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Competishun
52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar

Date: 19/01/2024
Time: 3 hours Max. Marks: 300

MFST-14_(23-24)_UTS-2_MT-8

Physics
Single Choice Question

Q1 A small point mass carrying some positive charge on it, is released from the edge of a
table. There is a uniform electric field in this region in the horizontal direction. Which
of the following options then correctly describe the trajectory of the mass? (Curves
are drawn schematically and are not to scale).

a) b) c) d)

Q2 A particle executes S.H.M. of amplitude A along x-axis. At t = 0, the position of the

particle is and it moves along positive x-axis the displacement of particle in time
t as the function of x = A sin (ωt + δ), then the value δ will be :
a) b) c) d)

Q3 Figure shows a circuit that contains four identical resistors with resistance R = 2.0 \
(\Omega\), two identical inductors with inductance L = 2.0 mH and an ideal battery
with emf E = 9 V. The current 'i' just after the switch 'S' is closed will be:

a) 2.25 A b) 3.0 A c) 3.37 A d) 9A

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Q4 The truth table for the following logic circuit is :

a) b) c) d)

Q5 In LR circuit (shown in figure), current is lagging by in phase with applied voltage,

then select correct alternative :

a) b) c)
L= H, i = 10 A L= H, i = 5A L= H, i = 5A
d)
L= ,i=5 A

Q6 Figure shows a part of network of a capacitor and resistors. The potential indicated at
A, B and C are with respect to the ground. The charge on the capacitor in steady state
is

a) 4 μC b) 6 μC c) 10 μC d) 16 μC

Q7 In a vertical plane inside a smooth hollow thin tube a block of same mass as that of
tube is released as shown in figure. When it is slightly disturbed it moves towards
right. By the time the block reaches the right end of the tube then the displacement of
the tube will be (where ‘R’ is mean radius of tube). Assume that the tube remains in
vertical plane. (Horizontal plane is smooth)

a) b) c) d) R

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Q8 Find the current passing through 10\(\Omega\) resistance in the figure below

a) 5/31 A b) 6/31 A c) 4/31 A d) none of these

Q9 Consider a uniformly charged spherical shell of radius 'a'. Net charge on shell
is Q. The shell is surrounded by another uncharged concentric shell of radius
'b'. The work done by external agent in charging outer shell with uniform
charge –Q is.
a) b) c) d)

Q10 A uniform, constant magnetic field \(\overrightarrow B\) is directed at an angle of 45°
to the x-axis in the xy-plane, PQRS is a rigid square wire frame carrying a steady
current Ι0, with its centre at the origin O. At time t = 0, the frame is at rest in the
position shown in the figure, with its sides parallel to the x and y axes. Each side of
the frame is of mass M and length L.

The torque \(\overrightarrow \tau\) about O acting on the frame due to the magnetic
field will be

a) b)
\(\overrightarrow \tau\) = \(\overrightarrow \tau\)=
c) d)
\(\overrightarrow \tau\)= \(\overrightarrow \tau\) =

Q11 The frequency of oscillation of current in the inductor is :

a) b) c) d)

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Q12 Water flows through a frictionless horizontal duct with a cross-section varying as
shown in figure. Pressure p at points along the axis is represented by:

a) b) c)

d)

Q13 In the figure shown a block A of mass m is kept on block B of mass m. A is given a
velocity towards right as shown. The coefficient of friction between A and B is
and that between B and ground is µ.

a)
B will accelerate towards right with acceleration .
b)
B will accelerate towards left with acceleration .
c) B will not accelerate at all.
d) B will move towards right with acceleration µg.

Q14 A plano-convex lens of focal length 10 cm is silvered at its plane face. The distance d
at which an object must be placed in order to get its image on itself is:

a) 5 cm b) 20 cm c) 10 cm d) 2.5 cm

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Q15 As per the given graph choose the correct representation for curve A and curve B.
{Where XC = reactance of pure capacitive circuit connected with A.C. source
XL = reactance of pure inductive circuit connected with A.C. source
R = impedance of pure resistive circuit connected with A.C. source
Z = Impedance of the LCR series circuit}

a) A = XC, B = R b) A = XL, B = Z c) A = XC, B = XL d) A = XL, B = R

Q16 A ray is incident from air on a sphere of refractive index as shown in figure. Angle
of refraction of the ray inside sphere is 30º. The total deviation suffered by the ray is

a) 150° b) 120° c) 90° d) 45°

Q17 Two particles of combined mass M, placed in space with certain separation,
are released. Interaction between the particles is only of gravitational nature
and there is no external force present. Acceleration of one particle with respect
to the other when separation between them is R, has a magnitude :
a) b) c)

d) not possible to calculate due to lack of information

Q18 A diatomic ideal gas undergoes a thermodynamic change according to the P–V
diagram shown in the figure. The total heat given to the gas is nearly (use \(\ell\)n2 =
0.7) :

a) 2.5 P0V0 b) 1.4 P0V0 c) 3.9 P0V0 d) 1.1 P0V0

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Q19 A diatomic ideal gas is heated at constant volume until the pressure is doubled
and again heated at constant pressure until volume is doubled. The average
molar heat capacity for whole process is:
a) b) c) d)

Q20 A proton with a kinetic energy of 2.0 eV moves into a region of uniform magnetic
field of magnitude . The angle between the direction of magnetic field and
velocity of proton is 60°. The pitch of the helical path taken by the proton
is_______cm.
(Take, mass of proton = 1.6 × 10–27 kg and Charge on proton = 1.6 × 10–19 C).
a) 30 b) 35 c) 40 d) 42

Numerical

Q21 A circular coil of radius 10 cm is placed in a uniform magnetic field of 3.0 × 10–
5 T with its plane perpendicular to the field initially. It is rotated at constant
angular speed about an axis along the diameter of coil and perpendicular to
magnetic field so that it undergoes half of rotation in 0.2 s. The maximum
value of EMF induced (in μV) in the coil will be close to the integer _______.

Q22 The work functions of Aluminium and Gold are 4.1 eV and 5.1 eV respectively. The
ratio of the slope of the stopping potential versus frequency plot for Gold to that of
Aluminium is
Q23 A uniform metallic wire is elongated by 0.04 m when subjected to a linear force
F. The elongation, if its length and diameter is doubled and subjected to the
same force will be _____cm.
Q24 A proton and an α-particle are accelerated from rest by 2V and 4V potentials,
respectively. The ratio of their de-Broglie wavelength is K:1, find value of K.
Q25 A frictionless track ABCDE ends in a circular loop of radius R. A body slides down
the track from point A which is at height h = 5 cm. Find the maximum value of R in
cm for a body to complete the loop successfully.

Q26 The difference between (n + 2)th Bohr radius and nth Bohr radius is equal to
the (n – 2)th Bohr radius. The value of n is ?
Q27 Two sound sources produce progressive waves given by y1 =12 cos 100\(\pi\)t and y2
= 4 cos 102\(\pi\)t near the ear of an observer. When sounded together, then find beats
frequency heared by observer is :

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Q28 Given \(|{\vec A_1}| = 2\) , \(|{\vec A_2}| = 3\) and \(|{\vec A_1} + {\vec A_2}| =
3\) . Find the value of \(\frac{{({{\vec A}_1} + 2{{\vec A}_2}).(4{{\vec A}_2} -
3{{\vec A}_1})}}{{16}}\) .

Q29 A boat which can move with a speed of 5 m/s relative to water crosses a river
of width 480 m flowing with a constant speed of 4 m/s. Find the time (in sec.)
taken by the boat to cross the river along the path which is shortest.
Q30 A train stopping at two stations 2 km apart on a straight line takes 4 minutes for the
journey. Assuming that its motion is first uniformly accelerated and then uniformly
retarded. Find value of \({1 \over x} + {1 \over y}\)
[where ' x ' and ' y ' are the magnitude of the acceleration and retardation respectively
in (km/min2)].

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Chemistry
Single Choice Question

Q31 A sulphate of a metal (A) on heating evolves two gases (B) and (C) and an
oxide (D). Gas (B) turns K2Cr2O7 paper green while gas (C) forms a trimer in
which there is no S—S bond. Compound (D) with conc. HCI forms a Lewis
acid (E) which exists in a dimer. Compounds (A), (B), (C), (D) and (E) are
respectively:
a) FeSO 4 , SO 2 , SO 3 , Fe 2 O 3 , FeCI 3 b) AI 2 (SO 4 ) 3 ,SO 2 , SO 3 AI 2 O 3 , AICl 3
c) FeS, SO 2 , SO 3 , FeSO 4 , FeCI 3 d) FeS, SO 2 , SO 3 , Fe 2 (PO 4 ) 3 , FeCI 2

Q32 The correct order for the wavelength of absorption in the visible region is :
a) [Ni(NO 2 ) 6 ] 4– <[Ni(NH 3 ) 6 ] 2+ < [Ni(H 2 O) 6 ] 2+
b) Ni(NO 2 ) 6 ] 4– <[Ni(H 2 O) 6 ] 2+ <[Ni(NH 3 ) 6 ] 2+
c) [Ni(H 2 O) 6 ] 2+ <[Ni(NH 3 ) 6 ] 2+ < [Ni(NO 2 ) 6 ] 4–
d) [Ni(NH 3 ) 6 ] 2+ < [Ni(H 2 O) 6 ] 2+ <[Ni(NO 2 ) 6 ] 4–

Q33

Which step is wrong in above synthesis ?

a) (i) b) (ii) c) (iii) d) None

Q34 Consider the following diazonium ions :

The order of reactivity towards diazo-coupling with phenol in the presence of dil.
NaOH is –

a) I < IV < II < III b) I < III < IV < II c) III < I < II < IV d) III < I < IV < II

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Q35 Which of the following substances can not used directly as fertilizer?
a) (NH 4 ) 2 SO 4 b) Ca 3 (PO 4 ) 2 c) Ca(H 2 PO 4 ) 2 d) CaCN 2 + C

Q36 On heating NaNO3 gives :

a) O 2 b) NO 2 c) O2 + NO2 d) NaNO

Q37 If equivalent conductance of 1M benzoic acid is 12.8 ohm–1 cm2 eq–1 and if the
conductance of benzoate ion and H+ ion are 42 and 288.42 ohm–1 cm2 eq–
1
respectively. its degree of dissociation is
a) 39% b) 3.9% c) 0.35% d) 0.039%

Q38 What is [H+] of a solution that is 0.01 M in HCN and 0.02 M in NaCN (Ka for HCN =
6.2 ×10–10)
a) 3.1 × 10 10 b) 6.2 × 10 5 c) 6.2 × 10 –10 d) 3.1 × 10 –10

Q39 Which of the following order of energies of molecular orbitals of N2 is correct?

a) (π2py ) < (σ2pz) < (π2 ) ≈ (π2 ) b) (π2py ) > (σ 2pz) > (π2 ) ≈ (π2 )
c) (π2py ) < (σ 2pz) > (π2 ) ≈ (π2 ) d) (π2py ) > (σ 2pz) < (π2 ) ≈(π2 )

Q40 Riboflavin deficiency causes :

a) scurvy b) pellagra c) beri-beri d) cheilosis

Q41 Which of the following will not give four smell with CHCl3 / KOH ?
a) CH 3 –CH 2 –NH–CH 3 b) CH 3 –CH 2 –CH 2 –NH 2 c)

d)

Q42 Match the compounds of column-I with the reagent of column-II, which can
distinguish between the compounds of column-I.

a) P–3; Q–2; R–1 b) P–1; Q–2; R–3 c) P–2; Q–1; R–3 d) P–1; Q–3; R–2

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Q43 The correct IUPAC name of the compound is

a) (2R, 3R)-3-Bromo-2-butanol b) (2R, 3S)-3-Bromo-2-hydroxybutane

c) (2R, 3S)-3-Bromo-2-butanol d) (2S, 3R)-2-Bromo-3-butanol

Q44 Correct order of acidic strength of following compound is :

(i) (ii) (iii) (iv)

a) iv > ii > iii > i b) iii > ii > iv > i c) iv > iii > ii > i d) ii > iii > iv > i

Q45 The main factor for shorter B–F bonds in BF3 is :

a) Ionic- covalent resonance in BF 3 b) Large electronegativity of fluorine
c) pπ–pπ back bonding d) dπ–pπ back bonding

Q46

a) b) c) d)

Q47 The acid D obtained through the following sequence of reactions is

a) Succinic acid b) Malonic acid c) Maleic acid d) Oxalic acid

Q48 A Substance undergoes first order decomposition. The decomposition follows two
parallel first orderreactions as

The percentage distribution of B and C are

a) 75% B and 25% C b) 80% B and 20% C c) 60% B and 40% C

d) 76.83% B and 23.17% C

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Q49 Treatment of ammonia with excess of ethyl chloride will yield

a) Diethyl amine b) Ethane c) Tetraethyl ammonium chloride
d) Ethyl amine

Q50 Consider the following reaction,

the product Z, is
a) CH 2 =CH 2 b) CH 3 CH 2 OCH 2 CH 3 c) CH3CH2OSO3H d) CH3CH2OH

Numerical

Q51 The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg
pressure is _____ L. (Rounded off to the nearest integer) [Given R = 0.0826 L
atm K–1 mol–1]
Q52 C6H6 freezes at 5.5°C. The temperature at which a solution 10 g of C4H10 in
200 g of C6H6 freeze is _______ °C. (The molal freezing point depression
constant of C6H6 is 5.12°C/m.) (Rounded off to the nearest integer)
Q53 The solubility product of PbI2 is 8.0 × 10–9. The solubility of lead iodide in 0.1 molar
solution of lead nitrate is \(x \times 10^{-6}\) mol/L. The value of x is __________.
(Rounded off to the nearest integer)
[Given : \(\sqrt2 = 1.41\)]
Q54 Assuming ideal behaviour, the magnitude of log K for the following reaction at 25°C
is x × 10–1. The value of x is _______. (Integer answer)
\(3HC \equiv CH_{g} \rightleftharpoons C_6H_{6(\ell)}\)
[Given: \(\Delta\)ƒGo (HC \(\equiv\) CH) = –2.04 × 105 J mol–1; \(\Delta\)ƒGo(C6H6)
= –1.24 × 105 J mol–1; R = 8.314
J K–1 mol–1]
Q55 Number of amphoteric compound among the following is __________
(i) BeO (ii) BaO (iii) Be(OH)2 (iv) Sr(OH)2

Q56 For the reaction A(g) → (B)(g), the value of the equilibrium constant at 300 K and 1
atm is equal to 100.0. The value of \(\Delta\)rG for the reaction at 300 K and 1 atm in
J mol–1 is – xR, where x is ______ (Rounded of to the nearest integer)
(R = 8.31 J mol–1 K–1 and ln 10 = 2.3)
Q57 A proton and a Li3+ nucleus are accelerated by the same potential. If λLi and λP denote
the de Broglie wavelengths of Li3+ and proton respectively, then the value of \
(\lambda_{Li} \over \lambda_P\) is x × 10–1. The value of x is ____.
(Rounded off to the nearest integer)
(Mass of Li3+ = 8.3 mass of proton)

Q58 Gaseous cyclobutene isomerizes to butadiene in a first order process which

has a 'k' value of 3.3 × 10–4s–1 at 153°C. The time in minutes it takes for the
isomerization to proceed 40 % to completion at this temperature is _____.
(Rounded off to the nearest integer)

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Q59 The equivalent weight of HCl in the given reaction is :

K2Cr2O7 + 14HCl \(\longrightarrow\) 2KCl + 2CrCl3 + 3Cl2 + H2O
(Report your answer in terms of nearest integer)
Q60 Total charge required (in F) for the oxidation of two moles Mn3O4 into MnO42–
in presence of alkaline medium is :

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Mathematics
Single Choice Question

Q61 If a sin x + b cos (c + x) + b cos (c – x) = α, α > a, then the minimum value of | cosc |
is :
a) b) c) d)

Q62 The remainder when 230 ⋅ 320 is divided by 7 is :

a) 1 b) 2 c) 4 d) 6

Q63 The area (in sq. units) of the region

{(x, y)\(\in\) R2 | 4x2 \(\leq\) y \(\leq\) 8x + 12} is

a) b) c) d)

Q64 If p, q, r are positive and are in A.P., in the roots of quadratic equation px2 + qx + r =
0 are all real for
a) b) c) all p and r d) no p and r

Q65 How many words can be formed by rearranging the letters of the word "GENIUS"
such that each word neither start with 'G' nor end with 'S' ?

a) 480 b) 600 c) 504 d) 720

Q66 If , then the value of q is

a) 1 b) c) d)

Q67

a) abc > 1 b) abc > –8 c) abc < –8 d) abc > –2

Q68

a) (1, 4) b) (7, -2) c) (4, 1) d) (-2, 7)

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Q69

a) 1 and 2 b) 1 and 4 c) 2 and 3 d) 3 and 4

Q70

a) 12 b) 14 c) 17 d) 10

Q71
is equal to
a) loge 12 b) loge 3.loge 4 c) (loge 3.loge 4)−1 d) −6loge 3.loge 4

Q72
Let f : R \(\rightarrow\) R be a function defined as

Then, f is:
a) Continuous if a = –5 and b = 10 b) Continuous if a = 5 and b = 5
c) Continuous if a = 0 and b = 5 d) Not continuous for any values of a and b

Q73

a) b) c) d)

Q74

a) 0 b) 1 c) 5 d) 2

Q75

a) b) c) d)

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Q76

a) b) c) d)

Q77

a) parallel b) perpendicular c) d) none of these

inclined at

Q78
If Ι = , then

a) Ι= loge 2 b) Ι< loge 2 c) d)

Ι= loge 2 <Ι<

Q79

a) 2 b) 4 c) 6 d) 8

Q80

a) x4 + y4 + x2 y2 = c b) x4 + y4 + 3x2 y2 = c c) x4 + y4 + 6x2 y2 = c
d) x4 + y4 + 9x2 y2 = c

Numerical

Q81

Q82

Q83

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Q84 The mean of 9 observations is 15. If one more observation is added to the series, the
mean
becomes 16. The value of 10th observation is
Q85
If and .
Then the number of subsets of set A×(A \(\cap\) B) which contains exactly 3 elements,
is

Q86 If \(% MathType!MTEF!2!1!+- %

feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX %
garmWu51MyVXgatCvAUfKttLearyWqVvNCPvMCqnfaruavP1wzZbIt %
LDhis9wBH5garqqtubsr4rNCHbGeaGqiFCI8FfYJH8WrFfeuY-Hhbb %
a9v8qqaqFr0xc9pk0xbba9q8WqFfeaY-biLkVcLq-JHqpepeea0-as %
0Fb9pgeaYRXxe9vr0-vr0-vqpWqaaeaabaGaaiaacaqabeaadaabau %
aaaOqaaiaad2eacqGH9aqpdaWadaqaauaabeqadmaaaeaacaaIXaaa %
baGaam4yaaqaaiaaiodaaeaacaaIXaaabaGaaG4maaqaaiaaiodaae %
aacaaIYaaabaGaaGinaaqaaiaaisdaaaaacaGLBbGaayzxaaGaaiil % aiaad2eaaaa!455D!
M = \left[ {\begin{array}{*{20}{c}} 1&c&3\\ 1&3&3\\ 2&4&4 \end{array}}
\right],M\) is the adjoint of a 3 × 3 matrix N and det(N) = 4, then c is equal to

Q87
Let the equations of two ellipses be E1 : and E2 : . If the product

of their eccentricities is , then the largest possible length of the minor axis of ellipse
E2 is

Q88

Q89 If z1 and z2 are non zero solutions of equation where , then |z1 + z2 | is
equal to

Q90

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Answer Key
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Que. 1 2 3 4 5 6 7 8 9 10

Ans. B A A B C A C A D A

Que. 11 12 13 14 15 16 17 18 19 20

Ans. B A C C C A B C B C

Que. 21 22 23 24 25 26 27 28 29 30

Ans. 15 1 2 4 2 8 1 4 160 4

Que. 31 32 33 34 35 36 37 38 39 40

Ans. A A B B B A B D A D

Que. 41 42 43 44 45 46 47 48 49 50

Ans. A D C A C B A D C D

Que. 51 52 53 54 55 56 57 58 59 60

Ans. 5 1 141 855 2 1380 2 26 85 20

Que. 61 62 63 64 65 66 67 68 69 70

Ans. D B A B C D B B A D

Que. 71 72 73 74 75 76 77 78 79 80

Ans. D D D A C D C D D C

Que. 81 82 83 84 85 86 87 88 89 90

Ans. 0 4 2 25 220 11 16 24 2 8

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