MHT CET 2027 Sample Paper PCM

SAMPLE PAPER

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

MHT CET 2027 (PCM)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

150 150 180 Min +1 / 0

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 1 mark; there is no negative marking.

4. Total time allowed is 180 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

MHT CET 2027 (PCM)
SAMPLE QUESTION PAPER

Questions 150 Max Marks 150 Time 180 Min Marking +1 / 0

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

PHYSICS

1. 2.

In figure, there is a four way key at the middle. If key is The escape velocity of a body on a planet ‘A’ is 12 kms-1.
shown from situation BD to AD, then how much charge The escape velocity of the body on another planet 'B',
will flow through point 0? whose density is four times and radius is half of the
planet 'A’, is :

(A)

12 kms-1.

(B)

24 kms-1.

(C)
(A)

36 kms-1.

(D)

(B) 6 kms-1.

(C)

(D)

3. 4.

A current of 10 A is flowing in a wire of length 1.5 m. A A prism has a refracting angle of 60°. When placed in the
force of 15 N acts on it when it is placed in a uniform position of minimum deviation, it produces a deviation of
magnetic field of 2 T. The angle between the magnetic 30°. The angle of incidence is
field and the direction of the current is
(A)
(A)
38°
30°
(B)
(B)
45°
45°
(C)
(C)
18°
60°
(D)
(D)
28°
90°

5. 6.

The resistance of an ammeter is 13 ohm and its scale is An electric current is passed through a circuit containing
graduated for a current upto 100 amps. After an two wires of same material, connected in parallel. If the
additional shunt has been connected to this ammeter it lengths and radii of the wires are in the ratio of 3:2 and
becomes possible to measure currents upto 750 amperes 2:3, then the ratio of the current passing through the
by this meter. The value of shunt-resistance is wire will be

(A) (A)

2 ohm 3:2

(B) (B)

3 ohm 8:9

(C) (C)

4 ohm 8:27

(D) (D)

5 ohm 1:2

7. 8.

A planet in a distant solar system is 10 times more In a series LR circuit X = R and power factor of the
L
massive than the earth and its radius is 10 times smaller, circuit is P . When capacitor with capacitance C such that
1
Given that the escape velocity from the earth's surface is X =X is put in series, the power factor becomes P . The
L C 2
11 km s"!, the escape velocity from the surface of the ratio P /P is:
1 2
planet would be
(A)
(A)
1/2
1.1 km s-1
(B)
(B)

10 km s-1

(C)

110 km s-1 (C)

(D) 1:1

1 km s-1 (D)

2:1

9. 10.

A circular disc of radius R is removed from a bigger A particle is executing simple harmonic motion with
circular disc of radius 2R such that the circumferences of amplitude A. When the ratio of its kinetic energy to the
the discs coincide. The centre of mass of the new disc is potential energy is 1/4, its displacement A from its mean
o/R form the centre of the bigger disc. The value of a is position is

(A) (A)

1/2

(B)

1/3
(B)
(C)

1/5

(D)
(C)
1/7
2A

(D)

1/2 A

11. 12.

The period of oscillation ofa magnet in a vibration If p is the density and is coefficient of viscosity of fluid
magnetometer is 2 sec. The period of oscillation ofa
which flows with a speed v in the pipe of diameter d, the
magnet whose magnetic moment is four times that of the
correct formula for Reynolds number R is
c
first magnet is

(A)
(A)

1 sec

(B)
(B)
5 sec

(C)

8 sec

(D) (C)

0.5 sec

(D)

13. 14.

In a reverse biased diode when the applied voltage The electric field in a region of space is given by,
changes by 1 V, the current is found to change by
The flux of
The reverse bias resistance of the diode is
the field through a circular surface of radius 0.02 m
parallel to the Y-Z plane is nearly:
(A)

(A)

0.125Nm2/C
(B)
(B)

0.02Nm2/C

(C)
(C)
0.005Nm2/C
200 ohm

(D)
(D)
3.14Nm2/C
2 ohm

15. 16.

The fringe width in a Young’s double slit experiment can An electromagnetic wave going through vacuum is
be increased if we decrease
described by

(A)

width of slits Which of the following equations is true?

(B) (A)

separation of slits

(C)
(B)
wavelength of light used

(D)

distance between slits and screen (C)

(D)

None of these

17. 18.

For a given photosensitive material and frequency (> A pure semiconductor has equal electron and hole
threshold frequency) of incident radiation, the
concentration of Doping by indium Increases
photoelectric current varies with the intensity of incident
light as Then, the value of n in the doped
e
semiconductor is
(A)

(A)

(B)

(C)
(B)

(D)

(C)

(D)

19. 20.

A physical quantity P is described by the relation In the figure, a very large plane sheet of positive charge
is shown. P1 and P2 are two points at distance land 2l
If the relative errors in the
from the charge distribution. If is the surface charge
measurement of a, b, c and d respectively, are 2%, 1%,
density, then the magnitude of electric fields E1 and E2
3% and 5%, then the relative error in P will be :
at P1 and P2 respectively are :

(A)

8%

(B)

12%

(C)
(A)

32%

(D)

25% (B)

(C)

(D)

21. 22.

A vessel contains oil (density = 0.8 gm/cm3) over mercury The moment of inertia of a circular disc of mass M and
(density = 13.6 gm/cm3). A homogeneous sphere floats radius R about an axis passing through the centre of
with half of its volume immersed in mercury and the mass is I . The moment of inertia of another circular disc
o
other half in oil. The density of the material of the sphere of same mass and thickness but half the density about
in gm/cm3 is the same axis is

(A) (A)

6.9

(B)

2.3
(B)

(C)

7.2

(D)
(C)

12.8

(D)

23. 24.

A ray of light passes from vacuum into a medium of A fly wheel is accelerated uniformly from rest and rotates
through 5 rad in the first second. The angle rotated by
refractive index the angle of incidence is found to be
the fly wheel in the next second, will be:
twice the angle of refraction. Then the angle of incidence
is
(A)

(A) 7.5rad

(B)

15rad

(B) (C)

20rad

(D)

(C) 30rad

(D)

25. 26.

If three equal masses m are placed at the three vertices The transition from the state n=4 to n=31 n a hydrogen
of an equilateral triangle of side 1/m then what force acts like atom results in ultraviolet radiation. Infrared
on a particle of mass 2m placed at the centroid? radiation will be obtained in the transition from

(A) (A)

2 2-1

(B) (B)

1 3-2

(C) (C)

0 4-5

(D) (D)

1/2 5-4

27. 28.

In a series resonant circuit, having L,C and Ras its A current of I ampere flows in a wire forming a circular
elements, the resonant current is i. The power dissipated
arc of radius r metres subtending an angle at the
in circuit at resonance is
centre as shown. The magnetic field at the centre O in

(A) tesla is

1

(B)

0

(C)

2
(A)

(D)

i2R

(B)

(C)

(D)

29. 30.

The maximum range for the tropospheric transmission of A proton, a deuteron and an a-particle with same kinetic
radio wave of wavelength 3m using the transmitting energy enter into a uniform magnetic field at right angle
antenna and receiving antenna of hights 100m and 60m to magnetic field. The ratio of the radii of their respective
respectively is circular paths is :

(A) (A)

800 km

(B)

(B)
18 km

(C)

8 km (C)

(D)

1 km
(D)

31. 32.

A rod PQ of mass M and length L is hinged at -end P. The Two projectiles thrown at 30° and 45° with the horizontal
rod is kept horizontal by a massless string tied to point Q respectively, reach the maximum height in same time.
as shown in figure. When string is cut, the initial angular The ratio of their initial velocities is :
acceleration of the rod is
(A)

(B)

1:2

(C)

(A) 2:1

2g
(D)

(B) 1:1

3g

(C)

2g/6L

(D)

3g/2L

33. 34.

The coefficient of apparent expansion of mercury in a A parallel beam of light of wavelength 900 nm and
intensity 100 Wm-2is incident on a surface perpendicular
glass vessel is and in a steel vessel is
to the beam. The number of photons crossing 1 cm2 area
If ot for steel is then that perpendicular to the beam in one second is :

of glass is
(A)

(A)
3x 1016

(B)

(B) 4.5 x 1016

(C)

4.5 x 1017
(C)

(D)
1

4.5 x 1020
(D)

0

35. 36.

The distance of the Sun from earth is 1.5 x 1011m and its Two simple harmonic motions are represented by the
angular diameter is (2000) s when observed from the
earth. The diameter of the Sun will be:
equations and
(A)

2.45 x 1010m

The phase difference of the velocity of particle 1 with
(B)
respect to the velocity of particle 2 is

1.45 1010m
(A)

(C)

1.45 * 109m

(D)
(B)
0.14 x 109m

(C)

(D)

1/2

37. 38.

A spherical solid ball of volume V is made of a material of A soap film of surface tension 3 x 10-2 formed in are
density p It is falling through a liquid of density rectangular frame cam support a straw as shown in Fig. If
1.
g= 10 ms-12, the mass of the straw is
Assume that the liquid applies a viscous

force on the ball that is proportional to the square of its

speed v, i.e., The terminal

speed of the ball is

(A)

(A)

(B) 0.006g

(B)

0.06 g

(C)
(C)

0.6 g

(D)

6g
(D)

39. 40.

For the same cross-sectional area and for a given load, Two radiations of photons energies 1 eV and 2.5 eV,
the ratio of depressions for the beam of a square cross- successively illuminate a photosensitive metallic surface
section and circular cross-section is of work function 0.5 eV. The ratio of the maximum speeds
of the emitted electrons is
(A)
(A)

1:4

(B) (B)

1:2

(C)
(C)

1:1

(D)

(D)
1:5

41. 42.

A plano-convex lens is made of material of refractive
Magnetic flux in weber in a closed circuit of resistance
index 1.6. The radius of curvature of the curved surface
is 60 cm. The focal length of the lens is 10 ohm varies with time (sec) as = 6t2— 5t + 1. The

magnitude of induced current at t= 0.25s is
(A)

50cm (A)

0.2 A
(B)

100cm (B)

0.6 A
(C)

200cm (C)

0.3 A
(D)

400cm (D)

0.7 A

43. 44.

Two metallic blocks M and M of same area of cross- For an ideal gas graph is shown for three processes.
1 2
section are connected to each other (as shown in figure). Process 1, 2 and 3 are respectively.
If the thermal conductivity of M is K then the thermal
1
conductivity of M will be : [Assume steady state heat
2
conduction}

(A)
(A)

10 K
Isobaric, adiabatic, isochoric

(B)
(B)

8K
Adiabatic, isobaric, isochoric

(C)
(C)

12.5 K
Isochoric, adiabatic, isobaric

(D)
(D)

2K
Isochoric, isobaric, adiabatic

45. 46.

Equipotential surfaces are shown in figure. Then the A mass m is revolving in a vertical circle at the end of a
electric field strength will be Y string of length 20 cm. By how much does the tension of
the string at the lowest point exceed the tension at the
topmost point?

(A)

2mg

(B)

(A) 4mg

(C)

6mg
(B)

(D)

8mg

(C)

(D)

47. 48.

The displacement-time graphs of two particles A and B The primary of a transformer has 400 turns while the
are straight lines making angles of 30° and 60° secondary has 2000 turns. If the power output from the
respectively with the time axis. If the velocity of A is v secondary at 1000 V is 12 kW, what is the primary
A
and that of B is v , the value of v /v is voltage?
B A B

(A) (A)

1 200V

(B) (B)

2 300V

(C) (C)

1/2 400V

(D) (D)

1/3 500V

49. 50.

A force F acting on an object varies with distance x as A given ray of light suffers minimum deviation in an
shown here. The force is in N and x in m. The work dong equilateral prism P. Additional prism Q and R of identical
by the force in moving the object from x=0 to x=6 m is shape and of the same material as P arc now added as
shown in the figure. The ray will now suffer

(A)

greater deviation
(A)
(B)
18.0 J
no deviation
(B)
(C)
13.5 J
same deviation as before
(C)
(D)
9.0 J
total internal reflection
(D)

4.5 J

CHEMISTRY

51. 52.

Which of the following compounds will undergo self aldol Which of the following represents a redox reaction?
condensation in the presence of cold dilute alkali?
(A)
(A)

(B)
(B)

(C)
(C)

(D)
(D)

53. 54.

100 g of an ideal gas is kept in a cylinder of 416 L Mark the oxide which is amphoteric in character
volume at 27°C under 1.5 bar pressure. The molar mass
of the gas is ...... gmol-1 (A)

CO
(A) 2

4 (B)

H O
(B) 2

10 (C) SnO
2
(D)
(C)
O
2
2

(D)

3.5

55. 56.

One mole of an ideal gas is allowed to expand reversibly The compound which reacts fastest with Lucas reagent at
and adiabatically from a temperature of 27°C. If the work room temperature is
done during the process is 3 kJ, the final temperature will
be equal to (C =205K-1) (A)
v

butan-1-ol
(A)

150K (B)

butan-2-ol
(B)

100K (C)

2-methyl propan-1-ol
(C)

26.85K (D)

2-methylpropan-2-ol
(D)

295K

57. 58.

The covalent bond length is the shortest in which one of Predict the product C obtained in the following reaction
the following bonds? of butyne-1.

(A)

C—O

(B) (A)

C—C

(C)

C=N

(D)
(B)
O—H

(C)

(D)

59. 60.

High concentration of which of the following in The polymer used in making synthetic hair wigs is made
atmosphere leads to stiffness of flower buds which up of
eventually fall off from plants?
(A)
(A)

NO
2

(B)
(B)

SO
2

(C)
(C)

CFC

(D)
(D)
Smog

61. 62.

Henry’s law constant of oxygen is 1.4 x 10-3 mol-1 lit, atm
-1 at 298 K. How much of oxygen is dissolved in 100 ml at

298 K when the partial pressure of oxygen is 0.5 atm?

(A)

14g
In the above reaction product 'P' is
(B)
(A)
32g

(C)

224mg

(D)

(B)
224mg

(C)

(D)

63. 64.

According to Le-chatelier ’s principle, adding heat to a Which of the following bicarbonates does not exist as

solid liquid equilibrium will cause the solid?

(A)
(A)

HCO
temperature to increase 3

(B)
(B)

NH
temperature to decrease 3

(C)
(C)

CsHCO
amount of liquid to decrease 3

(D)
(D)

LiHCO
amount of solid to decrease 3

65. 66.

Chlorine is liberated when we heat Identify Z in the sequence

(A)

(A)

(B)

(B)

(C)

(C)

(D)

(D)

67. 68.

Calcination is used in metallurgy for removal of ? Which of the following polymer is used for manufacturing
of buckets, dustbins, pipes etc ?
(A)
(A)
Water and sulphide
Low density polythene
(B)
(B)
Water and CO
2
High density polythene
(C)
(C)
CO and H S
2 2
Teflon
(D)
(D)
H O and H S
2 2
Polyacrylonitrile

69. 70.

Which of the following is not present in a nucleotide?
Element with electronic configuration

(A)
belongs to the
Guanine following group of the periodic table

(B) (A)

Cytosine 5th

(C) (B)

Adenine 15th

(D) (C)

Tyrosine 3rd

(D)

17th

71. 72.

The major product formed when 2-bromobutane is In a solution of CuSO how much time will be required to
4
treated with alcoholic KOH is precipitate 2 g copper by 0.5 ampere current ?

(A) (A)

2-Butanol 12157.48 sec

(B) (B)

1-Butene 102 sec

(C) (C)

1-Butanol 510 sec

(D) (D)

trans-2-butene 642 sec

73. 74.

Which of the following statements regarding fuel cell is
incorrect?

(A)

These cells are eco-friendly.

(B)
(A)
These cells convert energy of combustion of fuels like H , CH
2
, CH OH etc., directly into electrical energy.
2 2

(C)

H — O fuel cell is used in Apollo space programme
2 2

(D)

Fuel cells produce electricity with an efficiency of about
(B) 100%.

(C)

(D)

75. 76.

In which of the following, Tyndall effect is not observed ?

(A)

Suspensions (A)

(B) 40kJ mol-1

Emulsions (B)

(C) 50 kJ mol-1

Sugar solution (C)

(D) 30 kJ mol-1

Goldsol (D)

60 kJ mol-1

77. 78.

Fluorobenzene (C H F) can be synthesized in the Which of the following is most powerful to coagulate the
6 5
laboratory negative colloid?

(A) (A)

by direct fluorination of benzene with F gas ZnSO
2 4

(B) (B)

by reacting bromobenzene with NaF solution Be

(C) (C)

by heating phenol with HF and KF AlCl
3

(D) (D)

from aniline by diazotisation followed by heating the NO
diazonium salt with HBF
4

79. 80.

1.00 g of a non-electrolyte solute (molar mass 250 g mol- P O is heated with water to give
2 5
1) was dissolved in 51.2 g of benzene. If the freezing

point depression constant, K of benzene is 5.12 K kg mol (A)
f
-1, the freezing point of benzene will be lowered by
hypophosphorous acid

(A)
(B)

0.3K
phosphorous acid

(B)
(C)

0.5K
hypophosphoric acid

(C)
(D)

0.4K
orthophosphoric acid

(D)

0.2K

81. 82.

When a metal is to be extracted from its ore and the The electric cookers have a coating that protects them
gangue associated with the ore is silica, then against fire. The coating is made of

(A) (A)

an acidic flux is needed heavy lead

(B) (B)

a basic flux is needed zinc oxide

(C) (C)

both acidic and basic fluxes are needed magnesiumoxide

(D) (D)

Neither of them is needed sodium sulphate

83. 84.

Polymer used in bullet proof glass is An ideal gas expands against a constant external
pressure of 2.0 atmosphere from 20 litre to 40 litre and
(A) absorbs 10 kJ of heat from surrounding. What is the
change in internal energy of the system? (given : l atm-
lexan
litre= 101.3 J)

(B)
(A)
PMMA
4052 J

(C)
(B)
nomex
5948 J

(D)
(C)
kevlar
14052 J

(D)

9940 J

85. 86.

Vitamin B is known as Percentages of free space in cubic close packed structure
6
and in body centered packed structure are respectively
(A)
(A)
pyridoxine
30% and 26%
(B)
(B)
thiamine
26% and 32%
(C)
(C)
tocopherol
32% and 48%
(D)
(D)
riboflavin
48% and 26%

87. 88.

What is X in the following reaction ?
The solubility (in mol L-1) of AgCl in

0.1 M KCl solution will be

(A)

(B)
(A)

(C)

(B)

(D)

(C)

(D)

89. 90.

How many significant figures are in each of the following.
Consider the ions/molecule For (1) 4.003; (ii) 6.023 x 1023; (iii) 5000
increasing bond order the correct option is :
(A)
(A)
3,4,1

(B)

4,3,2
(B)

(C)

4,4,4

(C)
(D)

3,4,3

(D)

91. 92.

The most probable product in the reaction given below is At anode in the electrolysis of fused NaCl

(A)

Na+ is oxidized

(B)

(A) Cl- is oxidized

(C)

Cl isreduced

(D)
(B)
Na is reduced

(C)

(D)

93. 94.

Which of the following is not an assumption of the kinetic The most stable +2 oxidation state is exhibited by
theory of gases?
(A)
(A)
Fe
Gas particles have negligible volume.
(B)
(B)
Sn
A gas consists of many identical particles which are in
continual motion. (C)

Pb
(C)

At high pressure, gas particles are difficult to compress. (D)

Si
(D)

Collisions of gas particles are perfectly elastic.

95. 96.

Which of the following compound can be best prepared The vapour pressure of a solvent A is 0.80 atm. When a
by Wurtz reaction? non-volatile substance B is added to this solvent its
vapour pressure drops to 0.6 atm. the mole fraction of B
(A) in the solution is

(A)

0.25

(B) (B)

0.50

(C)

(C) 0.20

(D)

0.60

(D)

97. 98.

van Arkel method of purification of metals involves Which among the following has lowest surface tension ?
converting the metal to a
(A)
(A)
Hexane
volatile stable compound
(B)
(B)
Soil
volatile unstable compound
(C)
(C)
Water
non volatile stable compound.
(D)
(D)
Salt
None of the above

99. 100.

The order of re activities of the following alkyl halides for Which of the following reactions is not of the first order?
a S 2 reaction is
N
(A)
(A)
Inversion of sucrose in the presence of acid
RF>RCI>RBr>RI
(B)
(B)
Acid-catalyzed hydrolysis of ethyl acetate
RF>RBr>RCI>RI
(C)
(C)
Hydrolysis of tertiary butyl halide using alkali
RCI>RBr>RF>RI
(D)
(D)

RI>RBr>RCI>RF

MATHEMATICS

101. 102.

The equation of a circle with centre at (1, 0) and

circumference units is
If then
(A)

equals
(B)

(A)

1
(C)

(B)

21
(D)
(C)

3

(D)

4

103. 104.

Negation of the Boolean expression is

(A)
If then det (adj (adj A)) is

(A)

(B)

(B)

(C)
14

(C)

132
(D)

(D)

1

105. 106.

If then f(p) is equal
If
to:

(A)
(A)

(B)
(B)

(C)
(C)

(D)

None of these (D)

None of these

107. 108.

If A denotes the cofactor of the element a of the An incomplete frequency distribution is given below
ij ij

determinant then value of

is

(A)

0 Median value is 46, the missing frequency is

(B) (A)

5 32

(C) (B)

10 22

(D) (C)

-5 34

(D)

25

109. 110.

The foot of the perpendicular drawn from the origin to a f the line passing through P(1, 2) making an angle with
plane is the point (1, -3, 1). What is the intercept cut on the x-axis in the positive direction meets the pair of lines
the x-axis by the plane? x2 + 4xy + y2 at A and B, then PA. PB =

(A) (A)

1 13/3

(B) (B)

3 12/3

(C) (C)

10 11/3

(D) (D)

11 1

111. 112.

is

If then z is equal to 3 + bi. The value of
(A)

‘b’ is
A tautology

(A)
(B)

1
A contradiction

(B)
(C)

2
Both a tautology and a contradiction

(C)
(D)

0
Neither a tautology nor a contradiction

(D)

3

113. 114.

If the slope of the tangent at(x, y) to a curve

If , then the value of
passing through

the equation of the curve is :
is
(A)

(A)

y/3

(B) (B)

y

(C)
(C)

3

(D)
(D)
1/2
0

115. 116.

The expression

If is equal to

(A)

1 (A)

(B)

2

(C) (B)

3 0 if n is even

(D) (C)

None of these

(D)

3 if n is odd

117. 118.

The equation of the plane containing the line The figure shows as triangle AOB and the parabola y= x2.
The ratio of the area of the triangle AOB to the area of
the region AOB of the parabola y = x2 is equal to
and the point (0, 7,—7), is

(A)

xt+yt+z=2

(B)

x+y+z=3

(C)
(A)
x+y+z=0
4/3

(D)
(B)
None of these
3/4

(C)

1/2

(D)

1

119. 120.

The maximum value of z = 6x + 8y subject to constraints
The contrapositive of is

and
(A)

(A)

90
(B)
(B)

120

(C) (C)

60

(D) (D)

80

121. 122.

For a biased dice, the probability for the different faces The fourth term of an A.P. is three times of the first term
to turn up are and the seventh term exceeds the twice of the third term
by one, then the common difference of the progression is

(A)

2
The dice is tossed and it is told that either the face 1 or
(B)
face 2 has shown up, then the probability that it is face 1,
is 3

(A) (C)

1/20 1

(B) (D)

2/3 0

(C)

5/20

(D)

5/21

123. 124.

If f(x)=1/(1-x) the number of points of discontinuity of f{f
[f(x)]} is :
The principal value of is:
(A)

(A)
2

(B)

1

(C) (B)

3

(D)

0
(C)

(D)

2/7

125. 126.

Ina binomial distribution n= 5, P(X= 1) = 0.4096 and P (X
= 2) = 0.2048, then the mean of the distribution is equal
to

(A)
(A)
cosx+xsinx+C
1

(B)
(B)

2

(C) (C)

sinx+xcosx+C 3

(D) (D)

xsinx—cosxt+C 4

127. 128.

If f:R->R be a function defined by f(x)=4x3—-7. Then If the tangent at (1, 7) to the curve x2 = y-6 touches the
circle x2 +y2 +16x+12y+c=0 then the value of c is :
(A)
(A)
f is one-one-into
18
(B)
(B)
f is many-one - into
85
(C)
(C)
f is many-one onto
95
(D)
(D)
f is objective
195

129. 130.

Let A, B, C be finite sets. Suppose that n(A) = 10,
If A and B are sets, then is
n(B)=15,n(C)=20, Then
the possible value of n (AUBUC) is
(A)

(A)

27
(B)

(B)
A

26
(C)

(C)
B

28
(D)

(D)
None of these

Any of three values 26, 27, 28 is possible

131. 132.

Find the mean deviation about the mean for the data.
If, 3,9), (5, 2, 1), are coplanar, then

the product of all possible values of is :

(A)

89/8 (A)

(B) 6

56/8 (B)

(C) 7.3

91/8 (C)

(D) 8

95/8 (D)

6.32

133. 134.

The internal angles of a convex polygon are inA.P. The Which of the following functions is NOT one- one ?
smallest angle is 120° and the common. difference is 5°.
The number to sides of the polygon is (A)

(A)

8
(B)

(B)

9

(C)
(C)

7

(D) (D)

0

135. 136.

Shamli wants to invest Rs 50,000 in saving certificates The distance of the point (1, —2, 3) from the plane
and PPF. She wants to invest atleast Rs 15,000 in saving x—y+z=5 measured parallel to the line x/2=y/3=z-1/-6 is
certificates and at least Rs 20,000 in PPF. The rate of
interest on saving certificates is 8% p.a. and that on PPF (A)

is 9% p.a. Formulation of the above problem as LPP to
1
determine maximum yearly income, is

(B)
(A)
2

(C)

3

(D)
(B)

4

(C)

(D)

137. 138.

The angles of a triangle, two of whose sides are

If and y (0) =2, then y (In 2) is equal to :
represented by the vectors and

where isa non-zero vector and is a unit vector are (A)

5
(A)

(B)

13

(C)

(B)
-2

(D)

7

(C)

(D)

139. 140.

Let f be the function defined by The equation of tangent to the curve

(A)

(A)

The function is continuous for all values of x
(B)
(B)

The function is continuous only for x > 1

(C)
(C)
The function is continuous at x = 1
1

(D)
(D)
The function is not continuous at x = 1
0

141. 142.

A fair coin is tossed 99 times. If X is the number of times Bag I contains 3 red, 4 black and 3 white balls and Bag II
head occurs, P(X = r) is maximum when r is contains 2 red, 5 black and 2 white balls. One ball is
transferred from Bag I to Bag IT and then a ball is draw
(A) from Bag II. The ball so drawn is found to be black in
colour. Then the probability, that the transferred ball is
49 or 50
red, is:

(B)
(A)
45
1/2

(C)
(B)
44
5/18

(D)
(C)
43
7/18

(D)

9/18

143. 144.

If are three non-coplanar vectors, then the The mean of a set of observation is If each

observation is divided by and then is

increased by 10, then the mean of the new set is
value of is:

(A)
(A)

0

(B)
(B)
1

(C)

2

(D) (C)

3

(D)

145. 146.

In a triangle ABC, equal to:

If matrix then
(A)

sin(A+B) K is

(B) (A)

sin(A—B) 7

(C) (B)

cos(A+B) -7

(D) (C)

None of these 15

(D)

11

147. 148.

The maximum value of z= 5x + 2y, subject to the

constraints is

If
(A)

then (gof) (x) is equal to 45

(A) (B)

25

(C)
(B)
35

(D)

(C) 10

Both are correct

(D)

None of these

149. 150.

Let A= {1,2,3, 4} and let R= {(2, 2), (3, 3), (4,4), (1, 2)} General solution of the equation
be a relation on A. Then R is:
is

(A)
(A)
reflexive

(B)

symmetric
(B)

(C)

transitive

(D)
(C)
None of these

(D)

None of these

ANSWER KEY

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

8. (B) 9. (B)Get Free Sample10.
Papers,
(A) Question Papers,
11.Mock
(A)Tests & Study Material
12. (C)at aglasem.com13. (B) 14. (A)

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

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

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

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

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

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

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

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

71. (D) 72. (A) 73. (B) 74. (D) 75. (C) 76. (D) 77. (D)

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

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

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

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

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

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

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

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

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

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

148. (C) 149. (C) 150. (A)