (C) 143. (B) 144. (C) 145. (C) 146. (D) 147. (C)

148. (D) 149. (D) 150. (C)