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Max. Marks: 300
Competishun
52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar
Date: 13/03/2023
Time: 3 hours
CMFST-16 (22-23)
Physics
Single Choice Question
Q1 A current loop, having two circular arcs joined by two radial lines is shown in the
figure. It carries a current of 10 A. The magnetic field at point O will be close to
a) 1.5 × 10 T b) 1.0 × 10 T c) 1.5 × 10 T d) 1.0 × 10 T
Q2 An electron (of mass m) and a photon have the same energy E in the range of a few
eV. The ratio of the de-Broglie wavelength associated with the electron and the
wavelength of the photon is (c = speed of light in vacuum)
a) b) c) d)
Q3 Two liquids of densities ρ and ρ (ρ = 2ρ ) are filled up behind a square wall of side
10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due
to these liquids exerted on upper part MN to that at the lower part NO is (Assume that
the liquids are not mixing)
a) 1/4 b) 1/2 c) 2/3 d) 1/3
-7 -5 -5 -7
1
c
( )
E
2m
1
2
( )
E
2m
1
2 c(2mE)
1
2
1
c
( )
2E
m
1
2
1 2 2 1

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Q4 Two light waves having the same wavelength λ in vacuum are in phase initially. Then
the first wave travels a path L through a medium of refractive index n while the
second wave travels a path of length L through a medium of refractive index n .
After this the phase difference between the two waves is
a) b)
c) d)
Q5 Take the breakdown voltage of the zener diode used in the given circuit as 6 V. For the
input voltage shown in figure below, the time variation of the output voltage is
(Graphs drawn are schematic and not to scale)
a) b)
c) d)
Q6 A ship is moving westward with a speed of 10 km/h and a ship B , 100 km south of A
is moving northwards with same speed. The time after which the distance between
them is shortest and the shortest distance are
a) 2h, 100 km b)
c) d)
Q7 A self propelled vehicle (assume it as a point mass) runs on a track with constant
speed V. It passes through three positions A, B and C on the circular part of the track.
Suppose N , N and N are the normal forces exerted by the track on the vehicle
when it is passing through points A, B and C respectively then
a) N = N = N b) N > N > N c) N > N > N d) N > N > N
Q8 A plate, of uniform thickness and uniform density, has a shape in the x-y plane
defined by the lines x = 0, y = 2, and y = x . The plate lies in first quadrant of x-y
plane. Then the x-coordinate of centre of mass of this plate is:
a) b) c) d)
1 1
2 2
( − )
2π
λ
n2 L1 n1 L2 ( − )
2π
λ
L1
n1
L2
n2
( − )
2π
λ
n1 L1 n2 L2 ( − )
2π
λ
L2
n1
L1
n2
5h, 50 km
2
–
√
5 h, 50km
2
–
√ 10 h, 50 km
2
–
√ 2
–
√
A B C
A B C B A C C A B B C A
1
2
2
1
2
3
2
4
3
3
4

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Q9 A uniform triangular plate ABC of moment of inertia Ι (about an axis passing through
A and perpendicular to plane of the plate) can rotate freely in the vertical plane about
point 'A' as shown in figure. The plate is released from the position shown in the
figure. Line AB is horizontal. The acceleration of centre of mass just after the release
of plate is :
a) b) c) d)
Q10 A metre stick swinging in vertical plane about an fixed horizontal axis passing
through its one end undergoes small oscillation of frequency f . If the bottom half of
the stick were cut off, then its new frequency of small oscillation would become :
a) f b) c) 2f d)
Q11 Three waveforms travelling along a straight line have the forms:
, ,
the amplitude of the resulting waveform is
a) b) c) d)
Q12 An ideal monoatomic gas initially at 300 K undergoes an isobaric expansion at a
pressure of 2.5 kPa. If the volume increases from 1m to 3m , then heat added to the
gas and its final temperature respectively are :
a) 12500 J, 450 K b) 12500 J, 600 K c) 12500 J, 900 K d) 25000 J, 1200 K
Q13 A point charge ' Q ' is placed at the centre of a spherical cavity of radius ' b ' carved
inside a solid conducting sphere of radius ' a '. Then total energy of the system is: [k =
]
a) b) c) d)
mg
3
√
a
2
I
mg
4
a
2
I
mg
2
a
2
I
3
√
mg
3
a
2
I
0
0 2
–
√ f0 0 2 2
–
√ f0
2Asin (kx − ωt + )
π
3
Acos (kx − ωt − )
3
–
√
π
3
2 Acos (kx − ωt + )
3
–
√
π
3
(2 + 3 A)
3
–
√ A
31
−
−
√ A
19
−
−
√ (2 − A)A
3
–
√
3 3
1
4π∈0
−
kQ
2
2a
kQ
2
2b
+
kQ
2
2a
kQ
2
2b
+
kQ
2
a
kQ
2
b
−
kQ
2
a
kQ
2
b

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Q14 A charged particle enters a uniform magnetic field with velocity vector at and angle
45 with the magnetic field. The pitch of helical path is P then find radius of helical
path :
a) b) c) d)
Q15 A conductor carries a current of 6.0 A along the closed path abcdefgha involving 8 out
of the 12 edges of a cube of side of 10 cm as shown in figure. If the system is in a
uniform field of , the torque on the system (in N.m.) at this
instant is :
a) b) c) d) zero
Q16 A ring of mass m, radius r having charge q uniformly distributed over it and free to
rotate about its own axis is placed in a region having a magnetic field B parallel to its
axis. If the magnetic field is suddenly switched off, the angular velocity acquired by
the ring is
a) b) c) d) None of these
Q17 In the given situation, for what value of i, the incidence ray will retrace its initial
path.
a) b)
c) d)
Q18 The current flowing through the resistor in a series L–C–R a.c. circuit, if I = ε / R.
Now the inductor and capacitor are connected in parallel and joined in series with the
resistor as shown in figure. The current in the circuit is now. (Symbols have their
usual meaning)
a) equal to I b) more than I c) less than I d) zero
o
P
π
2
√
P
2
–
√
P
2π
P
2
√
π
= (100tesla)
B
→
i
ˆ
6i
ˆ
6k
ˆ
−6k
ˆ
qB
m
2qB
m
qB
2m
co [ sin ( − si )]
s
−1
μ1
π
4
n
−1
μ
2
2
√ μ
1
si [ sin ( − si )]
n
−1
μ1
π
4
n
−1
μ
2
2
√ μ
1
si [ sin ( − si )]
n
−1
μ2
π
4
n
−1
μ
1
2
√ μ
2
co [ sin ( − si )]
s
−1
μ2
π
4
n
−1
μ
1
2
√ μ
2

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Q19 The resistance of each arm in the circuit shown in figure has same value. (i.e. R =
R = R = R = R = ..... etc.). The ratio Q /Q of the amounts of heat liberated
per unit time in conductors 1-2 and 3-4 is :
a) 4 : 1 b) 8 : 1 c) 16 : 1 d) none of these
Q20 The voltage applied to an X-ray tube is 20 kV. The minimum wavelength of X-ray
produced will be (h = 6.62 × 10 Js, c = 3 × 10 m/s, e = 1.6 × 10 coulomb) :
a) 1 Å b) 0.962 Å c) 0.2 Å d) 0.62 Å
Numerical
Q21 A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the
supply and is connected to another uncharged 60 pF capacitor in parallel. The
electrostatic energy that is lost in this process by the time the charge is redistributed
between them is (in nJ) _________.
Q22 Consider a uniform cubical box of side a on a rough floor that is to be moved by
applying minimum possible force F at a point b above its centre of mass (see figure).
If the coefficient of friction is μ = 0.4, the maximum possible value of for
box not to topple before moving is ___.
Q23 An asteroid is moving directly towards the centre of the earth. When at a distance of
10 R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s.
Neglecting the effect of earths atmosphere, what will be the speed of the asteroid
when it hits the surface of the earth (escape velocity from the earth is 11.2 km/s)?
Give your answer to the nearest integer in kilometer/s _______
Q24 If minimum possible work is done by a refrigerator in converting 100 grams of water
at 0°C to ice, how much heat (in calories) is released to the surroundings at
temperature 27°C (Latent heat of ice = 80 Cal/gram) to the nearest integer ?
Q25 A circular disc of mass M and radius R is rotating about its axis with angular speed
ω . If another stationary disc having radius and same mass M is dropped co-axially
on to the rotating disc. Gradually both discs attain constant angular speed ω . The
energy lost in the process is p% of the initial energy. Value of p is _____.
12
10 13 2O 24 12 34
–34 8 –19
100 ×
b
a
1
R
2
2

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Q26 A swimmer jumps from a bridge over a canal and swims 1 km up stream. After that
first km, he passes a floating cork. He continues swimming for half an hour and then
turns around and swims back to the bridge. The swimmer and the cork reach the
bridge at the same time. The swimmer has been swimming at a constant speed. How
fast does the water in the canal flow in km/hr.
Q27 Two blocks of masses 8kg and 6kg are connected with a string & placed on a rough
horizontal surface. Surface itself is accelerating up with 2 m/s . Two forces 60 N each
are acting on the two blocks as shown. Friction coefficient for 8kg is 0.5 & that for 6
kg is 0.6. Tension (in N) in the string is : (g = 10 m/s )
Q28 For a certain amount of monoatomic gas undergoes a process for which –
U α V
where U is internal energy and V is volume of gas. It is found that the ratio for
the process was . What is the value of β.
Q29 An LCR series circuit with 100 resistance is connected to an AC source of 200 V
and angular frequency 300 radians per second. When only the capacitance is removed,
the current lags behind the voltage by 60°. When only the inductance is removed, the
current leads the voltage by 60°. Calculate the average power dissipated in LCR
circuit in watts
Q30 In a potentiometer experiment to find internal resistance of battery in secondary
circuit balance point comes at 5.5 m. AB is uniform wire of length 10 m and having
resistance of 10 . (Neglect resistance of galvanometer and connecting wires). Then
'r' in ohms is ?
2
2
β
ΔU
ΔQ
1
3
Ω
Ω

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Chemistry
Single Choice Question
Q31 Which of the following statement is INCORRECT for Lucas Test which is used to
distinguish between 1º,2º and 3º alcohols.
a) Allyl alcohol and benzyl alcohol give immediate turbidity
b) Alcohols which reacts readily with Na-metals will give turbidity at a much faster
rate.
c) Alcohols which gives red colour during Victor Mayer test, will give turbidity at a
much slower rate
d) Lucas test involves Acid-Base reaction
Q32 In presence of PbS abd ZnS in a mineral, the froth floatation process requires NaCN
because
a) ZnS forms a soluble complex
b) Zn CN precipitated
c) PbS forms a soluble complex
d) ZnS forms an insoluble complex
Q33 Which of the following statement is INCORRECT for ‘Electrical Disintegration’
method for preparation of colloids?
a) It is also known as Bredig’s arc method
b) It involves both vaporization and condensation
c) It is used to prepare gold, silver and platinum sols
d) It needs an electric arc between the electrodes of the metal immersed in the
dispersed phase.
Q34 Which of the following antibiotic is bactericidal in nature
a) Erythromycin b) Ofloxacin
c) Tetracycline d) Chloramphenicol
Q35 Which of the following amino acid consists of two – NH group in it
a) Isoleucine b) Aspartic acid c) Glutamic acid d) Lysine
Q36 Which of the following statement regarding melamine is INCORRECT?
a) It is aromatic
b) It contains 6 pairs of non-bonding electrons
c) Its molecular formula is C H N
d) it is a heterocyclic compound
Q37 A metal crystallizes in bcc lattice. The % of edge length not covered by atom is
a) 10.4% b) 13.4% c) 12.5% d) 16%
2
3 8 6

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Q38 Both temporary and permanent hardness is removed on boiling water with
a) Ca(OH) b) NaHCO c) Na CO d) CaO
Q39 The increasing order of solubility of BaS, MnS, Sb S and K S is
a) BaS < MnS < Sb S < K S b) K S < MnS < Sb S < BaS
c) Sb S < MnS < BaS < K S d) Sb S < BaS < MnS < K S
Q40 Which of the following compounds will undergo Friedel-Craft alkylation with fastest
rate?
a) b)
c) d)
Q41
When
are treated with NaHCO solution, the gases released are
a) SO ,NO ,CO b) SO ,N O,CO c) CO ,CO ,CO d) CO ,NO ,CO
Q42 Select the correct statement about van der Waals constants ‘a’ and ‘b’
a) a, b are constants for a gas at any temp. and pressure
b) a, b are not strictly constants and vary with temperature and pressure.
c) The values of a, b are same according to different equations for real gases
d) For real gases, where T is the Boyle’s temperature
Q43 Consider two liquids (1) (2) having vapour pressures and in their pure forms
respectively. The plot of vs (where x and y are the mole fractions of liquid
(1) in liquid and vapour phase respectively, is linear with slope and y-intercept
respectively
a) b) c) d)
Q44 Which of the following is not obtained as a product during complete hydrolysis of
XeF ?
a) XeO b) Xe c) HF d) XeO F
Q45 Amphoteric oxides of Mn and Cr are
a) MnO, CrO b) Mn O ,Cr O c) MnO ,Cr O d) Mn O ,CrO
Q46 The complex having the highest magnetic moment is
a) b) c) d)
2 3 2 3
2 3 2
2 3 2 2 2 3
2 3 2 2 3 2
3
2 2 2 3 2 2 2 2 2 2 2 2
=
TB
2a
Rb
B
P
0
A
P
0
B
1
XA
1
YA
A A
4
3 2 2
2 3 2 3 2 2 3 2 7 3

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Q47 Consider the following reactions
(X) and (Y) respectively are:
a) (CH ) CH, CH (CH ) CH b) CH = C(CH ) , CH CH = CHCH
c) CH = C(CH ) , CH CH CH CH Cl d) (CH ) CH, CH CH CH CH Cl
Q48
a)
b)
c)
d)
Q49
(X) is :
a) b)
c) d)
Q50 Most suitable salt which can be used for efficient clotting of blood will be :
a) NaHCO b) FeSO c) Mg(HCO ) d) FeCl
Numerical
Q51 For the reaction the pressure increases from 150 mm Hg to 170 mm
Hg in 10 min. The rate of disappearance of X in mm per min. is…..
3 3 3 2 2 3 2 3 2 3 3
2 3 2 3 2 2 2 3 3 3 2 2 2
3 4 3 2 3

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Q52 Electrolysis of hot aqueous solution of NaCl gives NaClO . Then the number of
Faraday required to deposit 500 g of NaClO is….
(Molar mass of Na = 23 g mol , Cl = 35.5 g mol , O = 16 g mol )
Q53 How many mols of NaOH are required for complete neutralization of the compound
Q54
The degree of unsaturation of (X) is….
Q55 The number of chlorine atom(s) which is/are directly bonded to each beryllium in
solid beryllium chloride is….
Q56 A triatomic non linear gas is expanded according to PV = Constant under very high
temperature. What is the molar heat capacity of the gas in cal/mol (Take R = 2 cal
mol K ).
Q57 If x is the number of exchanges possible for 3d4 electronic configuration, then the
value of is ….
Q58 Consider the reaction
If at a given temperature is dissociated, then the ratio of equilibrium
constant (K ) and total pressure (P) at equilibrium is x × 10 , then the value of x
is….
Q59 K of AgCl is 1 × 10 , then its solubility in 0.1 M KNO is ‘S’ mol L , then the
value of – logS is….
Q60 If ‘x’ is the number of lp – bp repulsions at and ‘y’ is the number of lp – bp
repulsions at 90o in , then the value of is..........
4
4
–1 –1 –1
2
–1 –1
P
–2
SP
–10
3
–1

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Mathematics
Single Choice Question
Q61 The statement p (q p) is equivalent to :
a) p (p q) b) p (p q) c) p (p q) d) p (p q)
Q62 If the straight lines, x = 1 + s, y = –3 – s, z = 1 + s and x= , y= 1 + t, z = 2 – t
with parameters s and t respectively, are co-planar, then equals
a) 0 b) –1 c) d) –2
Q63 If are the unit vectors and mutually perpendicular, then value of
is equal to
a) 0 b) 1 c) –1 d) None of these
Q64 If the tangents to the parabola y = 4ax at (x , y ) and (x , y ) intersect at (x , y ),
then
a) x , x , x are in G.P b) x , x , x are n A.P.
c) y , y , y are in G.P d) y , y , y are in H.P.
Q65 The top of two poles of height 20m and 14m are connected by a wire. If the wire
makes an angle 30° with the horizontal, then the length of the wire is
a) 12m b) 8m c) 10m d) 6m
Q66
The sum of the series is
a) b) c) 2 d) 2
Q67 If f(x) = xe then f(x) is
a)
Increasing on
b) Decreasing on R
c) Increasing on R d)
Decreasing on
Q68 Solution of the differential equation y(xy + 2x y )dx + x(xy - x y )dy = 0 is, (c is
constant of integration)
a) b)
c) d) None of these
Q69 If P and Q are two points on the line 4x + 3y + 30 = 0 such that OP = OQ = 10, where
O is the origin, then the area of the OPQ is
a) 48 b) 16 c) 32 d) None of these
→ →
→ → → ∨ → ∧ → ↔
λ λ
t
2
λ
, ,
i
^
j
^
k
^
[ – – – ]
i
^
j
^
j
^
k
^
k
^
i
^
2
1 1 2 2 3 3
1 3 2 1 2 3
1 2 3 1 2 3
19 20
x(1-x)
2 2 2 2
Δ

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Q70
If f(x) = a + bx + cx , then equals
a) b)
c) d) None of these
Q71
If where and , then is a root of the
equation
a) b) c) d) None of these
Q72 If x = 1 is a critical point of the function f(x) = (3x + ax – 2 – a) e , then :
a)
x = 1 is a local maxima and is a local minima of f
b)
x = 1 and are local maxima of f.
c)
x = 1 and are local minima of f
d)
x = 1 is a local minima and is a local maxima of f
Q73 The tangent to the curve is equally inclined to the axes, then point of
contact, is
a) (1, 2) b) (4, 4) c) (16, 0) d) (0, 16)
Q74 The area bounded by the parabola's y = 4a(x + a) and y = –4a (x – a) is, (a > 0)
a) b) c) d) None of these
Q75 The general solution of the differential equation is (C is constant of
integration)
a) tan x = (c + sec x) y b) sec y = (c + tan y) x
c) sec x = (c + tan x) y d) None of these
Q76
is equal to
a) 1 b) 2 c) –1 d) 2
Q77
If then A is
a) b) c) d) None of these
2
2 x
+ = 4
x
−
−
√ y
√
2 2
64

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Q78 The minimum number of terms from the beginning of the series so
that the sum may exceed 1568, is
a) 25 b) 27 c) 28 d) 29
Q79 If the three linear equations x + 4ay + az = 0, x + 3by + bz = 0 and x + 2cy + cz = 0
have a non-trivial solution, then, (a, b, c R)
a) 2ac = bc + ab b) b = ac c) 2b = a + c d) None of these
Q80 Four digit numbers are formed by using the digits 1, 2, ... 8 (repetition of digits is not
allowed). One number from these four digit numbers is picked up at random. The
probability that the selected number contains unity is
a) b) c) d) None of these
Numerical
Q81
If then the value of is
Q82
The line intersect the curve then value of is
Q83 Let and f(f(x)) = x, then the value of is
Q84 A stick of length 10 units rests against the floor and a wall of a room. If the stick
begins to slide on the floor and the locus of its middle point is x + y = r then the
value is
Q85 If the lines x + y = a and x – y = b touch the curve y = x – 3x + 2 at the points where
the curve intersects the x-axis, then is equal to _______.
Q86 The number of observations in a group is 40. If the average of first 10 is 4.5 and that
of the remaining 30 is 3.5, then the average of the whole group is
Q87 If the sum of first n terms of an A.P. is cn and the sum of squares of these n terms is
then the value of is
Q88 If and are unit vectors, then the greatest value of is ______.
Q89
If and is equal to l then |λ| is
∈
2
2 2 2
2
2

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Q90 If complete set of values of k for which one root of the equation of x – (k + 1) x + k
+ k – 8 = 0 exceed 2 and other is smaller than 2 is (α, β) then is
2 2

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Answer Key
Que.
Ans.
1
B
2
A
3
A
4
C
5
C
6
B
7
B
8
D
9
C
10
B
Que.
Ans.
11
C
12
C
13
A
14
C
15
C
16
C
17
B
18
D
19
C
20
D
Que.
Ans.
21
6
22
75
23
16
24
8791
25
20
26
1
27
17
28
3
29
400
30
1
Que.
Ans.
31
B
32
A
33
D
34
B
35
D
36
C
37
B
38
C
39
C
40
B
Que.
Ans.
41
C
42
B
43
B
44
D
45
C
46
C
47
B
48
B
49
B
50
D
Que.
Ans.
51
4
52
33
53
3
54
5
55
4
56
10
57
2
58
12
59
5
60
4
Que.
Ans.
61
B
62
D
63
A
64
A
65
A
66
B
67
A
68
A
69
A
70
C
Que.
Ans.
71
B
72
D
73
B
74
A
75
C
76
B
77
C
78
D
79
A
80
A
Que.
Ans.
81
0
82
0
83
0
84
0
85
0
86
4
87
1
88
4
89
1
90
0