MikaStars39/nano-eval huggingface dataset:
A glass tube of radius $0.3$ mm is dipped vertically in water. Find upto what height the water will rise in the capillary? If the tube in inclined at an angle $30$ degree with the vertical, how much length of the capillary is occupied by water? Surface tension of water = $7.010^{-2}N/m$, density of water = $10^3kg/m^3$.

Options:
A. 5.6 cm
B. 5.2 cm
C. $7.2$ cm
D. 5.8 cm
E. $6.2$ cm
F. 6.0 cm
G. $5.4$ cm
H. $4.2$ cm
I. 5.5 cm
J. 5.7 cm
Answer: G
A particle experience a net force that is always parallel to y-axis. If it moves along the curve $xy=a^2$ where $a$ is a constant and the magnitude of the force is $y^n$, then $n$ is

Options:
A. 2
B. 6
C. 4
D. 7
E. 8
F. 5
G. 9
H. 0
I. 3
J. 1
Answer: J
Particle 'A' moves with speed $10 m/s$ in a frictionless circular fixed horizontal pipe of radius $5 m$ and strikes with 'B' of double mass that of

Options:
A. $\dfrac{5 \pi}{2}$ sec
B. \dfrac{7 \pi}{4} sec
C. $\dfrac{\pi}{2}$ sec
D. \dfrac{11 \pi}{4} sec
E. $\dfrac{2 \pi}{3}$ sec
F. \dfrac{9 \pi}{4} sec
G. $4 \pi$ sec
H. \dfrac{3 \pi}{2} sec
I. \dfrac{7 \pi}{2} sec
J. \dfrac{3 \pi}{4} sec
Answer: A
A proton is fired from very far away towards a nucleus with charge Q = 120 e, where e is the electronic charge. It makes a closest approach of 10 fm to the nucleus. The de Broglie wavelength (in units of fm) of the proton at its start is : (take the proton mass, $m_p = (5/3) \times 10^{-27}kg$ and$h/e = 4.2\times 10^{-15}J.s/C; \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 m/F; 1 fm = 10^{-15}m$)

Options:
A. $$5\ fm$$
B. $$14\ fm$$
C. $$11\ fm$$
D. $$13\ fm$$
E. $$6\ fm$$
F. $$12\ fm$$
G. $$8\ fm$$
H. $$10\ fm$$
I. $$9\ fm$$
J. $$7\ fm$$
Answer: J
A monochromatic light source S of wavelength $440$ nm is placed slightly above a plane mirror M as shown. Image of S in M can be used as a virtual source to produce interference fringes on the screen. The distance of source S from O is $20.0$cm, and the distance of screen from O is $100.0$ cm (figure is not to scale). If the angle $\theta =0.50\times 10^{-2}$ radians, the width of the interference fringes observed on the screen is?

Options:
A. $0.88$ mm
B. 1.32 mm
C. $1.76$ mm
D. $0.55$ mm
E. $2.20$ mm
F. $2.64$ mm
G. $1.10$ mm
Answer: F
The apparent frequency is $f_1$ when a source of sound approaches a stationary observer with a speed $u$ and $f_2$ when the observer approaches the stationary source with same speed. If $v$ is the velocity of sound, then :

Options:
A. $f_1 > f_2$ if $u < v$
B. $f_1 > f_2$ if $u = v$
C. relation between $f_1$ and $f_2$ cannot be predicted
D. $$f_1=f_2$$
E. $f_1 < f_2$ if $u < v$
F. $f_2 < f_1$ if $u > v$
G. $f_1 > f_2$ if $u > v$
H. $f_1 < f_2$ if $u > v$
I. $f_2 > f_1$ if $u< v$
J. $f_2 < f_1$ if $u < v$
Answer: I
A beam of some kind of particle of velocity $2\times {10}^{7}m/s$ is scattered by a gold $(z=79)$ foil. Find specific charge of this particle (charge/mass) if the distance of closest approach is $7.9\times {10}^{-14}m$.

Options:
A. 1.3 \times 10^4
B. 1.3 \times 10^5
C. $$9\times10^{3}$$
D. $$4.3\times10^8$$
E. 1.3 \times 10^9
F. 1.3 \times 10^6
G. $1.3\times10^8$
H. 1.3 \times 10^7
I. $$4.5\times10^{-4}$$
J. 4.5 \times 10^7
Answer: G
A charged particle $P$ leaves the origin with speed $v=v_0$ at some inclination with the $x-$axis. There is a uniform magnetic field B along the $x-$axis. $P$ strikes a fixed target $T$ on the $x-$axis for a minimum value of $B=B_0$. P will also strike T if

Options:
A. B=\dfrac{B_0}{2}, v=v_0
B. B=3B_0, v=v_0
C. $$B=3B_0, v=2v_0$$
D. $$B=2B_0, v=2v_0$$
E. $$B=B_0, v=2v_0$$
F. $$B=2B_0, v=v_0$$
G. B=2B_0, v=\dfrac{v_0}{2}
H. $$B=\dfrac {B_0}{2}, v=2v_0$$
I. B=B_0, v=\dfrac{v_0}{2}
J. B=\dfrac{B_0}{2}, v=\dfrac{v_0}{2}
Answer: F
A fish in an aquarium, 30 em deep in water can see a light bulb kept 50 em above the surface of water. The fish can also see the image of this bulb in the reflecting bottom surface of the aquarium. Total depth of water is 60 ern. Then the. apparent distance between the two images seen by the fish is ($\mu_w$ = 4/3).

Options:
A. $$\dfrac{760}{3}m$$
B. $$\dfrac{280}{3}cm $$
C. $$\dfrac{740}{3}m$$
D. $$\dfrac{780}{3}m$$
E. $$\dfrac{700}{3}m$$
F. $$\dfrac{320}{3} cm$$
G. $$\dfrac{720}{3}m$$
H. $$140 m$$
I. $$\dfrac{800}{3}m$$
J. $$\dfrac{380}{3} cm$$
Answer: A
Figure shows a wheel barrow of mass $15 \ kg$ carrying a load of $30 \ kgf$ with its centre of gravity at $A$. The points $B$ and $C$ are the centre of wheel and tip of the handle such that the horizontal distance $AB=20 \ cm$ and $AC=40 \ cm$. What is the minimum effort required to keep the leg just off the ground ?

Options:
A. $$25\,kgf$$
B. $$20\,kgf$$
C. $$30\,kgf$$
D. $$12.5\,kgf$$
E. $$18\,kgf$$
F. $$5\,kgf$$
G. $$15\,kgf$$
H. $$22.5\,kgf$$
I. $$10\,kgf$$
J. $$17.5\,kgf$$
Answer: G
Determine the period of oscillation of mercury of mass m = 200g poured into a bent tube whose right arm forms an angle $\theta$ = 30 with the vertical. The cross-sectional area of the tube S = 0.50 $cm^{2}$. The viscosity of mercury is to be neglected.

Options:
A. 1.0 sec
B. 0.7 sec
C. 0.8 sec
D. 0.5 sec
E. 0.4 sec
F. 0.6 sec
G. 0.9 sec
H. 0.3 sec
I. 0.1 sec
J. 1.1 sec
Answer: C
Two identical adiabatic vessels are filled with oxygen at pressure  $ P_{1}$ and $P_2\ ( P_1 > P_2) $. The vessels are interconnected with each other by a nonconducting pipe. If $ U_{i1}$ and $U_{i2} $ denote initial internal energies of oxygen in first and second vessel respectively and $  U_{f1}$ and $U_{f2} $ denote final internal energy values, then:

Options:
A. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{1}}{P_{2}},\ \ U_{f1}=U_{f2}$$
B. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{2}}{P_{1}},\ \ U_{f1}>U_{f2}$$
C. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{1}}{P_{2}},\ \ U_{f1}<U_{f2}$$
D. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{2}}{P_{1}},\ \ U_{f1}<U_{f2}$$
E. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{2}}{P_{1}},\ \ U_{f1}=U_{f2}$$
F. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{1}}{P_{2}},\ \ U_{f1}>U_{f2}$$
G. $$\dfrac{U_{i1}}{U_{i2}}=\dfrac{P_{2}}{P_{1}},\ \ U_{f1}<U_{i2}$$
Answer: B
A solid sphere moves at a terminal velocity of 20 m/s in air at a place where g=9.8 m/$s^2$. The sphere is taken in a gravity free hall having air at the same pressure and pushed down at a speed of 20 m/s.

Options:
A. its initial acceleration will be $9.8 m/s^2$ downward
B. its initial acceleration will be $9.8 m/s^2$
C. its initial acceleration will be $9.7 m/s^2$ downward
D. its initial acceleration will be $10 m/s^2$
E. it will eventually stop
F. its initial acceleration will be $9.8 m/s^2$ upward
G. its initial acceleration will be $10 m/s^2$ upward
H. its initial acceleration will be $10 m/s^2$ downward
I. the magnitude of acceleration will decrease as the time passes
J. its initial acceleration will be $9.9 m/s^2$ downward
Answer: I
Four tunnels are supposed to be bored through the earth between two places on a longitude as shown in the figure. One of them with midpoint at $A$ is straight, whereas other three have bent at their midpoints $B, C$ and $D$. Both the bent sections are coplanar. A particle released from one end of the tunnels, spends time intervals $T_A, T_B, T_C$ and $T_D$ respectively to reach the other end. If the particle passes the bent smoothly without a change on speed there, which of the following relations will these time intervals bear?

Options:
A. $$T_A=T_B=T_C=T_D$$
B. $$T_A= T_C < T_B > T_D$$
C. $$T_B < T_A =T_C < T_D$$
D. $$T_B < T_A = T_C > T_D$$
E. $$T_A=T_C > T_B= T_D$$
F. $$T_A = T_B > T_C = T_D$$
G. $$T_B > T_A = T_C > T_D$$
H. $$T_B > T_A = T_C < T_D$$
Answer: C
A magnetic flux through a stationary loop with a resistance $R$ varies during the time interval $\tau$ as $\phi=a:(\tau -t)$. Find the amount of heat generated in the loop during that time

Options:
A. $\cfrac { { 2a }^{ 2 }{ \tau }^{ 2 } }{ 3R }$
B. $\cfrac { { a }^{ 2 }{ \tau }^{ 3 } }{ 5R }$
C. $$\cfrac { { a }^{ 2 }{ \tau }^{ 3 } }{ 3R } $$
D. $$\cfrac { { 2a }^{ 2 }{ \tau }^{ 3 } }{ 3R } $$
E. $\cfrac { { a }^{ 2 }{ \tau }^{ 3 } }{ 4R }$
F. $$\cfrac { a{ \tau }^{ } }{ 3R } $$
G. $$\cfrac { a{ \tau }^{ 2 } }{ 2R } $$
H. $\cfrac { { a }^{ 2 }{ \tau }^{ 3 } }{ 2R }$
I. $\cfrac { { a }^{ 2 }{ \tau }^{ 2 } }{ 3R }$
J. $\cfrac { { a }^{ 2 }{ \tau }^{ 3 } }{ 6R }$
Answer: C
A mono-atomic ideal gas is compressed from volume V to V/2 through various process. For which of the following processes final pressure will be maximum:

Options:
A. isobaric
B. adiabatic
C. $$P{ V }^{ 6 }=constant$$
D. $$P{ V }^{ 2 }=constant$$
E. isothermal
F. $$P{ V }^{ 4 }=constant$$
G. $$P{ V }^{ 7 }=constant$$
H. $$P{ V }^{ 5 }=constant$$
I. $$P{ V }^{ 3 }=constant$$
J. isochoric
Answer: A
The linear speed $V$ of a particle moving in a circle of radius $R$ varies with time t as $V=V_0-Kt$, where $K$ is a positive constant and $V_0$ is initial velocity. The time at which magnitude of tangential acceleration and angular velocity becomes equal is :

Options:
A. $$\cfrac {(V_0+2KR)} {K}$$
B. $$\cfrac {(V_0-KR)} K$$
C. $$\cfrac {(V_0-KR)} K^2$$
D. $$\cfrac {(V_0-KR)} {K^2}$$
E. $$\cfrac {(V_0-KR)} {K}$$
F. $$\cfrac {(V_0-KR)} {2K}$$
G. $$\cfrac {(V_0+KR)} {2K}$$
H. $$\cfrac {(V_0+KR)} K$$
I. $$\cfrac {(V_0+KR)} {K^2}$$
J. $$\cfrac {(V_0+2KR)} {2K}$$
Answer: H
A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. let $r_p$, $r_e$ and $r_{He}$ be their respectively radii, then ,

Options:
A. r_e < r_p < r_{He}
B. $$r_e > r_p = r_{He}$$
C. \( r_e = r_p > r_{He} \)
D. $$r_e < r_p = r_{He}$$
E. \( r_e > r_p < r_{He} \)
F. \( r_e > r_p = r_{He} \)
G. $$r_e > r_p > r_{He}$$
H. \( r_e = r_p < r_{He} \)
I. r_e = r_p > r_{He}
Answer: D
A block $A$ of mass $2\ kg$ rests on a horizontal surface. Another block $B$ of mass $1\ kg$ moving at a speed of $1\ m/s$ when at a distance of $16\ cm$ from $A$, collides elastically with $A$. The coefficient of friction between the horizontal surface and each of the blocks is $0.2$. Then,$ (g=10\ m/s^{2})$

Options:
A. final separation between the blocks is $6\ cm$
B. final separation between the blocks is $4\ cm$
C. final separation between the blocks is $8\ cm$
D. final separation between the blocks is $2\ cm$
E. final separation between the blocks is $3\ cm$
F. final separation between the blocks is $5\ cm$
G. after collision block $B$ comes to rest
H. final separation between the blocks is $9\ cm$
I. after collision block $B$ rebounds
J. final separation between the blocks is $7\ cm$
Answer: F
In order to raise a mass of 100 kg a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with an acceleration 59/ 4 relative to the rope. The tension in the rope is $ \left( \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } \right) $

Options:
A. 1432 N
B. 1442 N
C. 642 N
D. 1522 N
E. 1428 N
F. 928 N
G. 1422 N
H. 1342 N
I. 1218 N
J. 1322 N
Answer: A
At 298K, the standard reduction potentials are 1.51 V for $MnO_4^-|Mn^{2+}, 1.36 V for Cl_2| Cl^-, 1.07 V $ for $Br_2|Br^-,$ and $0.54 V for I_2|I^-. $ At pH = 3 , permanganate is expected to oxidize: $(\frac{RT}{F} = 0.059 V)$

Options:
A. $Br^-$ and $I^-$
B. $Cl^-$ and $I^-$
C. $Cl^-, Br^- $ and $I^-$
D. $I^-$ only
E. $Cl^-$ and $Br^-$ only
F. $Br^-$ and $Cl^-$
G. Cl^- and $Br^-$
Answer: A
A force ($F = Mg$) is applied on the top of a circular ring of mass $M$ and radius $R$ kept on a rough horizontal surface. If the ring rolls without slipping, then minimum coefficient of friction required is

Options:
A. $$0.3$$
B. $$0.15$$
C. $$0.6$$
D. $$0.8$$
E. $$0.4$$
F. $$0.2$$
G. $$0.7$$
H. $$0.5$$
I. $$Zero$$
J. $$0.1$$
Answer: I
One mole of ${ N }_{ 2 }$ gas at 0.8 atmp takes 38 sec to diffuse through a pin hole, whereas one mole of the unknown compound of Xenon with F at 1.6 atmp takes 57 sec to diffuse through the same hole. Calculate the molecular formula of the compound. (At. wt. Xe = 138, F = 19)

Options:
A. $$XeF_4$$
B. $$XeF_5$$
C. $$XeF_6$$
D. $$XeF_8$$
E. $$XeF_7$$
F. $$XeF_3$$
G. $$XeF_2$$
H. $$None of these$$
Answer: C
The gravitational potential energy of interactions of a system of six identical particles,each of mass $m$ placed at the vertices of a regular hexagon of side $4a'$ is [PE=0 at infinite separation]

Options:
A. \dfrac{-4Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
B. \dfrac{-7Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
C. $$\dfrac{-3Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4}\right)$$
D. \dfrac{-9Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
E. $$\dfrac{-2Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4}\right)$$
F. \dfrac{-8Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
G. $$\dfrac{-6Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4}\right)$$
H. \dfrac{-10Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
I. \dfrac{-5Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4} \right)
J. $$-\dfrac{Gm^2}{a} \left (1+\dfrac{1}{\sqrt3}+ \dfrac{1}{4}\right)$$
Answer: G
A light balloon filled with helium of density $\rho_{He}$ is tied to a light string of length $L$. The string is tied to the ground forming an "inverted" simple pendulum (figure). If the balloon is displaced slightly from equilibrium as in figure and released, the period of the motion is. (Take the density of air to be $\rho_{air}$. Assume the air applied a buoyant force on the balloon but does not otherwise affect its motion.)

Options:
A. $$T = 2\pi \sqrt {\left (\dfrac {2\rho_{He}}{\rho_{air} - 2\rho_{He}}\right )\dfrac {L}{g}}$$
B. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{air} + \rho_{He}}{\rho_{He}}\right )\dfrac {L}{g}}$$
C. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{air} - \rho_{He}}{\rho_{He}}\right )\dfrac {L}{g}}$$
D. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{He}}{2\rho_{air} - \rho_{He}}\right )\dfrac {L}{g}}$$
E. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{He}}{2\rho_{air} + \rho_{He}}\right )\dfrac {L}{g}}$$
F. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{He}}{\rho_{air} + \rho_{He}}\right )\dfrac {L}{g}}$$
G. $$T = 2\pi \sqrt {\left (\dfrac {2\rho_{He}}{\rho_{air}}\right )\dfrac {L}{g}}$$
H. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{He}}{\rho_{air}}\right )\dfrac {L}{g}}$$
I. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{air}}{\rho_{He}}\right )\dfrac {L}{g}}$$
J. $$T = 2\pi \sqrt {\left (\dfrac {\rho_{He}}{\rho_{air} - \rho_{He}}\right )\dfrac {L}{g}}$$
Answer: H
A uniform circular disc of radius $r$ is placed on a rough horizontal surface and given a linear velocity $v_o$ and angular velocity $\omega$ as shown. The disc comes to rest after moving some distance to the right. It follows that :

Options:
A. $$3{v_0} = 5{\omega _0}r$$
B. $${v_0} = {\omega _0}r$$
C. $$2{v_0} = 5{\omega _0}r$$
D. $$3{v_0} = 2{\omega _0}r$$
E. $$2v = {\omega _0}r$$
F. $$2{v_0} = 3{\omega _0}r$$
G. $$3{v_0} = 4{\omega _0}r$$
H. $$4{v_0} = 3{\omega _0}r$$
Answer: D
An ideal monoatomic gas obeys the law $PV^{x}$ = constant. For what value of x, it has negative molar specific heat :-

Options:
A. x < 1.5
B. x < 1.67
C. x < 1.4
D. 1 < x < 1.4
E. 1 < x < 1.67
F. 1 < x < 1.47
G. 1 < x < 1.5
H. 1 < x < 1.7
I. x > 1.67
J. 1 < x < 1.45
Answer: E
A positively charged particle $P$ crosses a region of uniform electric field of intensity $E$. Velocity $u$ of the particle at the entry on the left side of the region is perpendicular to the electric field as shown in the first figure. Speed of the particle at exit on the right side is $v_{1}$. Now the experiment us repeated with a uniform magnetic field of induction $B$ suporimposed on the electric field as shown in the second in the second figure, keeping entry velocity of the particle unchanged. In this experiment, speed of the particle at exit on the right side is $v_{2}$. What can you conclude regarding the speed $v_{1}$ and $v_{2}$?

Options:
A. If $u=\dfrac{E}{B}$, then $v_{2}=v_{1}$
B. If $u>\dfrac{E}{B}$, then $v_{2}>v_{1}$
C. If $u>\dfrac{E}{B}$, then $v_{2}<v_{1}$
D. If $u>\dfrac{E}{2B}$, then $v_{2}>v_{1}$
E. If $u=\dfrac{E}{B}$, then $v_{2}>v_{1}$
Answer: C
A thin ring of $10\ cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of
$40\pi rad\ s^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its center is $3.8\times 10^{-9} T$, then the
charge carried by the ring is close to $(\mu_{0} = 4\pi \times 10^{-7} N/A^{2})$

Options:
A. $$6 \times 10^{-5}C$$
B. $$5 \times 10^{-5}C$$
C. $$5 \times 10^{-6}C$$
D. $$4 \times 10^{-6}C$$
E. $$9 \times 10^{-6}C$$
F. $$4\times 10^{-5}C$$
G. $$2\times 10^{-6}C$$
H. $$3\times 10^{-5}C$$
I. $$7\times 10^{-6}C$$
Answer: H
At $298$K, the standard reduction potentials are $1.51$V for $Mn{ O }^-_4$|$Mn^{2+}$, $1.36$V for $Cl_2$|$Cl^-$, $1.07$V for $Br_2$|$Br^-$ and $0.54$V for $I_2$|$I^-$. At pH$=3$ permanganate is expected to oxidize: $\left(\displaystyle\frac{RT}{F}0.059V\right)$.

Options:
A. $Br^-$ and $I^-$
B. Cl^-, I^- and Mn^{2+}
C. $I^-$ only
D. $Cl^-, Br^-$ and $I^-$
E. $Cl^-$ and $Mn^{2+}$
F. $Cl^-$ and $Br^-$
G. $Br^-, I^-$ and $Mn^{2+}$
H. $Br^-$ and $Mn^{2+}$
I. $Cl^-$ and $I^-$
J. Cl^-, Br^-, and Mn^{2+}
Answer: D
Electric field given by the vector $\vec{ E }=x\hat{i}+y\hat{j}$ is present in the XY plane. A small ring carrying charge +Q, which can freely slide on a smooth non conducting rod, is projected along the rod from the point (0, L) such that it can reach the other end of the rod. What minimum velocity should be given to the ring? (Assuming zero gravity)

Options:
A. $$2{ \left( { Q{ L }^{ 2 } }/{ m } \right) }^{ { 1 }/{ 2 } }$$
B. $$4{ \left( { Q{ L }^{ 2 } }/{ m } \right) }^{ { 1 }/{ 2 } }$$
C. $${ \left( { Q{ L }^{ 2 } }/{ m } \right) }^{ { 1 }/{ 2 } }$$
D. { \left( { Q{ L }^{ 2 } }/9{ m } \right) }^{ { 1 }/{ 2 } }
E. { \left( { Q{ L }^{ 2 } }/3{ m } \right) }^{ { 1 }/{ 2 } }
F. { \left( { Q{ L }^{ 2 } }/6{ m } \right) }^{ { 1 }/{ 2 } }
G. $${ \left( { Q{ L }^{ 2 } }/2{ m } \right) }^{ { 1 }/{ 2 } }$$
H. { \left( { Q{ L }^{ 2 } }/5{ m } \right) }^{ { 1 }/{ 2 } }
I. { \left( { Q{ L }^{ 2 } }/8{ m } \right) }^{ { 1 }/{ 2 } }
J. { \left( { Q{ L }^{ 2 } }/4{ m } \right) }^{ { 1 }/{ 2 } }
Answer: G
Upon titrating $50$ ml of $1.96\  (W/V)\  H_2SO_4$ with a KOH solution (containing 11.2 g KOH per litre of solution), on adding $50$  mL KOH solution :

Options:
A. pH of resulting solution $=4$
B. pH of resulting solution $=2$
C. Equivalence point has been just reached.
D. pH of resulting solution $=5$
E. Equivalence point has been crossed.
F. pH of resulting solution $=6$
G. pH of resulting solution $=3$
H. pH of resulting solution $=2.5$
I. pH of resulting solution $=7$
J. pH of resulting solution $=1$
Answer: B
A gas obeys $P(V-b)=RT$. Which of the following are correct about this gas?

Options:
A. Isochoric curves have slope $=\frac {R}{P}$ and intercept b
B. Isochoric curves have slope $= \frac{R}{P(V+d)}$
C. Isochoric curves have slope $= \frac{R}{P(V+a)}$
D. The attraction forces are overcome by repulsive forces
E. Isochoric curves have slope $= \frac{R}{P(V-b)}$
F. Isochoric curves have slope $= \frac{R}{P(V+c)}$
G. Isochoric curves have slope $= \frac{R}{P(V-b/2)}$
H. Isochoric curves have slope $= \frac{R}{P(V+b)}$
Answer: D
Two buffer solutions, A and B, each made with acetic acid and sodium acetate differ in their pH by one unit, A has salt : acid $=x : y$, B has salt $:$ acid $=y : x$. If $x > y$, then the value of $x : y$ is?

Options:
A. 317
B. 100
C. $$10,000$$
D. $$2.10$$
E. $$6.61$$
F. 3.17
G. $$31.7$$
H. 7.40
I. $$1,000$$
Answer: C
The angular displacement of the rod is defined as $\theta =\dfrac{3}{20}t^2$ where $\theta$ is in radian and t is in second. The collar B slides along the rod in such a way that its distance from O is, $r=0.9-0.12t^2$ where r is in metre and t is in second. The velocity of collar at $\theta =30^o$ is?

Options:
A. $0.45$ m/s
B. 0.33 m/s
C. $0.36$ m/s
D. $0.27$ m/s
E. 0.24 m/s
F. 0.30
G. 0.39 m/s
H. $0.48$ m/s
I. 0.30 m/s
J. $0.52$ m/s
Answer: D
An oil drop carrying a charge of 4 electrons has a mass of $3.2 \times 10 ^ { - 17 }$kg. It is falling freely in air with terminal speed. The electric field required to make the drop move upwards with the same speed is $\left( g = 10 m s ^ { - 2 } \right)$

Options:
A. 7 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
B. $$2 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }$$
C. $$8 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }$$
D. 3.5 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
E. 6 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
F. 5 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
G. 4 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
H. 9 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }
I. $$1 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }$$
J. $$3 \times 10 ^ { 3 } \mathrm { Vm } ^ { - 1 }$$
Answer: B
A radioactive substance has a constant activity of 2000 disintegration/minute. The material is separated into two fractions, one of which has an initial activity of 1000 disintegrations per second while the other fraction decays with $t_{1/2} = 24$ hours. The total activity in both samples after 48 hours of separation is

Options:
A. 1500
B. 1750
C. 1400
D. 1350
E. 1800
F. 1000
G. 1650
H. 1600
I. 1250
J. 2000
Answer: J
Two equal spheres A and B lie on a smooth horizontal circular groove at opposite ends of a diameter. At time $t = 0$, A is projected along the groove and it first impinges on B at time $t = T_1$ and again at time $t = T_2$. If e is the coefficient of restitution, the ratio $T_2 / T_1$ is :

Options:
A. $$\displaystyle \frac{(2 + e)}{2}$$
B. $$\displaystyle \frac{2}{e}$$
C. $$\displaystyle \frac{2(1 + e)}{e}$$
D. $$\displaystyle \frac{(1 + 2e)}{e}$$
E. $$\displaystyle \frac{(3 + e)}{e}$$
F. $$\displaystyle \frac{(2 + e)}{e}$$
G. $$\displaystyle \frac{3(e + 1)}{e}$$
H. $$\displaystyle \frac{2(e + 1)}{e}$$
I. \(\displaystyle \frac{2(e + 2)}{e}\)
Answer: F
The instantaneous values of alternating current and voltages in a circuit are given as $i = \dfrac{1}{\sqrt2}sin (100 \pi t)$  ampere$e = \dfrac{1}{\sqrt2}sin (100 \pi t + \pi/3)$  voltThe average power in Watts consumed in the circuit is -

Options:
A. \dfrac{1}{4}
B. $$\dfrac{1}{8}$$
C. \dfrac{\sqrt3}{16}
D. \dfrac{1}{16}
E. \dfrac{\sqrt3}{2}
F. $$\dfrac{1}{2}$$
G. \dfrac{\sqrt3}{8}
H. $$\dfrac{\sqrt3}{4}$$
Answer: H
The temperature of ice is $-10$ [Specific heat =$0.5  kcal/(kg-c)$]  and that of water 60C . They are mixed in equal amounts. what part of the ice will be melted?

Options:
A. Whole ice will be melted
B. \cfrac { 7 }{ 11 } th
C. \cfrac { 10 }{ 7 } th
D. $$\cfrac { 11 }{ 6 } th$$
E. None of these
F. \cfrac { 6 }{ 11 } th
G. \cfrac { 12 }{ 7 } th
H. \cfrac { 5 }{ 7 } th
I. $$\cfrac { 5 }{ 6 } th$$
J. \cfrac { 8 }{ 11 } th
Answer: D
When $5$ litres of a gas mixture of methane and propane is perfectly combusted at $0^o$C and $1$ atmosphere, $16$ litres of oxygen at the same temperature and pressure is consumed. The amount of heat released from this combustion in kJ $(\Delta H_{comb.}(CH_4)=890$ kJ $mol^{-1}$, $\Delta H_{comb.}(C_3H_8)=2220$ kJ $mol^{-1}$) is?

Options:
A. 32
B. $$38$$
C. 382
D. 347
E. 342
F. $$482$$
G. $$317$$
H. 422
I. $$477$$
Answer: B
To a one litre solution of $0.1N$ $HCl$, $0025mol$ of ${NH}_{4}Cl$ are added. Assuming $80$% dissociation of the solutes, the freezing point of the solution is: $({K}_{f}=1.85deg/molal)$

Options:
A. $$-{0.85}^{o}C$$
B. $$-{0.25}^{o}C$$
C. -{0.22}^{o}C
D. $$-{0.395}^{o}C$$
E. $$-{0.24}^{o}C$$
F. $$-{0.416}^{o}C$$
G. -{0.375}^{o}C
H. $$-{0.33}^{o}C$$
I. $$-{0.23}^{o}C$$
J. -{0.415}^{o}C
Answer: I
The coefficient of friction between block of mass $m$ and $2m$ is $\mu = 2 \tan {\theta}$. There is no friction between block of mass $2m$ and inclined plane. The maximum amplitude of the two block system for which there is no relative motion between both the block is:

Options:
A. $$None\ of\ these$$
B. \dfrac { 4mg\sin { \theta } }{ k }
C. 4\dfrac { mg\sin { \theta } }{ k }
D. 5\dfrac { mg\sin { \theta } }{ k }
E. 6\dfrac { mg\sin { \theta } }{ k}
F. $$\dfrac { mg\sin { \theta } }{ k } $$
G. $$3\dfrac { mg\sin { \theta } }{ k } $$
H. $$g\sin { \theta } \sqrt { \dfrac { k }{ m } } $$
I. 2\dfrac { mg\sin { \theta } }{ k}
Answer: G
5 charges each of magnitude $10^{-5} C$ and mass 1 kg are placed (fixed) symmetrically about a movable central charge of magnitude $5 \times 10^{-5}$C and mass 0.5 kg as shown. The charge at $P_1$ is removed. The acceleration of the central charge is :[Given $OP_2\, =\, OP_3\, =\, OP_4\,=\, OP_5\,= 1m;\, \displaystyle \frac {1}{4\,\pi\, \epsilon _0}\, =\, 9\, \times\, 10^9$ in SI units]

Options:
A. 9 m s$^{-2}$ upwards
B. 3.375 m s^{-2} upwards
C. 9 m s$^{-2}$ downwards
D. 4.5 m s$^{-2}$ downwards
E. 2.25 m s^{-2} downwards
F. 3.375 m s^{-2} downwards
G. 4.5 m s^{-2} upwards
H. 2.25 m s^{-2} upwards
Answer: A
Two wires AO and OC carry currents $i$ as shown in figure. One end of both the wires extends to infinity $\angle AOC$ =$\alpha$, the magnitude of magnetic field at a point P on the bisector of the two wires at a distance $r$ from O is

Options:
A. $$\dfrac{\mu _{0}i}{4\pi r}\sin\left ( \dfrac{\alpha }{2} \right)$$
B. \dfrac{\mu _{0}i}{2\pi r}\dfrac{\left ( 1+\cos\dfrac{\alpha }{2} \right )}{\cos\left ( \dfrac{\alpha }{2} \right )}
C. $$\dfrac{\mu_{0}i}{2\pi r}\cot\left ( \dfrac{\alpha}{2} \right)$$
D. $$\dfrac{\mu_{0}i}{2\pi r}\dfrac{\left ( 1+\cos\dfrac{\alpha }{2} \right )}{\sin\left ( \dfrac{\alpha}{2} \right)}$$
E. \dfrac{\mu _{0}i}{2\pi r}\dfrac{\left ( 1+\sin\dfrac{\alpha }{2} \right )}{\cos\left ( \dfrac{\alpha }{2} \right )}
F. $$\dfrac{\mu _{0}i}{2\pi r}\dfrac{\left ( 1-\sin\dfrac{\alpha }{2} \right )}{\cos\left ( \dfrac{\alpha }{2} \right )}$$
G. \dfrac{\mu _{0}i}{4\pi r}\dfrac{\left ( 1+\cos\dfrac{\alpha }{2} \right )}{\sin\left ( \dfrac{\alpha }{2} \right )}
H. $$\dfrac{\mu_{0}i}{4\pi r}\cot\left ( \dfrac{\alpha}{2} \right)$$
I. $$\dfrac{\mu _{0}i}{2\pi r}\dfrac{\left ( 1-\cos\dfrac{\alpha }{2} \right )}{\cos\left ( \dfrac{\alpha }{2} \right )}$$
J. $$\dfrac{\mu _{0}i}{2\pi r}\dfrac{\left ( 1-\cos\dfrac{\alpha }{2} \right )}{\sin\left ( \dfrac{\alpha }{2} \right )}$$
Answer: D
In case of a transverse wave in a string

Options:
A. In harmonic wave, particle speed is constant
B. In harmonic wave, particle velocity is proportional to the wave velocity
C. In harmonic wave, particle velocity is proportional to the wave frequency
D. If $\displaystyle \frac {\lambda} {2 \pi} > A_0 $ , maximum particle speed is more than the wave speed
E. In harmonic wave, wave velocity is proportional to the frequency
F. In harmonic wave, wave velocity is proportional to the amplitude
G. $\displaystyle \frac {\lambda} {2 \pi} = A_0 $ , maximum particle speed is equal to the wave speed
H. In harmonic wave, wave velocity is constant
I. In harmonic wave, wave velocity is proportional to the square of the amplitude
J. In harmonic wave, particle velocity is constant
Answer: H
A circular disc is made to rotate in a horizontal plane about its centre at the rate of $2 \ rps$. The greatest distance of a coin placed on the disc from its centre so that it does not skid is ($\mu$ is coefficient of friction, $g=10ms^{-2}$):

Options:
A. $$6.3\mu\  cm$$
B. $$\displaystyle \frac{2 \mu}{6.3}\  cm$$
C. $$\frac{6.3 \mu}{4} \ cm$$
D. $$\displaystyle \frac{\mu g}{6.3}\ cm$$
E. $$\displaystyle \frac{\mu}{6.3}\ cm$$
F. $$\frac{6.3 \mu}{2}\ cm$$
G. $$\frac{\mu g}{3.15}\ cm$$
H. $$\frac{6.3 \mu}{3.15} \ cm$$
I. $$\frac{3.15 \mu}{2} \ cm$$
J. $$\frac{6.3 \mu}{6.3} \ cm$$
Answer: A
One gram of the silver salt of organic dibasic acid on strong heating yields, $0.6$ g of silver approximately. Determine the molecular formula of the acid. [Atomic weight of $Ag=$$108 g$]

Options:
A. C_{4}H_{6}O_{7}
B. $$C_{4}H_{6}O_{4}$$
C. $$C_{4}H_{8}O_{6}$$
D. C_{4}H_{8}O_{7}
E. $$C_{4}H_{6}O_{6}$$
F. $$C_{2}H_{6}O_{2}$$
G. C_{4}H_{6}O_{5}
H. C_{3}H_{6}O_{6}
I. C_{4}H_{8}O_{5}
J. $$C_{5}H_{6}O_{5}$$
Answer: E
The equation $y =A\cos^2\left(2\pi\, nt -2\pi \dfrac{x}{\lambda}\right)$ represents a wave with

Options:
A. amplitude $A/2$, frequency $2n$& wavelength $\lambda$
B. amplitude $A/2$, frequency $n$& wavelength $\lambda/2$
C. amplitude $A/2$, frequency $n$& wavelength $\lambda$
D. amplitude $A$, frequency $n$& wavelength $\lambda$
E. amplitude $A/2$, frequency $n/2$& wavelength $\lambda/2$
F. amplitude $A$, frequency $n$& wavelength $2\lambda$
G. amplitude $A/2$, frequency $n$& wavelength $2\lambda$
H. amplitude $A/4$, frequency $n$& wavelength $\lambda/2$
I. amplitude $A/2$, frequency $2n$& wavelength $\lambda/2$
J. amplitude $A$, frequency $2n$& wavelength $2\lambda$
Answer: I
Two capacitors of capacity $6\mu F$ and $3\mu F$ are charged to
$100V$ and $50V$ separately and connected as shown in figure. Now
all the three switches ${S}_{1},{S}_{2}$ and ${S}_{3}$ are closed. Suppose ${q}_{1},{q}_{2}$ and ${q}_{3}$ be the magnitudes of charge flowing from switches ${S}_{1},{S}_{2}$ and ${S}_{3}$ after they are closed. Then :

Options:
A. $${q}_{1}={q}_{3}=2{q}_{2}$$
B. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{2}
C. ${q}_{1}={q}_{3}$ and ${q}_{2}=0$
D. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{3}
E. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{5}
F. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{7}
G. $${q}_{1}={q}_{2}={q}_{3}$$
H. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{4}
I. {q}_{1}={q}_{3}=\cfrac{{q}_{2}}{6}
Answer: G
A metallic rod of length $1\ m$ is rigidity clamped at its midpoint. Longitudinal stationary waves are set up in the rod in such a way that there are two nodes on either side of the midpoint. The amplitude of an antinode is $2\times 10^{-6}\ m$. ( Young's modulus $=2\times 10^{11}\ Nm^{-2}$ and density $=8000\ kg\ m^{-3}$)
Select the correct answers :

Options:
A. y_1=(1 \times 10^{-6})\sin (5\pi x-15 \times 10^3 \pi t)
B. y_1=(1 \times 10^{-6})\sin (5\pi x + 22 \times 10^3 \pi t)
C. The equation of one of the constituent waves in the rod is $y_1=(1\times 10^{-6})\sin (5\pi x+25\times 10^3\pi t)$
D. The equation of motion at a point $2\ cm$ from the midpoint is $y=2\times 10^{-6}\sin 10\pi x\cos 25\times 10^3\pi t$
E. y_1 = (1 \times 10^{-6})\sin (5\pi x - 25 \times 10^3 \pi t)
F. The equation of one of the constituent waves in the rod is \( y_1 = (1 \times 10^{-6})\sin (5\pi x - 20 \times 10^3 \pi t) \)
G. y_1=(1 \times 10^{-6})\sin (5\pi x + 20 \times 10^3 \pi t)
H. y_1=(1 \times 10^{-6})\sin (10\pi x-25 \times 10^3 \pi t)
Answer: C
A long tube of length $1.2\ m$ closed at both ends is lying horizontally. A mercury column of length $0.4\ m$ is filled in its middle and in rest of two parts, air is filled at atmospheric pressure. When the tube is turned to vertical position, find the displacement of mercury column. (atmospheric pressure $=0.75$ meter of $Hg$, density of water is $1000$ $kg/m^{3}$).

Options:
A. $0.2$ meter
B. 0.17 meter
C. 0.12 meter
D. 0.18 meter
E. $0.1$ meter
F. $0.4$ meter
G. 0.25 meter
H. 0.15 meter
I. $0.3$ meter
J. 0.22 meter
Answer: E
Which of the following is incorrect?

Options:
A. $\left( \frac { \partial U } { \partial V } \right) _ { T } = 0$ for an ideal gas.
B. A real gas behaves like an ideal gas over a wide range of pressure $( - 100$ atm ) at critical temperature of the gas.
C. $\left( \frac { \partial U } { \partial V } \right) _ { T } = \frac { a } { V ^ { 2 } }$ for a real gas obeying van der Waals' equation
D. A real gas behaves like ideal gas over a wide range of pressure $( - 100$ atm $)$ at Boyle point.
Answer: D
An object is taken from a point P to another point Q in a gravitational field.

Options:
A. The work done depends on the path taken between P and Q, even if both points are at the same height
B. If P is on the earth's surface and Q above it, the work done is minimum when it is taken along the straight line PQ
C. There is no work done if the object is taken from P to Q and then brought back to P along a closed loop path
D. The work done depends only on the position of P and Q and is independent of the path along which the particle is taken
E. Assuming the earth to be spherical, if both P and Q lie on the earth's surface, the work done is zero
F. There is no work done if the object is taken from P to Q and then brought back to P along a circular path
G. The work done depends only on the position of P and Q but is affected by the gravitational field strength along the path
H. There is no work done if the object is taken from P to Q and then brought back to P along a straight line path
I. There is no work done if the object is taken from P to Q and then brought back to P along any path
J. There is no work done if the object is taken from P to Q and then brought back to P along a specific path
Answer: I
For the reaction :
$$X_2O_4(l)\rightarrow 2XO_2(g)$$
$\triangle U=2.1kcal,\triangle S=20calK^{-1}$ at 300K
Hence $\triangle G$ is :-

Options:
A. 1.8 k cal
B. -9.3 k cal
C. -2.1 k cal
D. -7.2 k cal
E. 2.7 k cal
F. -2.7 k cal
G. 2.1 k cal
H. 9.3 k cal
I. 2.8 k cal
J. 7.2 k cal
Answer: E
Given that : $2C(s)+2O_2(g)\rightarrow 2CO_2(g)$;    $\Delta H=-787$ kJ$H_2(g)+1_{/2}O_2(g)\rightarrow H_2O(l)$;     $\Delta$H$=-286$ kJ$C_2H_2(g)+\displaystyle\frac{5}{2}O_2(g)\rightarrow 2CO_2(g)+H_2O(l)$;  $\Delta$H$=-1310$ kJ.Heat of formation of acetylene is:

Options:
A. $-800$ KJ
B. -1902 KJ
C. $+237$ KJ
D. -1702 KJ
E. $+1802$ KJ
F. -1750 KJ
G. -237 KJ
H. -1250 KJ
I. -1802 KJ
Answer: E
One mole of an ideal monoatomic gas $\left(C_{v.m.}= \dfrac{3}{2}R\right)$ initially present in an insulted piston at $500\ K$ is expanded reversibly from $10\ L$ to $80\ L$, then change in internal energy is-

Options:
A. $$5766.6\ J$$
B. $$4667.6\ J$$
C. $$-3766\ J$$
D. $$4766.6\ J$$
E. $$5676.6\ J$$
F. $$-4676.6\ J$$
G. $$-5766.6\ J$$
H. $$-4676\ J$$
I. $$3766\ J$$
Answer: G
The value of $C_p \,-\, C_v$ is $1.09 R$ for a gas sample in state $A$ and is $1.00 R$ in state $B$. Let $T_A,\, T_B$ denote the temperature and $P_A$ and $P_B$ denote the pressure of the states $A$ and $B$ respectively. Then:

Options:
A. P_A = P_B and T_A > T_B
B. $P_A= P_B$ and $T_A=T_B$
C. P_A < P_B and T_A < T_B
D. P_A < P_B and T_A > T_B
E. P_A = P_B and T_A < T_B
F. P_A \cdot T_A
G. $P_A>P_B$ and $T_A<T_B$
H. $$P_A\,+\,P_B$$
I. $$P_A\,T_B$$
J. $P_A\,>\,P_B$ and $T_A>T_B$
Answer: I
In the following reaction :$xA \to yB$
$$\log \left[ { - \dfrac{{d\left[ A \right]}}{{dt}}} \right] = \log \left[ {\dfrac{{d\left[ B \right]}}{{dt}}} \right] + \log 2$$
where -ve sign indicates rate of disappearance of the reactant. Thus, X : Y is:

Options:
A. $$3 : 1$$
B. 2 : 3
C. $$2 : 1$$
D. $$1 : 2$$
E. 3 : 2
F. 1 : 4
G. $$3 : 10$$
H. 1 : 1
I. 1 : 3
Answer: D
At certain temperature $(T)$ for the gas phase reaction$2H_{2}O(g) + 2Cl_{2}(g)\rightleftharpoons 4HCl(g) + O_{2}(g)\ K_{p} = 12\times 10^{8} atm$If $Cl_{2}, HCl$ and $O_{2}$ are mixed in such a manner than the partial pressure of each is $2\ atm$ and the mixture is brough into contact with excess of liquid water. What would be approximate partial pressure of $Cl_{2}$ when equilibrium is attained at temperature $(T)$?[Given: Vapour pressure of water is $380\ mm\ Hg$ at temperature $(T)$]

Options:
A. $$10^{-4} atm$$
B. $$3.6 \times 10^{-9} atm$$
C. $$3.6 \times 10^{-7} atm$$
D. $$3.6\times 10^{-3} atm$$
E. $$3.6 \times 10^{-8} atm$$
F. $$0.01\ atm$$
G. $$3.6\times 10^{-5}atm$$
H. $$3.6 \times 10^{-2} atm$$
I. $$3.6 \times 10^{-6} atm$$
J. $$3.6 \times 10^{-4} atm$$
Answer: D
A block is placed over a large plank (plank is kept on horizontal surface). The coefficient of friction between the block and the plank is $\mu=0.2$. Initially both are at rest, suddenly the plank starts moving horizontally with acceleration $a_0=4m/s^2$ with the help of some external force. The displacement of the block in 1s is $(g=10m/s^2)$

Options:
A. 1.4m relative to ground
B. $1.2m$ relative to plank
C. $0.8m$ relative to plank
D. zero relative to plank
E. $1.4m$ relative to plank
F. $1.2m$ relative to ground
G. $1m$ relative to ground
H. $2m$ relative to ground
I. $1m$ relative to plank
J. $1.6m$ relative to plank
Answer: I
Degree of dissociation for a reversible reaction at equilibrium is calculated as
$$\alpha=\dfrac{D-d}{(n-1)d}$$
$D=$ Initial vapour density, d = Vapour density at equilibrium The relation is correctly matched for which of the following reactions :

Options:
A. $$X(g) \rightleftharpoons \dfrac{5n}{7}Y(g) + \dfrac{n}{7}Z(g)$$
B. $$X(g)\rightleftharpoons \dfrac{n}{3}Y(g)+\dfrac{2n}{3}Z(g)$$
C. $$X(g) \rightleftharpoons \dfrac{2n}{3}Y(g)+\dfrac{n}{3}Z(g)$$
D. $$X(g)\rightleftharpoons \dfrac{n}{2}Y(g)+\dfrac{n}{2}Z(g)$$
E. $$X(g) \rightleftharpoons \dfrac{3n}{4}Y(g)+\dfrac{n}{4}Z(g)$$
F. $$X(g) \rightleftharpoons \dfrac{5n}{9}Y(g) + \dfrac{4n}{9}Z(g)$$
G. All of these
H. X(g) \rightleftharpoons \dfrac{4n}{5}Y(g) + \dfrac{n}{5}Z(g)
I. $$X(g)\rightleftharpoons \dfrac{5n}{6}Y(g)+\dfrac{n}{6}Z(g)$$
J. $$X(g) \rightleftharpoons \dfrac{7n}{8}Y(g) + \dfrac{n}{8}Z(g)$$
Answer: I
$Pt |H _{\text{2}} (g)| solution\ X ||KCl\ (saturated) |Hg _{\text{2}}$ $Cl _{\text{2}} |Hg|Pt$ For the given cell, the observed EMF at 25$ ^\circ C $ was 600 mV. When solution $X$ was replaced by a standard phosphate buffer with $pH = 7.00$, the emf was 718 mV. Find the $_PH$ of the solution $X$:

Options:
A. 4.5
B. 6
C. 5
D. 3
E. 3.8
F. 4
G. 3.7
H. 4.2
I. 3.5
J. 5.5
Answer: F
A sample of $NaClO_3$ is converted by heat $NaCl$ with a loss of 0.16 g of oxygen. The residue is dissolved in water and precipitated as $AgCl$. The mass of $AgCl$ (in g) obtained will be : (Given : Molar mass of $AgCl=143.5 g mol^{-1}$)

Options:
A. 0.40
B. 0.39
C. 0.36
D. 0.41
E. 0.48
F. 0.44
G. 0.38
H. 0.35
I. 0.37
J. 0.54
Answer: E
Two point charges ${ q }_{ 1 }\left( \sqrt { 10 } \mu C \right) $ and ${ q }_{ 2 }\left( -25\mu C \right) $ are placed on the x-axis at x=1 m and x=4 m respectively. The electric field (in v/m) at a point y=3 m on y-axis is,

Options:
A. $$\left( 63\hat { i } -27\hat { j } \right) \times { 10 }^{ 2 }$$
B. $$\left( -27\hat { i } -63\hat { j } \right) \times { 10 }^{ 2 }$$
C. $$\left( -81\hat { i } -81\hat { j } \right) \times { 10 }^{ 2 }$$
D. $$\left( -81\hat { i } +81\hat { j } \right) \times { 10 }^{ 2 }$$
E. $$\left( -63\hat { i } -27\hat { j } \right) \times { 10 }^{ 2 }$$
F. $$\left( 63\hat { i } +27\hat { j } \right) \times { 10 }^{ 2 }$$
G. $$\left( -27\hat { i } +63\hat { j } \right) \times { 10 }^{ 2 }$$
H. $$\left( -63\hat { i } +27\hat { j } \right) \times { 10 }^{ 2 }$$
I. $$\left( 81\hat { i } -81\hat { j } \right) \times { 10 }^{ 2 }$$
J. $$\left( -27\hat { i } +81\hat { j } \right) \times { 10 }^{ 2 }$$
Answer: A
Magnetic induction as a function of distance r from the axis of a radially symmetrical parallel stream of electrons is $B=ar^2$ where a is a constant.The expression for current density as a function of r is

Options:
A. $$\dfrac{ar}{\mu_0}$$
B. \dfrac{4ar}{\mu_0}
C. \dfrac{4ar^2}{\mu_0}
D. \dfrac{ar^2}{\mu_0}
E. $$\dfrac{2ar}{\mu_0}$$
F. $$\dfrac{2ar}{3\mu_0}$$
G. \dfrac{2ar^2}{\mu_0}
H. $$\dfrac{3ar}{\mu_0}$$
I. \dfrac{ar^2}{3\mu_0}
J. $$\dfrac{ar^2}{2\mu_0}$$
Answer: A
An observer and a vehicle, both start moving together from rest ( towards right ) with acceleration $5 m/s^2$ and $2 m/s^2$, respectively. There is a $1 kg$ block on the floor of the vehicle and coefficient of friction is $\mu$ = $0.3$ between their surfaces. What is the magnitude of the work done (in $J$) by frictional force on the $1 kg$ block observed by the running observer, during first second of the motion.

Options:
A. $$4.5 J$$
B. 5.0 J
C. 3.5 J
D. $$4.0 J$$
E. 3.2 J
F. 2.5 J
G. $$3.0 J$$
H. 5.5 J
I. $$2.0 J$$
Answer: G
Two conducting spheres of radius $r$ and $2r$ at very large separation. Each sphere is having charge $Q$. These sphere are connected with a very long conducting wire of resistance $R$. Then, the current flowing in the wire at $t=2\mu s$. (where $r=30cm.R=90k\Omega$ and $Q=10\mu C$)

Options:
A. $$\cfrac{100}{3e}A$$
B. $$\cfrac{25}{3e}A$$
C. \cfrac{110}{3e}A
D. \cfrac{200}{3e}A
E. \cfrac{150}{3e}A
F. \cfrac{75}{3e}A
G. $$\cfrac{5}{3e}A$$
H. \cfrac{175}{3e}A
I. $$\cfrac{50}{3e}A$$
J. \cfrac{125}{3e}A
Answer: A
When ferrous oxalate is titrated against $K_{2}Cr_{2}O_{7}$ , m eq . of  $Fe^{+} , C_{2}O_{4}^{2-} $ and  $Cr_{2}O_{7}^{2-}$ in the redox reaction are X, Y and Z respectively , then :-

Options:
A. X+Y=Z
B. 2X+Y=Z
C. 2X+Y=2Z
D. X+2Y=Z
E. 2X+2Y=Z
F. X+2Y=2Z
G. X+Y=2Z
H. 2X+6Y=6Z
I. 3X+2Y=Z
J. X=Y
Answer: J
A neutron having kinetic energy $E$ collides head on with a stationary hydrogen atom in ground state, which is initially at rest but free to move. Assume the mass of the neutron to be equal to that of $H$ atom. Use the energy of the $nth$ state for $H$ atom as $E_{1} = -13.6\ eV; E_{2} = 3.4\ eV; E_{3} = -1.5\ eV$. (Whether collision is elastic or inelastic depends on the energy of the neutron, and in case of elastic collision they can be treated as ordinary particles)
Now choose the correct options

Options:
A. If \( E > 20.4\ eV \) the kinetic energy of the neutron will become half after the collision
B. The collision will be perfectly elastic if $E$ is less than $20.4\ eV$
C. If $E > 20.4\ eV$ the kinetic energy of the neutron will be reduced but not to zero after the collision
D. If \( E = 20.4\ eV \) the hydrogen atom will not be excited and the neutron will continue with the same kinetic energy
E. If $E > 20.4\ eV$ the kinetic energy of the neutron will become zero after the collision
F. If $E < 20.4\ eV$ the kinetic energy of the neutron will become zero after the collision
G. If \( E > 20.4\ eV \) the hydrogen atom will not be excited and the neutron will continue with the same kinetic energy
Answer: E
Two blocks of masses ${m}_{1}={m}_{2}=m$ are connected by a string of neglected mass, which passes over a frictionless pulley fixed on the top of an inclined pane shown in the given figure. When angle of inclination $\theta={30}^{o}$, the mass $m$, just begins to move up the inclined plane. what is the coefficient of friction between the block ${m}_{1}$ and the inclined plane?

Options:
A. $$\cfrac { 1 }{ 2\sqrt { 2 } } $$
B. $$\cfrac { 1 }{2 \sqrt { 3 } } $$
C. $$\cfrac { 1 }{ \sqrt { 2 } } $$
D. \cfrac{1}{\sqrt{3} + 1}
E. \cfrac{1}{2\sqrt{3} - 1}
F. \cfrac{1}{2\sqrt{2} + 1}
G. $$\cfrac { 1 }{ \sqrt { 3 } } $$
H. \cfrac{1}{2\sqrt{2} - 1}
I. \cfrac{1}{2\sqrt{3} + 1}
J. \cfrac{1}{2\sqrt{3} + 2}
Answer: C
The density of A is 10 g $\mathrm { cm } ^ { - 3 }$  The quantity of electricity needed to plate an area 10 cm x 10 cm to a thickness of $10 ^ { - 2 }$  cm using $\mathrm { ASO } _ { 4 }$  solution would be (Atomic mass of A = 193 )

Options:
A. 7500 \mathrm { C }
B. 12500 \mathrm { C }
C. $$40000 \mathrm { C }$$
D. 7000 \mathrm { C }
E. $$20000 \mathrm { C }$$
F. $$5000 \mathrm { C }$$
G. 3000 \mathrm { C }
H. 6000 \mathrm { C }
I. $$10000 \mathrm { C }$$
J. 2500 \mathrm { C }
Answer: F
Two identical disc each of mass M(=4 m) and radius R are rotating in opposite sense with equal angular speed $\omega_0$ about vertical axes passing through their centres, (as shown in figure). A person of mass m sitting on circumference of disc A jumps with a tangential relative velocity u(after jumping) w.r.t. one rotating disc(A) and lands on other disc (B) also tangential. Now the second disc(B) comes to a stop. Find the relative velocity u.

Options:
A. $$u=2\omega_0 R$$
B. $$u=\dfrac{\omega_0 R}{2}$$
C. $$u=\dfrac{3\omega_0 R}{4}$$
D. $$u= \omega_0 R$$
E. $$u=\dfrac{9\omega_0 R}{4}$$
F. $$u=\dfrac{5\omega_0 R}{2}$$
G. $$u=\dfrac{7\omega_0 R}{4}$$
H. $$u=\dfrac{5\omega_0 R}{4}$$
I. $$u=\dfrac{11\omega_0 R}{4}$$
J. $$u=\dfrac{3\omega_0 R}{2}$$
Answer: B
In a certain circuit having three parallel branches , the instantaneous branch currents are represented by $i_1$ = 20 sin $\omega$t , $i_2$ = 20 sin ($\omega$t - 37), $i_3$ = 8$\sqrt{2}$ sin ($\omega$t + 135). if net current flows through a 10 $\Omega $ resistor, the power dissipated in the resistor is $lpha$ kW.

Options:
A. 3
B. 2.8
C. 2.9
D. 2.5
E. 2.6
F. 4
G. 2.75
H. 2
I. 5
J. 2.7
Answer: A
A charged particle $P$ leaves the origin with speed $v=v_0$ at some inclination with the $x-$axis. There is a uniform magnetic field B along the $x-$axis. $P$ strikes a fixed target $T$ on the $x-$axis for a minimum value of $B=B_0$. If the pitch of the helical path is equal to the maximum distance of the particle from the x-axis, then which of the following are not correct?

Options:
A. $$sin\theta =\dfrac {1}{\pi}$$
B. tan\theta = \dfrac{\pi}{2}
C. $$tan\theta =\dfrac {1}{\pi}$$
D. tan\theta = \dfrac{6}{\pi}
E. $$cos\theta =\dfrac {1}{\pi}$$
F. tan\theta = \dfrac{2}{\pi}
G. tan\theta = \dfrac{3}{\pi}
H. tan\theta = \dfrac{4}{\pi}
I. tan\theta = \dfrac{5}{\pi}
J. $$tan\theta =\pi$$
Answer: C
Electric field in space is given by $\vec{E}=y\vec{i}+x\vec{j}$. If potential at $(1, 2, 1)$ is $1V$, then the potential at $(0, 0, 0)$ is

Options:
A. 6V
B. $$4V$$
C. 1V
D. $$none\ of\ these$$
E. $$5\ V$$
F. 3V
G. $$10V$$
H. $$2V$$
Answer: G
A cylinder of mass m and radius R is spined to a clockwise angular velocity ${ \omega  }_{ 0 }$. and then gently placed on an inclined plane for which coefficient of friction $\mu = tan \theta$, $\theta$ is the angle of inclined plane with horizontal. The centre of mass of the cylinder will remain stationary for time.

Options:
A. $${ 2\omega }_{ 0 }3R/ gsin \theta$$
B. 3\omega_{0}R / 2gsin\theta
C. $${ \omega }_{ 0 }R/ gsin \theta$$
D. ${ 3\omega }_{ 0 }R/ 4gsin \theta$
E. $$\omega_{0}R / 5gsin\theta$$
F. $${ 2\omega }_{ 0 }R/ 5gsin \theta$$
G. $${ \omega }_{ 0 }R/ 3gsin \theta$$
H. $${ 2\omega }_{ 0 }R/ 3gsin \theta$$
I. $${ \omega }_{ 0 }R/ 2gsin \theta$$
J. ${ 4\omega }_{ 0 }R/ 5gsin \theta$
Answer: I
A heavy mass $M$ resting on the ground is connected to a lighter mass $m$ through a light inextensible string passing over an ideal pulley. The string connected to mass $M$ is loose. Let lighter mass $m$ be allowed to fall freely through a height $h$ such that the string becomes taut. If $t$ is the time from this instant onward when the heavier mass again makes contact with the ground and $\Delta E$ is change in kinetic energy then

Options:
A. $$t=\cfrac { 2m }{ 2M+m } \sqrt { \cfrac { 2h }{ g } }$$
B. $$t=\cfrac { 2m }{ M+3m } \sqrt { \cfrac { 2h }{ g } }$$
C. $$\Delta E=-\left( \cfrac { Mm }{ m+m } \right) gh$$
D. $$t=\cfrac { 2m }{ M+m } \sqrt { \cfrac { 2h }{ g } }$$
E. $$\Delta E=-Mgh$$
F. $$t=\cfrac { 2m }{ M+2m } \sqrt { \cfrac { 2h }{ g } }$$
G. $$t=\cfrac { 2m }{ M-m } \sqrt { \cfrac { 2h }{ g } } $$
H. $$t=\cfrac { 2m }{ 2M+3m } \sqrt { \cfrac { 2h }{ g } }$$
I. $$t=\cfrac { 2m }{ 3M-m } \sqrt { \cfrac { 2h }{ g } }$$
Answer: F
For one mole of ideal gas if $p\ = \cfrac { { p }_{ 0 } }{ 1+(\frac { V }{ { V }_{ 0 } } ) } $ where ${ P }_{ 0 }$ and ${ V }_{ 0 }$ are constant, then temperature of gas when $V= { V }_{ 0 }$ is:

Options:
A. $$\frac { { P }_{ 0 }{ V }_{ 0 } }{ 4R } $$
B. \frac { { P }_{ 0 }{ V }_{ 0 } }{ 7R }
C. $$\frac { { P }_{ 0 }{ V }_{ 0 } }{ R } $$
D. \frac { { P }_{ 0 }{ V }_{ 0 } }{ 8R }
E. \(\frac { { P }_{ 0 }{ V }_{ 0 } }{ 6R }\)
F. $$\frac { { P }_{ 0 }{ V }_{ 0 } }{ 3R } $$
G. $$\frac { { P }_{ 0 }{ V }_{ 0 } }{ 2R } $$
H. \frac { { P }_{ 0 }{ V }_{ 0 } }{ 10R }
I. \frac { { P }_{ 0 }{ V }_{ 0 } }{ 9R }
J. \frac { { P }_{ 0 }{ V }_{ 0 } }{ 5R }
Answer: C
The maximum K.E found in alpha particle of natural origin is $7.7$ MeV. Find the closest distance of approach for the gold nucleus $(Z = 79$ for gold$)$[Note : At closest distance of approach, kinetic energy is converted into potential energy]

Options:
A. 3 \times 10^{-11} m
B. $3 \times 10^{-16}$ m
C. $3 \times 10^{-14}$ m
D. 3 \times 10^{-15} m
E. $3 \times 10^{-13}$ m
F. 3 \times 10^{-10} m
G. $3 \times 10^{-12}$ m
Answer: G
In which of the following cells, $E_{cell}=E^{o}_{cell}$?

Options:
A. $$Pt|H_{2}(1 atm), H^{+}(pH=1)||Zn^{2+}(0.01M)|Zn_{(s)}$$
B. $$Pt|H_{2}(1 atm), H^{+}(0.01M)||Zn^{2+}(0.1M)|Zn_{(s)}$$
C. $Pt|H_{2}(1 atm), H^{+}(1M)||Zn^{2+}(0.1M)|Zn_{(s)}$
D. $$Cu_{(s)}|Cu^{+2}(0.01 M)||Ag^{+}(0.1 M)|Ag_{(s)}$$
E. $$Pt|H_{2}(1 atm), H^{+}(pH=1)||Zn^{2+}(1M)|Zn_{(s)}$$
F. $Pt|H_{2}(1 atm), H^{+}(0.1M)||Zn^{2+}(1M)|Zn_{(s)}$
G. $$Pt|H_{2}(1 atm), H^{+}(0.1M)||Zn^{2+}(0.01M)|Zn_{(s)}$$
H. $Pt|H_{2}(1 atm), H^{+}(0.01M)||Zn^{2+}(1M)|Zn_{(s)}$
I. $Pt|H_{2}(1 atm), H^{+}(0.1M)||Zn^{2+}(0.1M)|Zn_{(s)}$
Answer: G
$10$ gm of ice at $-20C$ is added to $10$ gm of water at $50C$. Specific heat of water $=1 cal/g-c$. specific heat of ice $= 0.5 cal/gm-C$.Latent heat of ice $= 80 cal/gm$. Then resulting temperature is

Options:
A. $$15C$$
B. $$12C$$
C. $$50C$$
D. 30C
E. $$0C$$
F. 18C
G. $$-20C$$
H. 25C
I. 10C
J. 20C
Answer: C
A quill tube contains a mercury column of length 19 cm. The length of air column is 24 cm when it is held vertically. On inverting it with its open end downwards the length of air column will be_______cm. (atmospheric pressure = 76 cm of Hg)

Options:
A. 39 cm
B. 38 cm
C. 25 cm
D. 30 cm
E. 36 cm
F. 20 cm
G. 35 cm
H. 40 cm
I. 32 cm
J. 34 cm
Answer: H