MikaStars39/nano-eval huggingface dataset:
A bullet of mass m moving with velocity  u just grazes the top of a solid cylinder of mass M and radius R resting on a rough horizontal surface as shown in the figure.Assume that the cylinder rolls without slipping the angular velocity of the cylinder is $\omega$ and the final velocity of the bullet is $v$, then

Options:
A. $$\omega =\dfrac{4mu}{(8m+3M)R}$$
B. v=\dfrac{14mu}{(8m+3M)}
C. $$\omega =\dfrac{2mu}{(8m+3M)R}$$
D. $$v=\dfrac{8mu}{(8m+3M)}$$
E. v=\dfrac{8mu}{(8m+3m)}
F. v=\dfrac{6mu}{(8m+3M)}
G. v=\dfrac{12mu}{(8m+3M)}
H. v=\dfrac{10mu}{(8m+3M)}
I. v=\dfrac{10mu}{(8m+3m)}
J. $$v=\dfrac{2mu}{(8m+3m)}$$
Answer: D
A 10kg block is pullled along a frictionless surface in the form of an arc of a vertical circle of radius 10m, as shown in figure. The tangential applied force is 200 N. If the block started from rest at point P, then its velocity at Q will be (take $g=10m/s^2$)

Options:
A. 17 m/s
B. $$16 m/s$$
C. $$18 m/s$$
D. $$20 m/s$$
E. 19 m/s
F. 21 m/s
G. $$15 m/s$$
H. 20.5 m/s
I. 22 m/s
J. 19.5 m/s
Answer: D
Compare momentum of $10^{5}\ eV$ $X-$ray photon $(P_{x})$ with that of a $10^{5}\ eV$ electron $(P_{e})$

Options:
A. $$\dfrac {P_{e}}{P_{x}}=\dfrac {51}{16}$$
B. $$\dfrac {P_{e}}{P_{x}}=\dfrac {1}{5}$$
C. \dfrac {P_{e}}{P_{x}}=\dfrac {16}{51}
D. \dfrac {P_{e}}{P_{x}}=\dfrac {10}{3}
E. \dfrac {P_{e}}{P_{x}}=\dfrac {51}{8}
F. $$\dfrac {P_{e}}{P_{x}}=\dfrac {5}{1}$$
G. \dfrac {P_{e}}{P_{x}}=\dfrac {51}{10}
H. $$\dfrac {P_{e}}{P_{x}}=\dfrac {16}{5}$$
I. \dfrac {P_{e}}{P_{x}}=\dfrac {16}{1}
J. \dfrac {P_{e}}{P_{x}}=\dfrac {16}{8}
Answer: A
A ball of mass $m=100\ gm$ is suspended from a point $A$ by an inextensible thread of length $l$. Ball is drawn a side and held at same level as $A$ but at a distance $\dfrac{\sqrt{3}}{2}l$ from $A$ as shown in figure. Now ball is released.
Then:
(assume string applies only that much jerk which is required so that velocity along string becomes $0$)

Options:
A. impulse applied by string $\sqrt{\dfrac{gl}{22}}
B. impulse applied by string $\sqrt{\dfrac{gl}{18}}$
C. velocity of ball just after experiencing jerk is $\sqrt{\dfrac{3gj}{2}}$
D. velocity of ball just before experiencing jerk is $\sqrt{gl}$
E. impulse applied by string $\sqrt{\dfrac{gl}{20}}$
F. impulse applied by string $\sqrt{\dfrac{gl}{15}}$
G. ball will experience jerk after reaching to point $B$
H. impulse applied by string $\sqrt{\dfrac{gl}{10}}$
I. impulse applied by string $\sqrt{\dfrac{gl}{24}}$
J. impulse applied by string $\sqrt{\dfrac{gl}{25}}$
Answer: E
Three different circuits (I, II and III) are constructed using identical batteries and resistors of R and $2R$ ohm. What can be said about current I in arm AB of each circuit?

Options:
A. $$I_{I} = I_{II} = I_{III}$$
B. $$I_{II} < I_{I} < I_{III}$$
C. $$I_{I} > I_{II} = I_{III}$$
D. I_{I} > I_{III} > I_{II}
E. $$I_{I} > I_{II} > I_{III}$$
F. I_{I} < I_{II} < I_{III}
G. $$I_{I} < I_{II} = I_{III}$$
H. $$I_{I} < I_{III} < I_{II}$$
Answer: A
A cylindrical tank has a hole of $2cm^2$ at its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $100cm^3/s,$ then the maximum height up to water can rise in the tank $(Take {\,\,} g= 10m{\,\,} s^{-2})$

Options:
A. $$3.5\times10^{-2}m$$
B. $$5.5\times10^{-2}m$$
C. 4.0 \times 10^{-2}m
D. 4.5 \times 10^{-2}m
E. 6.5 \times 10^{-2}m
F. $$1.5\times10^{-2}m$$
G. 5.6 \times 10^{-2}m
H. $$2.5\times10^{-2}m$$
I. 4.6 \times 10^{-2}m
J. 5.0 \times 10^{-2}m
Answer: B
A sealed vessel contains water upto height h = 3.5 m. The space above the water contains compressed air at pressure 4.2 $P_0 (P_0 = 1 x 10^5 P_a$, atmospheric pressure). The vessel connected to a tube at the bottom as shown in figure. Area of cross-section of the tube is uniform and small as compared to the vessel. Temperature of air remains constant.

Options:
A. 16.6 m/s
B. 36.6 m/s
C. 46.6 m/s
D. 56.6 m/s
E. 21.6 m/s
F. 10.6 m/s
G. Initial speed of the efflux of water is (approximately)
H. 15.6 m/s
I. 12.6 m/s
J. 26.6 m/s
Answer: G
An atom of an element loses two electrons to form an ion. The quantum numbers of the electrons lost are $n=4$ and $l=0$. If another atom of the same element loses one more electron to form an ion, the quantum numbers (Principle and Azimuthal) of this electron lost are______.

Options:
A. 2,2
B. 1,1
C. 2,3
D. 2,1
E. 3,5
F. 1,3
G. 1,2
H. 3,2
I. 1,0
J. None of these
Answer: G
For the one-dimensional motion, described by x=t-sint

Options:
A. v(t)lies between 0 and 2
B. $v(t) < 0$ for all t>0
C. $x(t) < 0 $ for all t>0
D. $x(t) > 0 $ for all t>0
E. $v(t) = 0$ for all t>0
F. $a(t) > 0 $ for all t>0
G. $v(t) \leq 1$ for all t>0
H. x(t) < 1 for all t>0
I. $v(t) > 0 $ for all t>0
Answer: D
The minimum stoping potential required for an electron, which was emiited from a metal surface $({ w }_{ 0 }) = 4.5 eV$ when the surface is radiated with radiation of $2\times { 10 }^{ 15 }$ Hz, frequency, is:

Options:
A. 3.59 V
B. $$3.78 V$$
C. $$2.81 V$$
D. 3.54 V
E. 3.57 V
F. $$3.12 V$$
G. 3.69 V
H. 3.45 V
I. $$4.75 V$$
Answer: F
The collision of two balls of equal mass takes place at the origin of coordinates. Before collision, the components of velocities are $(V_x = 50 c m s^{-1},  V_{y} = 0)$ and $(V_{x} = -40 c m s^{-1}$ and $V_{y} = 30 c m s^{-1})$. The first ball comes to rest after collision. The velocity (components $V_{x}$ and $V_{y}$ respectively) of the second ball are

Options:
A. 10 and 25 $c m s^{-1}$
B. 15 and $5 c m s^{-1}$
C. 10 and 30 $c m s^{-1}$
D. 30 and 10 $c m s^{-1}$
E. 20 and 10 $c m s^{-1}$
F. 10 and 15 $c m s^{-1}$
G. 15 and 25 $c m s^{-1}$
H. 10 and 40 $c m s^{-1}$
I. 5 and 15 $c m s^{-1}$
J. 5 and 20 $c m s^{-1}$
Answer: I
For a tribasic acid, $H_{3}A$, $K_{a1} = 2 \times 10^{-3}$, $K_{a2} = 5 \times 10^{-9}$ and $K_{a3} = 4 \times 10^{-12}$. The value of $\frac{[A^{3-}]}{[H_{3}A]}$ at equillibrium in an aqueous solution originally having $0.2 M - H_{3}A$ is

Options:
A. 6 \times 10^{-19}
B. $$2 \times 10^{-22}$$
C. 2 \times 10^{-18}
D. $$1 \times 10^{-17}$$
E. $$5 \times 10^{-9}$$
F. 6 \times 10^{-18}
G. 3 \times 10^{-18}
H. 4 \times 10^{-18}
I. 4 \times 10^{-19}
J. $$5 \times 10^{-18}$$
Answer: J
A satellite of mass $m$ is launched vertically upwards with an initial speed $u$ from the surface of the earth. After it reaches height R(R= radius of the earth), it ejects a rocket of mass $\dfrac{m}{10}$ so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is ($G$ is the gravitational constant; $M$ is the mass of the earth) :

Options:
A. \dfrac{m}{20}\left(u^2+\dfrac{111}{200}\dfrac{GM}{R}\right)
B. \dfrac{m}{20}\left(u^2+\dfrac{117}{200}\dfrac{GM}{R}\right)
C. \dfrac{m}{20}(u^2+\dfrac{119}{200}\dfrac{GM}{R})
D. $$\dfrac{m}{20}\left(u-\sqrt{\dfrac{2GM}{3R}}\right)^2$$
E. \dfrac{m}{20}\left(u^2+\dfrac{115}{200}\dfrac{GM}{R}\right)
F. $$\dfrac{m}{20}(u^2+\dfrac{113}{200}\dfrac{GM}{R})$$
G. \dfrac{m}{20}\left(u^2+\dfrac{121}{200}\dfrac{GM}{R}\right)
H. \dfrac{m}{20}\left(u^2+\dfrac{112}{200}\dfrac{GM}{R}\right)
I. $$5m(u^2-\dfrac{119}{200}\dfrac{GM}{R})$$
J. $$\dfrac{3m}{8}\left(u+\sqrt{\dfrac{5GM}{6R}}\right)^2$$
Answer: I
A shell of some mass fried with speed $V_0$ at an angle $\theta$ = $30^o$ to the horizontal explodes at the highest point of its motion into two equal fragments. If one fragment is at rest after explosion, then the distance at which the other fragment falls from the gun is

Options:
A. $$\frac { 3{ V }_{ 0 }^{ 2 } }{ 4g } $$
B. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 7g }
C. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 6g }
D. $$\frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 2g } $$
E. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 9g }
F. $$\frac { \sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 2g } $$
G. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 8g }
H. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 5g }
I. $$\frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 4g } $$
J. \frac { 3\sqrt { 3 } { V }_{ 0 }^{ 2 } }{ 10g }
Answer: D
The coefficient of friction between the wheels of a car and the ground is $0.5$. The car starts from rest and moves along a perfectly horizontal road. If $g = 10 ms^{-2}$, the car

Options:
A. Can attain a speed of $20ms^{-1}$ in minimum distance of $40 m$
B. Can attain a speed of $20ms^{-1}$ in minimum distance of $70 m
C. Can acquire a maximum acceleration of $5ms^{-2}$ without slipping
D. Can attain a speed of $20ms^{-1}$ in minimum distance of $55 m
E. After acquiring a speed of $50 ms^{-1}$, can come to rest, with the engine shut off and brakes not applied, in a time of $10s$.
F. Can attain a speed of $20ms^{-1}$ in minimum distance of $80 m
G. Can attain a speed of $20ms^{-1}$ in minimum distance of $50 m$
H. Can go up to a speed of $100ms^{-1}$ in $10s$
I. Can attain a speed of $20ms^{-1}$ in minimum distance of $60 m$
J. Can attain a speed of $20ms^{-1}$ in minimum distance of $45 m$
Answer: A
Suppose a photon of frequency (v) causes photoelectric emission from a surface with threshold frequency $(v_o)$, what is the de-Broglie wavelength of the photoelectron of maximum kinetic energy in terms of $\Delta v = v - v_0$ ?

Options:
A. \lambda = \left(\dfrac{h}{7 \pi \Delta v} \right)^{1/2}
B. \lambda = \left(\dfrac{h}{4 \pi \Delta v} \right)^{1/2}
C. $$\left[\dfrac{1}{v_0} - \dfrac{1}{v} \right] = \dfrac{mc^2}{h}$$
D. $$\lambda = \left(\dfrac{h}{2 \pi \Delta v} \right)^{1/2}$$
E. \lambda = \left(\dfrac{h}{8 \pi \Delta v} \right)^{1/2}
F. \lambda = \left(\dfrac{h}{3 \pi \Delta v} \right)^{1/2}
G. $$\Delta v = \dfrac{h}{\lambda}$$
H. $$\Delta v = \dfrac{h}{Zm \lambda}$$
I. \lambda = \left(\dfrac{h}{\pi \Delta v} \right)^{1/2}
J. \lambda = \left(\dfrac{h}{6 \pi \Delta v} \right)^{1/2}
Answer: H
For a wave 
$$y=0.0002\sin \left[2\pi \left(110t-\dfrac{x}{3}\right)+\dfrac{\pi}{3}\right]$$
is travelling in a medium. The energy per unit volume being transferred by wave if density of medium is $1.5\ kg/m^3$, is :

Options:
A. $$1.43\times 10^{-4}\ J/m^3$$
B. 134.2 \times 10^{-4}\ J/m^3
C. 143.2 \times 10^{-2}\ J/m^3
D. $$14.3\times 10^{-4}\ J/m^3$$
E. $$14\times 10^{-4}\ J/m^3$$
F. 143.2 \times 10^{-3}\ J/m^3
G. $$143.2\times 10^{-4}\ J/m^3$$
H. 1432 \times 10^{-4}\ J/m^3
I. 143.0 \times 10^{-4}\ J/m^3
J. 143.2 \times 10^{-5}\ J/m^3
Answer: G
The speed of sound in a certain metal is $V$. One end of a long pipe of that metal of length $L$ is struck a hard blow. A listener at the other end hears two sounds, one from the wave that has travelled along the pipe and the other from the wave that has travelled through the air. $v$ is the speed of sound in air. Suppose that $t=1.00\ s$ and the metal is steel. Choose the correct options :

Options:
A. Time interval elapses between the arrivals of the two sounds is $L(V+v)/Vv$
B. Length $L$ is $364\ m$
C. Length $L$ is $432\ m$
D. Length $L$ is $372\ m$
E. Length $L$ is $374\ m$
F. Length $L$ is $366\ m$
G. Length $L$ is $418\ m$
H. Length $L$ is $360\ m$
I. Length $L$ is $420\ m$
Answer: B
A wedge of mass M$=4$m lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by?

Options:
A. $$\dfrac{2v^2}{6g}$$
B. $$\dfrac{2v^2}{5g}$$
C. \dfrac{2v^2}{3g}
D. \dfrac{2v^2}{4g}
E. $$\dfrac{v^2}{2g}$$
F. \dfrac{2v^2}{9g}
G. \dfrac{2v^2}{11g}
H. \dfrac{2v^2}{8g}
I. $$\dfrac{v^2}{g}$$
J. $$\dfrac{2v^2}{7g}$$
Answer: B
The first & second stage of the two stages rocket separately weigh $100\ kg$ and $10\ kg$ and contain $800\ kg$ and $90\ kg$ fuel respectively. If the exhaust velocity of gases is $2\ km/sec$ then velocity of rocket after second stage is (nearly) $(\log_{10}5=0.6990)$ (neglect gravity)

Options:
A. 8.1 \times 10^{3}m/s
B. 8.2 \times 10^{3}m/s
C. $$7.8\times 10^{3}m/s$$
D. $$6.1\times 10^{3}m/s$$
E. 8.4 \times 10^{3}m/s
F. $$2.4\times 10^{3}m/s$$
G. 7.5 \times 10^{3}m/s
H. 8.0 \times 10^{3}m/s
I. 8.6 \times 10^{3}m/s
J. $$9.3\times 10^{3}m/s$$
Answer: C
A linear charge having linear charge density $\lambda=\dfrac {x\lambda_0}{B}+\lambda_0$, where $x$ is distance from point $A$ on wire and $B$ is a positive constant having unit of metre. This linear charge is placed inside a cube. If point $A$ of wire is at one of the vertices of cube so that maximum flux is associated with the cube of side $L$ then the magnitude of charge enclosed by the cube.

Options:
A. \dfrac {\lambda_0 L^2}{2B}+\lambda_0L\sqrt[4]{3}
B. \dfrac {\lambda_0 L^2}{2B}+\lambda_0 L\sqrt 2
C. \dfrac {\lambda_0 L^2}{2B}+\lambda_0L\sqrt[3]{3}
D. $$\dfrac {\lambda_0 L^2}{2B}+\lambda_0 L\sqrt 3$$
E. \dfrac{\lambda_0 L^2}{2B} + \lambda_0 L \sqrt[3]{2}
F. $$\dfrac{3\lambda_0 L^2}{2B}+\lambda_0L\sqrt 3$$
G. $$\dfrac {\lambda_0 L^2}{2B}+\lambda_0L$$
H. \dfrac {\lambda_0 L^2}{2B}+\lambda_0 L \sqrt[4]{2}
Answer: G
An aeroplane flies along a straight line from A to B with a speed $v$$_{0}$ and back again with the same speed $v$$_{0}$. A steady wind $v$ is blowing. If $AB = l$ then

Options:
A. total time for the trip increase because of the presence of wind
B. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}-2v^{2}}$ if wind blows along the line AB
C. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}-3v^{2}}$
D. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}+2v^{2}}$
E. total time for the trip decrease because of the presence of wind
F. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}-v^{2}}$ if wind blows along the line AB
G. total time for the trip is $\dfrac{2l}{\sqrt{v_{0}^{2}-v^{2}}}$, if wind blows perpendicular to the line AB
H. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}-4v^{2}}$ if wind blows along the line AB
I. total time for the trip is $\dfrac{2v_{0}l}{v_{0}^{2}+v^{2}}$
J. total time for the trip is \(\dfrac{2v_{0}l}{v_{0}^{2}-3v^{2}}\)
Answer: A
A cubical block of mass $M$ is kept inside a liquid of variable density ${ \rho  }_{ y }={ \rho  }_{ 0 }\left( 1+by \right) ,$ where y is the distance from the free surface. Initially $\dfrac{1^{th}}{4}$ of cubical block is immersed. What is the mass M of the additional block kept on the first block to immerse it just completely ? (where ${ \rho  }_{ 0 }$ and $b$ are constant, side of cube $=l$)

Options:
A. None of these
B. M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 11 }{ 32 } bl \right]
C. M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 8 }{ 32 } bl \right]
D. M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 13 }{ 32 } bl \right]
E. $$M\prime =\dfrac { 3 }{ 4 } M$$
F. $$M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 15 }{ 32 } bl \right] $$
G. M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 10 }{ 32 } bl \right]
H. $$M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 12 }{ 32 } bl \right] $$
I. $$M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 7 }{ 32 } bl \right]$$
J. $$M\prime =\left[ \dfrac { 3 }{ 4 } +\dfrac { 9 }{ 32 } bl \right]$$
Answer: E
A parachutist drops freely from an aeroplane for $8s$ before the parachute opens out. Then he descends with a net retardation of $2\ ms^{-2} $ reaching thr ground with a velocity of $6\ ms^{-1} $. The height from which he bails out of the aeroplane is $ (g = 10\ ms^{-2}) $

Options:
A. $$2000\ m $$
B. 1611\ m
C. 1610\ m
D. 1601\ m
E. $$1929\ m $$
F. 1581\ m
G. 1911\ m
H. 1609\ m
I. $$1591\ m $$
Answer: I
Which transition of $Li^{2+}$ is associated with same energy change as n = 6 to n = 4 transition in $He^+$ ?

Options:
A. n = 3 to n = 1
B. n = 4 to n = 2
C. n = 5 to n = 1
D. n = 8 to n = 6
E. n = 2 to n = 1
F. n = 6 to n = 3
G. n = 3 to n = 2
H. n = 9 to n = 6
I. n = 9 to n = 5
J. n = 4 to n = 1
Answer: A
A particle of mass m is performing simple harmonic motion along line AB with amplitude 2a with centre of oscillation as O. At time $t=0$ particle is at point $C(OC=a)$ and is moving towards B with velocity $v = a\sqrt{3}$ m/s. The equation of motion can be given by

Options:
A. $$x = a(\sqrt{3} \sin t + \cos t)$$
B. x = a(\sqrt{3} \sin t - \cos t)
C. x = 2a(\sin t - \sqrt{3} \cos t)
D. $$x = 2a(\sin t + \sqrt{3} \cos t)$$
E. x = 2a(\sin t - \cos t)
F. x = a(\sin t + \sqrt{3} \cos t)
G. x = a(\sin t - \sqrt{3} \cos t)
H. \( x = a(\sqrt{3} \sin t - \cos t) \)
I. $$\displaystyle x = 2a\sin \left(t + \frac{\pi}{6}\right)$$
Answer: A
One mole of steam is condensed at ${100}^{o}C$ the water is cooled to ${0}^{o}C$ and frozen to ice. Which of the following statements are correct, given heat of vapourization and fusion are $540cal/gm$ and $80cal/gm$ (average heat capacity of liquid water $=1cal$ ${gm}^{-1}$ ${degree}^{-1}$?

Options:
A. Total entropy change is $-37.35cal/_{ }^{ o }{ C }
B. Total entropy change is $-37.45cal/_{ }^{ o }{ C }
C. Total entropy change is $-36.95cal/_{ }^{ o }{ C }$
D. Total entropy change is $-37.50cal/_{ }^{ o }{ C }$
E. Entropy change during the condensation of steam is $-26.06cal/_{ }^{ o }{ C }$
F. Entropy change during cooling of water from ${100}^{o}C$ to ${0}^{o}C$ is $-5.62cal/_{ }^{ o }{ C }$
G. Entropy change during freezing of water at ${0}^{o}C$ is $-5.27cal/_{ }^{ o }{ C }$
H. Total entropy change is $-37.00cal/_{ }^{ o }{ C }
I. Total entropy change is $-37.15cal/_{ }^{ o }{ C }
J. Total entropy change is $-37.05cal/_{ }^{ o }{ C }$
Answer: C
A layer of glycerin of thickness 1 mm is present between a large surface area and a surface area of $ 0.1 m^2 $. With what force the small surface is to be pulled so that it can move with a velocity of  1 m/s?  (Given that coefficient of viscosity $= 0.07 Kg-m^{-1}s^{-1} Y ) $

Options:
A. 70 N
B. 7.7 N
C. 0.77 N
D. 7.0 N
E. 0.7 N
F. 0.070 N
G. 0.70 N
H. 700 N
I. 0.07 N
J. 7 N
Answer: A
It costs Rs. $10$ to electrodeposit $1$ g of Mg from a solution of MgSO$_4$. The cost of electrodepositing $1$ g of Al from Al$_2$(SO$_4$)$_3$ solution at the same temperature is (atomic weight of Mg = $24$, Al = $27$)

Options:
A. Rs. $9.25$
B. Rs. $13.33$
C. Rs. $8.4$
D. Rs. $11.25$
E. Rs. $6.66$
F. Rs. $10.80
G. Rs. $8.80
H. Rs. $10$
I. Rs. $9.60
J. Rs. $12.50
Answer: H
What is the energy (eV) associated the de-excitation of an electron from n = 6 to n = 2 in ${\text{H}}{{\text{e}}^{\text{ + }}}\;$ ion?

Options:
A. 1.429 \times 10^{-22}
B. $$3.429\times10^{-19}$$
C. 1.229 \times 10^{-22}
D. $$1.129\times10^{-22}$$
E. 2.129 \times 10^{-22}
F. $$0.429\times10^{-19}$$
G. 1.229 \times 10^{-19}
H. $$2.429 \times 10^{-19}$$
I. 1.429 \times10^{-19}
J. $$5.429\times10^{-19}$$
Answer: D
An inductor $20 mH$ a capacitor $100 F$ and a resistor $50 \Omega$ are connected in series across a source emf $V=10 \sin \pi t$ . Then the power loss in the circuit is

Options:
A. 0.81 W
B. $$1.13 W$$
C. $$0.43 W$$
D. 0.76 W
E. 0.84 W
F. 0.78 W
G. $$2.74 W$$
H. 0.82 W
I. $$0.79 W$$
J. 0.89 W
Answer: I
A ray of light coming along the line 3x + 4y -5 =0 gets reflected from the line ax + by - 1 =0 and goes along the line 5x - 12y - 10 =0, then

Options:
A. $$a=\frac { 64 }{ 115 } ,\quad b=\frac { 112 }{ 15 } $$
B. a=\frac{64}{115},\quad b=\frac{112}{345}
C. a=\frac { 64 }{ 115 } ,\quad b=\frac { 112 }{ 230 }
D. a=\frac{64}{115},\quad b=\frac{112}{30}
E. $$a=\frac { 64 }{ 115 } ,\quad b=-\frac { 8 }{ 115 } $$
F. $$a=-\frac { 64 }{ 115 } ,\quad b=\frac { 8 }{ 115 } $$
G. a=\frac{64}{115},\quad b=\frac{112}{23}
H. a=\frac{64}{115},\quad b=\frac{112}{115}
I. $$a=-\frac { 64 }{ 115 } ,\quad b=-\frac { 8 }{ 115 } $$
Answer: A
The second overtone of an open organ pipe A and a closed pipe B have the same frequency at a given temperature. It follows that the ratio of the  :

Options:
A. frequencies of first overtone of A & B is 10 : 7
B. frequencies of first overtone of A & B is 11 : 9
C. lengths of B to that of A is 5 : 6
D. frequencies of first overtone of A & B is 8 : 9
E. frequencies of first overtone of A & B is 10 : 9
F. frequencies of first overtone of A & B is 11 : 10
G. frequencies of first overtone of A & B is 9 : 10
H. length of A and B is 4 : 3
I. frequencies of first overtone of A & B is 10 : 8
J. fundamental frequencies of A & B is 5 : 6
Answer: E
The foci of the hyperbola ${ 9x }^{ 2 }-{ 16y }^{ 2 }+18x+32y-151=0$ are

Options:
A. None of these
B. (2,1),(5,3)
C. (2,3),(6,1)
D. $$(2,3),(5,7)$$
E. (2,3),(-6,3)
F. (2,3),(-6,1)
G. $$(4,1),(-6,1)$$
H. (2,3),(-6,7)
I. (4,1),(-6,3)
J. $$(0,0),(5,3)$$
Answer: D
Hydrogen atoms in a sample are excited to $n=5$ state and it is found that photons of all possible wavelengths are present in the emission spectra. The minimum number of hydrogen atoms in the sample would be

Options:
A. 8
B. $$6$$
C. $$infinite$$
D. 4
E. 3
F. 7
G. 9
H. $$5$$
I. 10
Answer: B
A pump motor is used to lift water to a height 4 m and to deliver water of $0.12 m^3/minute$ with a velocity of 10 m/s. The power of pump is [density of water=$10^3 kg/m^3,g=10 m/s^2$]

Options:
A. 280 W
B. 170 W
C. 200 W
D. 140 W
E. 120 W
F. 160 W
G. 180 W
H. 100 W
I. 190 W
J. 150 W
Answer: H
The reaction, $A+OH^-\rightarrow Products$, obeys rate law expression as, $\frac {-d[A]}{dt}=K[A][OH^-]$. If initial concentrations of [A] and $[OH^-]$ are 0.002 M and 0.03 M respectively and if it takes 30 sec for 1% A to react at $25^oC$, the rate constant for the reaction:

Options:
A. 1.22 \times 10^{-3} litre mol^{-1} sec^{-1}
B. 1.32 \times 10^{-3} litre mol^{-1} sec^{-1}
C. 2.12 \times 10^{-3} litre mol^{-1} sec^{-1}
D. 2.42 \times 10^{-3} litre mol^{-1} sec^{-1}
E. None of these
F. $$1.12\times 10^{-3} litre mol^{-1} sec^{-1}$$
G. 4.52 \times 10^{-3} litre mol^{-1} sec^{-1}
H. 1.52 \times 10^{-3} litre mol^{-1} sec^{-1}
I. $$3.22\times 10^{-3} litre mol^{-1} sec^{-1}$$
J. $$6.32\times 10^{-3} litre mol^{-1} sec^{-1}$$
Answer: F
A ray of light is sent along the line $x - 2y - 3 = 0$. Upon reaching the line $3x - 2y + 7 = 0$, the ray is. reflected from it. Find the equation of the line containing the reflected-ray.

Options:
A. $$29x - 2y - 31 = 0$$
B. 29x - 2y - 25 = 0
C. 29x - 2y - 21 = 0
D. 29x - 2y - 23 = 0
E. 29x - 2y - 29 = 0
F. 29x - 2y - 33 = 0
G. $$31x - 12y - 6 = 0$$
H. $$10x - 50y - 15 = 0$$
I. $$20x - 1y - 11 = 0$$
J. 29x - 2y - 27 = 0
Answer: A
In an FCC unit cell, a cube is formed by joining the centres of all the tetrahedral voids to generate a new cube. Then the new cube would contain voids as:

Options:
A. 1 full Tetrahedral void, 1 full Octahedral void
B. 2 full Tetrahedral voids, 1 full Octahedral void
C. 1 full Octahedral void onlt
D. 8 full Tetrahedral voids and 1 full Octahedral void
E. 2 full Tetrahedral voids and 1 full Octahedral void
F. 2 full Tetrahedral voids and 2 full Octahedral voids
G. 1 full Tetrahedral void, 2 full Octahedral voids
H. 2 full Tetrahedral voids, 2 full Octahedral voids
I. 1 full Tetrahedral void only
J. 1 full Tetrahedral void, 3 full Octahedral voids
Answer: A
System shown in figure is released from rest pulley and spring is massless and friction is absent everywhere. The speed of 5kg block when 2 kg block leaves the contact with ground is given by $n\sqrt{2} $ m/sec then find the value of n, (K=40N/m & g=10$m/s^2$)

Options:
A. 2.1
B. 2.7
C. 1
D. 3
E. 4
F. 2
G. 2.2
H. 2.3
I. 2.5
J. 1.5
Answer: F
To get maximum current in resistance of $3\Omega$, one can use $n$ parallel rows of $m$ cells each connected in series. If the total no. of cells is $24$ and the internal resistance is $0.5$ ohm then:

Options:
A. m=12, n=2.5
B. $$m=2, n=12$$
C. m=10, n=2.4
D. $$m=6,n=4$$
E. m=12, n=3
F. m=4, n=6
G. $$m=8, n=3$$
H. m=10,n=2.5
I. $$m=12,n=2$$
Answer: I
An ideal gas expands isothermally from a volume ${ V }_{ 1 }$ to ${ V }_{ 2 }$ and then compressed to original volume ${ V }_{ 1 }$ adiabatically. Initial pressure is ${ p }_{ 1 }$ and final pressure is ${ p }_{ 3 }$. The total work done is $w$. Then:

Options:
A. $${ p }_{ 3 }={ p }_{ 1, }\quad w=0$$
B. $${ p }_{ 3 }>{ p }_{ 1, }\quad w<0$$
C. { p }_{ 3 }<{ p }_{ 1, }\quad w=0
D. { p }_{ 3 }>{ p }_{ 1, }\quad w=0
E. { p }_{ 3 }<{ p }_{ 1, }\quad w>0
F. $${ p }_{ 3 }0$$
G. { p }_{ 3 }={ p }_{ 1, }\quad w>0
H. $${ p }_{ 3 }>{ p }_{ 1 } ;\quad w>0$$
I. { p }_{ 3 }={ p }_{ 1, }\quad w<0
J. { p }_{ 3 }<{ p }_{ 1, }\quad w<0
Answer: B
One mole of air $\displaystyle\left(C_v=\dfrac{5R}{2}\right)$ is confined at atmospheric pressure in a cylinder with a piston at $0^\circ C.$ The initial volume occupied by the gas is $V$. After the equivalent of $13200\:J$ of heat is transferred to it, the volume of gas $V$ is nearly $(1\:atm=10^5\:N/m^2)$:

Options:
A. $$22\:L$$
B. 55\:L
C. 65\:L
D. 75\:L
E. $$60\:L$$
F. $$30\:L$$
G. $$37\:L$$
H. 50\:L
I. 58\:L
J. 70\:L
Answer: E
One mole of an ideal gas is kept enclosed under a light piston (area=$10^{-2}m^{2}$) connected by a compressed spring (spring constant $100\ N/m$).            The volume of gas is $0.83^{3}$ and its temperature is $100\ K$. The gas is heated so that it compresses the spring further by $0.1\ m$. The work done by the gas in the process is: (Take $R = 8.3\ J/K$-mole and suppose there is no atmosphere).

Options:
A. $$6\ J$$
B. 2\ J
C. 3.5\ J
D. $$9\ J$$
E. 4.5\ J
F. 2.5\ J
G. 1.75\ J
H. 12\ J
I. $$1.5\ J$$
J. $$3\ J$$
Answer: I
An artificial satellite (of mass m) of the earth (radius $R$ and mass $M$) mass in an orbit whose radius is n times the radius of the earth. Assuming resistance to the motion to be proportional to the square of velocity, that bis, $F=av^2$, find how long the satellite will take to fall on to the earth.

Options:
A. t=\dfrac{m}{a\sqrt{gR}}(\sqrt{n}-3)
B. t=\dfrac{m}{a\sqrt{gR}}(\sqrt{n}+2)
C. t=\dfrac{m}{a\sqrt{gR}}(2\sqrt{n}-1)
D. $$t=\dfrac{m}{a\sqrt{gR}}(\sqrt{n}-1)$$
E. $$t=\dfrac{m}{a\sqrt{gR}}$$
F. t=\dfrac{m}{a\sqrt{gR}}(n+1)
G. t=\dfrac{m}{a\sqrt{gR}}(2\sqrt{n}+1)
H. $$t=\dfrac{m}{a\sqrt{gR}}(\sqrt{n}-2)$$
I. $$t=\dfrac{m}{a\sqrt{gR}}(n-1)$$
J. t=\dfrac{m}{a\sqrt{gR}}(\sqrt{n}+1)
Answer: E
An iron ball of diameter $6 cm$ and is $0.01mm$ too large to pass through a hole in a brass plate when the ball and plate are at a temperature of $20^\circ C$. The temperature at which (both for ball and plate) the ball just pass through the hole is:
$$(lpha_{iron} = 12 \times 10^{-6}/ 1^\circ C; lpha_{brass} = 18 \times 10^{-6}/1^\circ C)$$

Options:
A. $$40^\circ C$$
B. 64^\circ C
C. 52^\circ C
D. 54^\circ C
E. $$28^\circ C$$
F. 78^\circ C
G. $$68^\circ C$$
H. 62^\circ C
I. $$48^\circ C$$
J. 58^\circ C
Answer: G
At high altitude a body at rest explodes into two fragments of equal masses, with one fragment receiving horizontal velocity of $10\ ms^{-1}$. Time taken by the two radius vectors connecting to point of explosion to both the fragments to make $90^{0}$ is $(g=10\ ms^{-1})$

Options:
A. 5 s
B. 3 s
C. 2 s
D. 6 s
E. $$1 s$$
F. $$10 s$$
G. 4 s
Answer: E
If an element  (at. mass=$50$) crystallises in fcc lattice, with $a=0.50 nm$. What is the density of unit cell if it contains $0.25\%$ Schottky defects (use $N_{A}=6\times 10^{23}$?

Options:
A. 2.3 g/cc
B. none of these
C. $$3.06 g/cc$$
D. 2.1 g/cc
E. 2.5 g/cc
F. 2.25 g/cc
G. $$2.0 g/cc$$
H. $$2.66 g/cc$$
I. 2.4 g/cc
J. 2.05 g/cc
Answer: G
At what temperature, the speeds of nitrogen as molecules at $C_1=300$ m/s and $C_2=600$ m/s, are associated with equal value of Maxwell distribution function $f(c)$?

Options:
A. $-34.5^o$C
B. $64.5^o$C
C. $337.5^o$C
D. $-95.75^o$C
E. 129^oC
F. 89.5^oC
G. $-64.5^o$C
H. 264.5^oC
I. $94.5^o$C
J. $402^o$C
Answer: B
Which atomic number is likely to have quantum numbers $n=4,\ I=0,\ m=0+1/2$ for its last electron?

Options:
A. 16
B. 24
C. $$19$$
D. 17
E. $$20$$
F. 21
G. 23
H. 22
I. $$ 18$$
Answer: I
A reversible reaction is at temperature $T$ $(K)$. Both enthalpy change and entropy change have positive values. Let $T'$ represents the equilibrium temperature. For the reaction to be spontaneous, which of the following conditions should be satisfied?

Options:
A. $$T' = T/2$$
B. $$T = 2T'$$
C. T' = T/3
D. $$T = T'$$
E. T' = 3T/4
F. $$T' <  T$$
G. $$T' = 2T$$
H. T' = T/4
I. $T'$ $ >$ $T$
Answer: F
The mass of $_{ 17 }{ { CI }^{ 35 } }$ is $34.9800$ amu. Calculate its binding energy (mass of $_{ 0 }{ { n }^{ 1 } }=1.008665$ amu $_{ 1 }{ { H }^{ 1 } }=1.007825$ amu):

Options:
A. 28.88 MeV
B. 28.0 MeV
C. 288 MeV
D. $$28.8 MeV$$
E. 2800 MeV
F. $$2.88 MeV$$
G. $$2880 MeV$$
H. 28.00 MeV
I. $$280 MeV$$
Answer: I
A jumper of mass m and length  $l$ is placed on two parabolic rails in x-y plane. Shape of the rails can be described by 
$$Rail 1 : y = x^2 (and z = 0)$$
$$Rail 2 : y = x^2 (and z = l)$$
If x is horizontal and y is vertical direction and magnetic field in the space is $B_0 \hat{j}$, the jumper can remain in equilibrium when y coordinate of its ends is (i = current in jumper)

Options:
A. $$\left(\dfrac{iB_0 l}{mg}\right)^2$$
B. \dfrac{iB_0 l}{8mg}
C. \dfrac{iB_0 l}{3mg}
D. $$\dfrac{iB_0 l}{2mg}$$
E. $$\left(\dfrac{iB_0 l}{2mg}\right)^2$$
F. \dfrac{iB_0 l}{7mg}
G. $$\dfrac{iB_0 l}{mg}$$
H. \dfrac{iB_0 l}{6mg}
I. \dfrac{iB_0 l}{5mg}
J. \dfrac{iB_0 l}{4mg}
Answer: D
Consider the following reversible reaction at a particular temperature and pressure,                 $N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)$for which the equilibrium constants in terms of mole fraction (x) and partial pressure (p) are defined as $K_x=\displaystyle\frac{x^2_{NH_3}}{x_{N_2}x^3_{H_2}}$ and $\displaystyle K_P=\frac{P^2_{NH_3}}{P_{N_2}P^3_{H_2}}$, respectively. Let an equilibrium mixture contain $3$ mol of $N_2$, $1$ mol of $H_2$ and $1$ mol of $NH_3$ $(K_x=8.33)$. Now, keeping the temperature constant, if $5$ mol of $N_2$ are added to this mixture, the correct statement(s) is/are.

Options:
A. The equilibrium will shift to the left producing more \( N_2 \), if the \( N_2 \) addition is at constant volume
B. The equilibrium will shift to the left producing more \( NH_3 \), if the \( N_2 \) addition is at constant volume
C. The equilibrium will shift to the right producing more $NH_3$, if the $N_2$ addition is at constant volume
D. The equilibrium will shift to the left producing more $H_2$, if the $N_2$ addition is at constant pressure
E. The equilibrium will shift to the left producing more $N_2$, if the $N_2$ addition is at constant volume
F. The equilibrium will shift to the right producing more $H_2$, if the $N_2$ addition is at constant volume
G. The equilibrium will shift to the left producing more \( H_2 \), if the \( N_2 \) addition is at constant volume
H. The equilibrium will shift to the left producing more $N_2$, if the $N_2$ addition is at constant pressure.
I. The equilibrium will shift to the left producing more $NH_3$, if the $N_2$ addition is at constant pressure
Answer: C
The speed of a proton is one hundreadth of the speed of light vacuum. What is its de-Broglie of proton wavelength? Assume that one mole of protons has a mass equal to one gram $\left[ {h = 6.626 \times {{10}^{ - 27}}\,\,erg\,\sec } \right]$

Options:
A. $$1.31 \times {10^{ - 2}}\mathop A\limits^ \circ $$
B. 1.34 \times {10^{ - 2}}\mathop A\limits^ \circ
C. $$13.31 \times {10^{ - 3}}\mathop A\limits^ \circ $$
D. 1.32 \times {10^{ - 3}}\mathop A\limits^ \circ
E. $$13.13 \times {10^{ - 2}}\mathop A\limits^ \circ $$
F. $$1.33 \times {10^{ - 3}}\mathop A\limits^ \circ $$
G. 1.30 \times {10^{ - 2}}\mathop A\limits^ \circ
H. 1.35 \times {10^{ - 2}}\mathop A\limits^ \circ
I. 1.33 \times {10^{ - 2}}\mathop A\limits^ \circ
J. 1.32 \times {10^{ - 2}}\mathop A\limits^ \circ
Answer: A
A particle starts from rest & moves in a circle of radius 3 m. Angular acceleration of the particle varies as $lpha $ = 4 t rad/${ sec }^{ 2 }.$ Then:

Options:
A. After 1 sec, speed of the particle will be 9 m/sec.
B. Angle between the velocity & the acceleration vector will be $45^{ 0 }$ after 1 sec
C. After 1 sec, speed of the particle will be 4 m/sec.
D. After 1 sec, speed of the particle will be 2 m/sec.
E. After 1 sec, speed of the particle will be 6 m/sec.
F. After 1 sec, speed of the particle will be 10 m/sec.
G. After 1 sec, speed of the particle will be 8 m/sec.
H. Particle will travel a distance of 2 m after 1 sec
I. particle is moving in a uniform circular motion
Answer: E
System shown in the figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5kg$ block when $2kg$ block leaves the contact with ground is : (Take force constant of the spring $K = 40 N/m$ and $g = 10m/s$)

Options:
A. $$\sqrt{8} m/s$$
B. 3 m/s
C. 3\sqrt2 m/s
D. \(\sqrt{10} m/s\)
E. $$2 m/s$$
F. $$2\sqrt2 m/s$$
G. $$\sqrt2 m/s$$
H. 4 m/s
I. $$4\sqrt2 m/s$$
Answer: F
A star moves away from earth at speed $0.8\ c$ while emitting light of frequency $6\times 10^{14}Hz$. What frequency will be observed on the earth (in units of $10\ Hz$)( $c=$ speed of light)

Options:
A. 0.36
B. $$1.2$$
C. 1.5
D. 0.84
E. 1.08
F. $$0.24$$
G. 1.44
H. $$3.3$$
I. $$30$$
J. 0.72
Answer: B
With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).

Options:
A. The chlorate ion reduces the sulfite ion.
B. The molecular shape of only chlorate ion is influenced by the lone pair of electrons of Cl.
C. The hypochlorite ion reduces the perchlorate ion.
D. The hypochlorite ion oxidizes the chlorate ion.
E. The hypochlorite ion reduces the chlorate ion.
F. The hypochlorite ion oxidizes the sulfite ion.
G. The hypochlorite and chlorate ions disproportionate to give rise to identical set of ions.
Answer: F
A circuit contains $L, C$ and $R$ in series across a.c. mains and impedance of circuit is $Z$ when $H_L = X_C =R$. The frequency of source is changed till capacitive reactance $(X_C)$ gets doubled. The impedance of circuit will becomes-

Options:
A. \dfrac{Z\sqrt{21}}{2}
B. $$\dfrac{Z\sqrt{19}}{2}$$
C. \dfrac{Z\sqrt{23}}{2}
D. \dfrac{Z\sqrt{20}}{2}
E. $$Z$$
F. $$Z\sqrt{2}$$
G. \dfrac{Z\sqrt{17}}{2}
H. \dfrac{Z\sqrt{15}}{2}
I. $$\dfrac{Z\sqrt{13}}{2}$$
Answer: B
$0.2\ gm$ of solution of mixture of $NaOH$ and $Na_2CO_3$ and inert impurities was first titrated with phenolphthalein and $N/10$ $HCl$ $17.5ml$ of $HCl$ was required at the endpoint. After this methyl orange was added and $2.5ml$ of same $HCl$ was again required for next endpoint. Find out percentage of $NaOH$ and $Na_2CO_3$ in the mixture.

Options:
A. % $NaOH = 36$ , % $Na_2CO_3 = 12.5$
B. % $NaOH = 25$ , % $Na_2CO_3 = 30$
C. % $NaOH = 33.5$ , % $Na_2CO_3 = 15.5$
D. % $NaOH =13.5$ , % $Na_2CO_3= 35$
E. % $NaOH =18$ , % $Na_2CO_3= 40$
F. % $NaOH = 33$ , % $Na_2CO_3 = 16$
G. % $NaOH =35$ , % $Na_2CO_3= 13.5$
H. % $NaOH = 40$ , % $Na_2CO_3= 18$
I. % $NaOH = 30$ , % $Na_2CO_3= 25$
J. % $NaOH = 34$ , % $Na_2CO_3 = 14.5$
Answer: G
${ I }_{ 2 }$ molecule dissociates into atoms after absorbing light of 4500 ${ A }^{ \circ  }$. If one quantum of energy is absorbed by each molecule, the KE of iodine atoms will be 
(BE of ${ I }_{ 2 }$ = 240 kJ/mol)

Options:
A. $${ 240\times 10 }^{ -19 }J$$
B. 2.40 \times 10^{-22}J
C. ${ 2.40 \times 10 }^{ -20 }J$
D. $${ 0.216\times 10 }^{ -19 }J$$
E. 2.40 \times 10^{-21}J
F. 2.10 \times 10^{-19}J
G. ${ 2.35 \times 10 }^{ -19 }J$
H. $${ 2.16\times 10 }^{ -19 }J$$
I. ${ 2.40 \times 10 }^{ -18 }J$
J. $${ 2.40\times 10 }^{ -19 }J$$
Answer: A
A bullet moving with a uniform velocity v, stops suddenly after hitting the target and the whole mass melts be m, specific heat S, initial temperature $25^oC$, melting point $475^oC$ and the latent heat L. Then v is given by-

Options:
A. \(mL=mS(475-25)-\dfrac{1}{2}\dfrac{mv^2}{2J}\)
B. $$mL=mS(475-25)+\dfrac{1}{2}\dfrac{mv^2}{J}$$
C. mL=mS(475-25)+\dfrac{1}{4}\dfrac{mv^2}{J}
D. $$mS(475-25)-mL=\dfrac{mv^2}{2J}$$
E. $$mL=mS(475-25)+\dfrac{mv^2}{2J}$$
F. $$mS(475-25)+mL=\dfrac{mv^2}{J}$$
G. mL=mS(475-25)-\dfrac{1}{2}\dfrac{mv^2}{J}
H. $$mS(475-25)+mL=\dfrac{mv^2}{2J}$$
I. mL=mS(475-25)-\dfrac{1}{2}\dfrac{mv^2}{2J}
J. $$mL=mS(475-25)+\dfrac{1}{2}\dfrac{mv^2}{2J}$$
Answer: B
Calculate the pH of a 0.1 M $K_2PO_4$ solution. The third dissociation constant of phosphoric acid is $10^{-12}$. Given $(0.41)^{1.2}=0.64$; log $3=0.48$.

Options:
A. 12.45
B. $$12.44$$
C. $$12.25$$
D. 12.75
E. 11.85
F. 12.65
G. 12.15
H. $$12$$
I. 12.34
J. $$12.5$$
Answer: J
A long cylindrical pipe of radius $20cm$ is closed at its upper end and has an airgight piston of negligible mass as shown. When a $50kg$ mass is attached to the other end of th episton, it moves down. If the air in the enclosure is cooled from temperature $T$ to $T-\Delta T$, the piston moves back to its original position. Then $\Delta T/T$ is close to (Assuming air to be an ideal gas, $g=10m/{s}^{2}$, atmospheric pressure is ${10}^{5}$ Pascal)

Options:
A. $$0.09$$
B. 0.05
C. $$0.04$$
D. $$0.01$$
E. $$0.02$$
F. 0.08
G. 0.06
H. 0.07
I. 0.03
Answer: D
An inductor of 0.5 H and $ 200 \Omega$ resistor are connected in series with A.C. source of  230 V and frequency 50 Hz, then calculate (1) Maximum current in the inductor (2) Phase difference between current and voltage and time difference (time lag)

Options:
A. I_{max}=1.28 A, 38^0,8'\, and 2.3\,ms
B. I_{max}=1.28 A, 40^0,8'\, and 2.4\,ms
C. $$ I_{max}=1.28 A, 38^0,8'\, and 24.2\,ms$$
D. $$ I_{max}=1.28 A, 38^0,8'\, and 2.1\,ms$$
E. I_{max}=1.28 A, 40^0,8'\, and 2.1\,ms
F. I_{max}=1.28 A, 36^0,8'\, and 24.2\,ms
G. I_{max}=1.28 A, 38^0,8'\, and 2.4\,ms
H. $$ I_{max}=1 A, 36^0,8'\, and 2.1\,ms$$
I. $$ I_{max}=1 A, 38^0,8'\, and 2.1\,ms$$
J. I_{max}=1.28 A, 36^0,8'\, and 2.1\,ms
Answer: D
The wavelength of de-Broglie waves associated with neutrons at room temperature T is (E=kT)

Options:
A. $$\dfrac { 30.7 }{ \sqrt { T } } \mathring { A } $$
B. \dfrac { 15.35 }{ T } \mathring { A }
C. \dfrac { 3.64 }{ \sqrt { T } } \mathring { A }
D. \dfrac { 25.7 }{ \sqrt { T } } \mathring { A }
E. $$\dfrac { 1.82 }{ T } \mathring { A } $$
F. \dfrac { 18.2 }{ \sqrt { T } } \mathring { A }
G. $$\dfrac { 1.82 }{ \sqrt { T } } \mathring { A } $$
H. \dfrac { 15.35 }{ \sqrt { T } } \mathring { A }
I. $$\dfrac { 30.7 }{ T } \mathring { A } $$
J. \dfrac { 10.35 }{ \sqrt { T } } \mathring { A }
Answer: A
For the cyclic trimerisation of a acetylene to give one mole of benzene $K_{c}=4li^{2}\ mol^{-2}$ if the equilbrium concentration of benzene is $0.5\ mol\ L^{-1}$ calculate the equilbrium concentration of acetylene.

Options:
A. $$0.1\ mol\ L^{-1}$$
B. 0.15\ mol\ L^{-1}
C. $$0.9\ mol\ L^{-1}$$
D. $$0.5\ mol\ L^{-1}$$
E. 0.3\ mol\ L^{-1}
F. 0.2\ mol\ L^{-1}
G. 0.7\ mol\ L^{-1}
H. $$0.6\ mol\ L^{-1}$$
I. 0.8\ mol\ L^{-1}
J. $$0.4\ mol\ L^{-1}$$
Answer: A
4 moles of $\mathrm { H } _ { 2 }$ at 500$\mathrm { K }$ is mixed with 2 moles of He at 400$\mathrm { K }$ . The mixture attains a temperature T and volume V. Now the mixture is compressed adiabatically to a volume $V$ and temperature T. If $\frac { T ^ { \prime } } { T } = \left( \frac { V } { V ^ { \prime } } \right) ^ { n } ,$ find the value of 13$n$

Options:
A. 9
B. 3
C. $$4$$
D. 8
E. 10
F. $$5$$
G. $$6$$
H. $$13$$
I. 7
Answer: G
A block of mass 2 kg is hanging over a smooth and light pulley through a light string. The other end of the string is pulley by a constant force $F = 40N.\;{\text{At}}\;t = 0$ the system is at rest as shown. Then in the time interval from $t = 0\;{\text{to}}\;{\text{t}}\; = \frac{2}{{\sqrt {10} }}$ seconds, pick up the correct statement (s) $\left( {g = 10m/{s^2}} \right)$

Options:
A. Work done by tenion on block is 80J.
B. Work done by gravity is -20 J
C. Work done by tension on block is 90J.
D. Work done by tension on block is 60J.
E. Work done by tension on block is 70J.
F. Work done by tension on block is 100J.
G. Work done by tension on block is 120J.
H. None of these
I. Tension in the string is 40 N.
J. Work done by tension on block is 40J.
Answer: A
Imagine an atom made of a proton and a hypothetical particle of double the mass of the electron but having the same charge as the electron. Apply Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength [Rydberg Constant = R] equal to

Options:
A. $$\displaystyle\frac{36}{5R}$$
B. \frac{36}{5R}
C. \frac{18}{10R}
D. \frac{36}{10R}
E. $$\displaystyle\frac{18}{5R}$$
F. \frac{36}{20R}
G. \frac{36}{25R}
H. $$\displaystyle\frac{4}{R}$$
I. \frac{18}{15R}
J. $$\displaystyle\frac{9}{5R}$$
Answer: E
In a parallel plate capacitor the distance between the plates is $10\,cm.$ Two dielectric slabs o thickness $5\,cm$ each and dielectric constants $K_{1} = 2$ and $K_{2} = 4$ respectively, are inserted between the plates. A potential of $100\,V$ is applied across the capacitor as shown in the figure. The value of the net bound surface charge density at the interface of the two dielectrics is:-

Options:
A. $$-\dfrac{2000}{3}\epsilon_{0}$$
B. $$-250\epsilon_{0}$$
C. -\dfrac{1000}{3}\epsilon_{0}
D. $$\dfrac{2000}{3}\epsilon_{0}$$
E. -\dfrac{1500}{3}\epsilon_{0}
F. -\dfrac{2500}{3}\epsilon_{0}
G. -\dfrac{1750}{3}\epsilon_{0}
H. -\dfrac{4000}{3}\epsilon_{0}
I. -\dfrac{2250}{3}\epsilon_{0}
Answer: A
A copper ring with a radius of $  r=100 \mathrm{cm}  $ and a cross sectional area of $  A=4 \mathrm{mm}^{2}  $ is to be fitted on to a steel rod with a radus $  R=100.125 \mathrm{cm} $. With what force F will the ring the be expanded if the modulus of elasticity of copper $  E=12 \times 10^{5} N m m^{2} ? $ (Disregard the deformation of the rod)

Options:
A. 500 N
B. \frac{600}{25} \times N
C. $
\frac{500}{2 \pi} N
$
D. \frac{500}{28} \times N
E. \frac{600}{26} \times N
F. \frac{600}{28} \times N
G. 600 N
H. \frac{500}{27} \times N
I. \frac{500}{25} \times N
J. $
\frac{600}{27} \times N
$
Answer: J
Two adjacent plant cells are depicted below. A few statements regarding them are made. Mark the correct statement
Cell ACell B$\Psi =-1200kpa$$\Psi =-800Kpa$${ \Psi  }_{ P }=800Kpa$${ \Psi  }_{ P }=600KPa$${ \Psi  }_{ S }=-2000KPa$${ \Psi  }_{ S }=-1400KPa$

Options:
A. The direction of movement of water by osmosis will be from Cell B to Cell A
B. The Cell A has a higher solute potential than B
C. The Cell B has a higher pressure potential than A
D. The Cell A has a higher water potential than B
E. At equilibrium, the two cells will have a potential value of $-1700kPa$
F. The Cell A has a higher pressure potential than B
G. The direction of movement of water by osmosis will be from Cell A to Cell B
H. The Cell B has a higher solute potential than A
I. Assuming that the solute potentials of the two cells do not change at equilibrium, the pressure potential of Cell B will be $400KPa$
J. The Cell B has a higher water potential than A
Answer: D
The number of unpaired electrons in $G.S.$, first $E.S.$ and second $E.S.$ of $S(Z=16)$ are respectively,

Options:
A. 2, 4, and 8
B. 0, 4, and 2
C. $2,4$ and $4$
D. 2, 4, and 4
E. $2,4$ and $6$
F. 2, 6, and 4
G. 2, 4, and 2
H. $0,4$ and $6$
I. $0, 2$ and $4$
J. $2, 6$ and $4$
Answer: E
Two hydrogen atoms are in excited state with electrons residing in $n=2$. The first one is moving toward left and emits a photon of energy $E_1$ toward right. The second one is moving toward right with the same speed and emits a photon of energy $E_2$ toward left. Taking recoil of nucleus into account, during the emission process

Options:
A. $$E_1>E_2$$
B. $$E_1< E_2$$
C. $$E_1=E_2$$
D. E_1 < E_2 + 1 \times 10^{-12}
E. $$E_1 \neq E_2$$
F. Information insufficient
G. $$E_1 > E_2 + 1 \times 10^{-12}$$
Answer: B
The amount of metal deposited at cathode on passing electric current of 0.75 ampere in aqueous ferric sulphate solution for 30 minutes, will be -(atomic wt. of Fe $= 56 )$

Options:
A. 0.00870 g
B. 0.00435$g$
C. 0.00405\mathrm{~g}
D. 0.522$\mathrm { g }$
E. 0.00435 \mathrm{~g}
F. 0.783$\mathrm { g }$
G. 0.00870\mathrm{~g}
H. 0.01305 g
I. 0.261$\mathrm { g }$
Answer: B
Statement -1: If an electron has the same wavelength as a photon, they have the same energy.
Statement-2 : By debroglie hypothesis, $p=h/\lambda $ for both the electron and the photon.

Options:
A. Statement -1 is true, statement-2 is false
B. Statement -1 is false, statement-2 is false and statement is NOT correct explanation for statement-1.
C. Statement -1 is false, statement-2 is false and statement is correct explanation for statement-1.
D. Statement -1 is true, statement-2 is true and statement is correct explanation for statement-1.
E. Statement -1 is false, statement-2 is true and statement is NOT correct explanation for statement-1.
F. Statement -1 is false, statement-2 is true
G. Statement -1 is true, statement-2 is true and statement is NOT correct explanation for statement-1.
H. Statement -1 is true, statement-2 is false and statement is correct explanation for statement-1.
I. Statement -1 is true, statement-2 is false and statement is NOT correct explanation for statement-1.
J. Statement -1 is false, statement-2 is true and statement is correct explanation for statement-1.
Answer: D
Two inclined planes intersect in a horizontal plane. their inclinations to the horizontal being $lpha$ and $\beta$. If a particle is projected with velocity u at right angle to the former from a point on it,  find the time after which the velocity vector will become perpendicular to the other inclined plane.

Options:
A. t = \dfrac{u sin (lpha - \beta)}{g sin \beta}
B. t = \dfrac{u sin (lpha - \beta)}{g cos \beta}
C. t = \dfrac{u cos (lpha + \beta)}{g sin (2\beta)}
D. $$t = \dfrac{u cos (lpha + \beta)}{g sin \beta}$$
E. t = \dfrac{u cos (lpha - \beta)}{g sin \beta}
F. $$t = \dfrac{u cos (lpha + \beta)}{g cos \beta}$$
G. $$t = \dfrac{u sin (lpha + \beta)}{g cos \beta}$$
H. $$t = \dfrac{u sin (lpha + \beta)}{g sin \beta}$$
I. t = \dfrac{u sin (2\alpha - \beta)}{g cos \beta}
J. t = \dfrac{u sin (lpha + \beta)}{g cos (2\beta)}
Answer: F
The amplitude of  $e ^ { e ^ { - i \theta } } =$

Options:
A. $$e ^ { \sin \theta }$$
B. \cos \theta
C. $$- \sin \theta$$
D. e ^ { \cos (2\theta) }
E. e ^ { - \sin \theta }
F. $$\sin \theta$$
G. -e ^ { \sin \theta }
H. $$e ^ { \cos \theta }$$
I. e ^ { - \cos \theta }
J. -\cos \theta
Answer: C
A person in topless jeep is travelling with uniform velocity $20\ ms^{-1}$ away from a vertical mountain. The person blows horn of the jeep and hears its echo from the mountain. If actual frequency of horn is  $630\ Hz,$ the apparent decrease in the frequency of echo with respect to actual frequency of the horn is  $($velocity of sound in air $=340\ ms^{-1})$

Options:
A. $$90 Hz$$
B. $$70 Hz$$
C. 75 Hz
D. $$35 Hz$$
E. 60 Hz
F. 85 Hz
G. 80 Hz
H. $$45 Hz$$
I. 55 Hz
J. 65 Hz
Answer: B
In the given circuit, initially switch $S_1$ is closed, and $S_2$ and $S_3$ are open. After charging of capacitor, at $t=0, S_1$ is opened and $S_2$ and $S_3$ are closed. If the relation between inductance, capacitance and resistance is $L=4CR^2$, then find the time (in s) after which current passing through capacitor and inductor will be same (given $R=ln2 m\Omega, L=2mH)$:

Options:
A. 1.3
B. 1.6
C. 1.1
D. 2
E. 1.7
F. 1.5
G. 1.4
H. 1
I. 1.2
J. 2.8
Answer: H
Three unequal resistors in parallel are equivalent to a resistant 1 ohm. If two of them are in the ratio 1 :2 and if no resistance value is fractional, the largest of the three resistance in ohm is :-

Options:
A. 12
B. 14
C. 18
D. 8
E. 16
F. 9
G. 15
H. 6
I. 4
J. 10
Answer: H
Consider a YDSE setup oriented in vertical plane in which light consisting of two wavelengths, 300 nm and 500 nm, is allowed to pass through each slit to form an intensity pattern on the screen kept 1 m away from the slit plane. The separation between the slits is 2 mm. Think about all the regions of total darkness on the screen and out of all these regions, consider the one closest to the center of the screen and lying above it. A particle of mass 'm' is dropped at t = 0 from this 'dark' band and allowed to freely fall under earth's gravity starting from rest. At what time will it be crossing the center of the screen? (Take $g = 10m/sec^2$)

Options:
A. 10\sqrt{3/4m} sec
B. $$10\sqrt{1/2m} sec$$
C. None of these
D. $$10msec$$
E. 10\sqrt{2}msec
F. 10\sqrt{2m} sec
G. $$10\sqrt{5/4m} sec$$
H. $$10\sqrt {3m} sec$$
I. 10\sqrt{3/4}sec
J. $$10\sqrt {3/2m} sec$$
Answer: D
The locus of a point which moves such that its distance from $(3,2)$ is twice its distance from the line $2x-3y+1=0$ is a

Options:
A. circle
B. hyperbola
C. rectangular hyperbola
D. parabola
E. ellipse
Answer: D
Thallium chloride (atomic mass $= 240 $ g mol$^{-1}$) crystallises in either a simple cubic lattice or a face centered cubic lattice with chloride ions at the face-centres and $Ti^+$ ions in the holes. If the density of the solid is $9.0$ g cm$^{-3}$ and edge of the unit cell is $3.85\, \times\, 10^{-8}$ cm, what is the unit geometry?

Options:
A. HCP
B. BCC
C. SC
D. FCC
Answer: C
A square coil $ABCD$ lying in $x-y$ plane with it's centre at origin. A long straight wire passing through origin carries a current $i=2t$ in negative $z$-direction. The induced current in the coil is

Options:
A. Alternating
B. Anticlockwise
C. Zero
D. Clockwise
Answer: C
A rod Ab of length 15 cm rests in between two coordinate axes in such a way that the end point A lies on x-axis and ens point B lies on y-axis. A point P(x, y) is taken on the rod in such a way that AP = 6 cm. The locus of P is

Options:
A. a parabola
B. an ellipse
C. a circle
D. a hyperbola
E. hyperbola
Answer: C