MikaStars39/nano-eval huggingface dataset:
The temperature of a wire of length $1$ meter and area of cross-section $c{m^2}$ is increased from ${0^ \circ }C$ to ${100^ \circ }C$ rod is not allowed to increase in length$,$ the force required will be $(lpha  = {10^{ - 5}}{/^ \circ }C$ and $Y = {10^{11}}N/{M^2})$

Options:
A. 10^6N
B. ${10^7}N$
C. $${10^5}N$$
D. ${10^4}N$
E. $${10^9}N$$
F. $${10^3}N$$
G. ${10^8}N$
H. ${10^2}N$
I. ${10^6}N$
Answer: C
A motorist travelling at $54\ km/hr$ when he observes a traffic signal at a distance of $280\ m$ ahead turning red at time $t=0$. If he decides to decelerate & then accelerates by the same magnitude, so as to pass the signal at $54\ km/hr$ at $t=28$ seconds, when the signal turns green, then

Options:
A. Minimum speed reached is $7.5\ m/s$
B. Minimum speed reached is $11.5\ m/s$
C. Minimum speed reached is $9.5\ m/s$
D. Minimum speed reached is $12.5\ m/s$
E. Minimum speed reached is $5\ m/s$
F. Minimum speed reached is $8.5\ m/s$
G. Minimum speed reached is $10\ m/s$
H. Minimum speed reached is $11\ m/s$
I. Magnitude of deceleration is $1 m/s^{2}$
J. Magnitude of deceleration is $\dfrac{5}{7}m/s^{2}$
Answer: G
A 10 watt source of sound of frequency 1000Hz sendsout waves in air. The displacement amplitude at a distance of 10m from the source is (speed of sound in air $= 340 m/s$ and density of air $= 1.29  { kg } / { m } ^ { 3 } )$

Options:
A. 1.12 \mu m
B. $$0.62 \mu m$$
C. $$4.2 m $$
D. 1.02 \mu m
E. $$0.96 \mu m$$
F. $$0.74 \mu m$$
G. 0.88 \mu m
H. 1.2 \mu m
I. 0.86 \mu m
J. $$1.6 \mu m$$
Answer: E
Sodium has a bcc structure with nerast neighbour distance $365.9pm$ Calculate its density. (Atomic mass of $Na = 23$)

Options:
A. 2.54 \times 10^{31}g/cc
B. $$3.64\times 10^{32}g/cc$$
C. 2.64 \times 10^{31}g/cc
D. $$1.51\times 10^{31}g/cc$$
E. $$3.44\times 10^{33}g/cc$$
F. 1.34 \times 10^{31}g/cc
G. 2.44 \times 10^{32}g/cc
H. $$2.44\times 10^{31}g/cc$$
I. 1.44 \times 10^{32}g/cc
J. 1.44 \times 10^{31}g/cc
Answer: H
An air bubble starts rising from the bottom of a lake. Its diameter is $3.6 mm$ at the bottom and $4 mm$ at the surface. The depth of the lake is $250 cm$ and the temperature at surface is ${ 40 }^{ o } C$.
What is the temperature at the bottom of the lake? Given atmospheric pressure $=76 cm$ of $Hg$ and $g=980 { cm }/{ { s }^{ 2 } }$.

Options:
A. ${ 10.35 }^{ o }C$
B. $${ 10.37 }^{ o }C$$
C. ${ 10.52 }^{ o }C$
D. ${ 10.39 }^{ o }C$
E. $${ 11 }^{ o }C$$
F. ${ 10.42 }^{ o }C$
G. $${ 12.36 }^{ o }C$$
H. ${ 10.55 }^{ o }C$
I. $${ 13 }^{ o }C$$
J. ${ 10.41 }^{ o }C$
Answer: B
$1$ mol of $Fe^{\displaystyle2+}$ is oxidized to $Fe^{\displaystyle3+}$ using $K_2Cr_2O_7$ and $KMnO_4$ solutions separately. Which of the following are correct for the titration of $Fe^{\displaystyle2+}$ to $Fe^{\displaystyle3+}$?

Options:
A. Moles of $K_2Cr_2O_7>$ Moles of $KMnO_4$
B. Equivalents of $K_2Cr_2O_7 < Equivalents of $KMnO_4$
C. Equivalents of $K_2Cr_2O_7=$ Equivalents of $KMnO_4$
D. Equivalents of $K_2Cr_2O_7 \neq$ Equivalents of $KMnO_4$
E. Moles of $K_2Cr_2O_7 < Moles of $KMnO_4$
F. Equivalents of $K_2Cr_2O_7 >$ Equivalents of $KMnO_4$
G. $V_{\displaystyle K_2Cr_2O_7}:V_{\displaystyle KMnO_4}:\::6:5$, if both have molarity $1\:M$
Answer: C
Two blocks $m_1$ and $m_2$ are placed in contact with each other on a rough horizontal surface with a coefficient of friction $\mu$. A horizontal force 'F' is applied on the block $m_1$ as shown in figure.With the force 'F' acting in its original direction on the block $m_1$, identify the correct statement related to the normal reaction 'N' between the two blocks.

Options:
A. If $F \leq \mu m_1 g$, N = \frac{\mu m_1 g}{2}
B. If $F \leq \mu m_1 g$, N = 0
C. If $F \leq \mu m_1 g$, N = \frac{\mu m_1 g}{3}
D. If $F \leq \mu m_1 g$, N = \mu m_1 g
E. If $F > \mu (m_1 + m_2) g, \ N = \frac{m_2F}{m_1 + m_2}$
F. All of the above
G. If $F \leq \mu m_1 g$, N = \frac{\mu m_1 g}{4}
H. If $\mu m_1 g \leq F \leq \mu (m_1 + m_2) g, \ N = F - \mu m_1 g$
I. If $F \leq \mu m_1 g$, N = \mu m_2 g
J. If $F \leq \mu m_1 g$, N = \frac{\mu m_1 g}{5}
Answer: B
A strong current of trivalent gaseous boron passed through a germanium crystal decreases the density of the crystal due to part replacement of germanium by boron and due to interstitial vacancies created by missing Ge atoms. In one such experiment, one gram of germanium is taken and the boron atoms are found to be $150$ ppm by weight when the density of the Ge crystal decreases by $4\%$. Calculate the percentage of missing vacancies due to germanium which are filled up by boron atoms. Atomic weight of Ge $= 72.6$ amu and $B = 11$ amu.

Options:
A. None of the above
B. 2.8\, \%
C. 3.0\, \%
D. $$6.6\, \%$$
E. 4.2\, \%
F. 3.6\, \%
G. $$1.2\, \%$$
H. 4.8\, \%
I. $$2.4\, \%$$
J. 3.2\, \%
Answer: I
Which of the following statements/relationship is not correct in thermodynamics changes:-

Options:
A. W= -nRTln \frac{v_{2}}{2v_{1}}
B. $\Delta S_{total > 0}$ ( for spontaneous process)
C. W= -nRTln \frac{v_{2}}{3v_{1}}
D. $W= -nRTln \frac{v_{2}}{v_{1}}$ (isothermal reversible expansion of aan ideal gas )
E. W= -nRTln \frac{v_{1}}{v_{2}}
F. W= -nRTln \frac{2v_{1}}{v_{2}}
G. W= -nRTln \frac{3v_{2}}{2v_{1}}
H. W= -nRTln \frac{2v_{2}}{v_{1}}
I. $q= -nRTln \frac{v_{2}}{v_{1}}$ (isothermal reversible expansion of an ideal gas )
J. $\Delta U=0 $ (isothermal reversible expansion of an ideal gas)
Answer: D
A ray of light passing through the point A$(1, 2, 3)$, strikes the plane $x + y + z = 12$ at B on reflection passes through point C$(3, 5, 9)$. The coordinates of point B are

Options:
A. $$(2, 5, 5)$$
B. (-7, 0, 18)
C. (-7, 0, 23)
D. (-7, 0, 21)
E. $$(0, -5, 17)$$
F. (-7, 0, 22)
G. $$(-4, 6, 10)$$
H. (-7, 0, 17)
I. (-7, 0, 20)
J. $$(-7, 0, 19)$$
Answer: J
At a certain temperature for which $RT =2.0\ lit\ atm\ mol^{-1}$, the density of a gas, in $gm\ lit^{-1}$, is $d=2.00 p+0.020p^{2}$,where $p$ is the pressure in atmosphere. What is the molecular weight of the gas in $gm\ mol^{-1}?$

Options:
A. 65
B. $$100$$
C. $$45$$
D. $$50$$
E. $$25$$
F. 70
G. $$60$$
H. $$75$$
Answer: D
After a time $t$ from the instant the sphere was placed on the belt, it starts pure rolling and moves with a velocity $v$ relative to the ground. Which of the following are correct expressions for $t$ and $v$?

Options:
A. v =\dfrac {2v_0}{13}
B. $$v =\dfrac {2v_0}{5}$$
C. v =\dfrac {3v_0}{8}
D. $$v =\dfrac {2v_0}{7}$$
E. v =\dfrac {2v_0}{11}
F. v =\dfrac {3v_0}{5}
G. $$t =\dfrac {2v_0}{5\mu_k g}$$
H. v =\dfrac {3v_0}{7}
I. v =\dfrac {2v_0}{9}
Answer: D
A solid element (monoatomic) exists in cubic crystal. If its atomic radius is $1.0\mathring { A } $ and the ratio of packing fraction and density is $0.1{cm}^{3}/g$, then the atomic mass of the element is $\left( { N }_{ A }=6\times { 10 }^{ 23 } \right) $

Options:
A. $$4\pi $$
B. 20\pi
C. 10\pi
D. 24\pi
E. $$80\pi $$
F. 6\pi
G. $$8\pi $$
H. $$16\pi $$
I. 12\pi
J. 32\pi
Answer: G
Parallel rays are incident on a solid sphere of the glass of diameter $12cm$. Where will the rays be centralized after refraction finally? Refractive index of glass $=1.5$.

Options:
A. At a distance of $3cm$ behind the sphere
B. At a distance of $5cm$ behind the sphere
C. At a distance of $4.5cm$ behind the sphere
D. At a distance of $3cm$ in front of the sphere
E. At a distance of 5.5cm behind the sphere
F. At a distance of $3.5cm$ behind the sphere
G. At a distance of $4cm$ in front of the sphere
H. At a distance of $6cm$ behind the sphere
I. At a distance of $6cm$ in front of the sphere
J. At a distance of $4cm$ behind the sphere
Answer: A
When a particle of mass m moves on the x-axis in a potential of the form $V(x)={ kx }^{ 2 },$ it performs simple harmonic motion. The corresponding time period is proportional to $\sqrt { \dfrac { m }{ k }  } $ as can be seen easily using diamensional analysis , However , the motion of a particle can be periodic even when its potential energy increase on the both sides of x=0 in a way different form ${ kx }^{ 2 }$ and its total energy is such that the particle does not escape to infinity . Consider a particle of mass m moving on the x-axis . its potential energy is $V(x)={ ax }^{ 4 }(a>0)$ for |x| near the origin and becomes a constant equal to ${ V }_{ 0 }for|x|{ x }_{ 0 }$ (see figure)
(1) For periodic motion of small amplitude A , the time period T of this particle is Proportional to :

Options:
A. A\sqrt { \dfrac { m }{ 2a } }
B. \dfrac { A }{ \sqrt { \dfrac { a }{ m } } }
C. A\sqrt { \dfrac { m }{ 3a } }
D. $$A\sqrt { \dfrac { m }{ lpha } } $$
E. $$A\sqrt { \dfrac { a }{ m } } $$
F. A\sqrt { \dfrac { m }{ 4a } }
G. None of these
H. $$\dfrac { 1 }{ A } \sqrt { \dfrac { a }{ m } } $$
I. A\sqrt { \dfrac { 2m }{ a } }
J. A\sqrt { \dfrac { m }{ 5a } }
Answer: D
The locus of the mid point of the line segment joining the focus to a moving point on the parabola $y^{2}=4ax$ is another parabola with directrix

Options:
A. x=a
B. x=-a
C. x=$\frac {a}{2}$
D. x=\frac{a}{3}
E. x=-\frac{3a}{2}
F. x=\frac{3a}{2}
G. x=0
H. x=\frac{2a}{3}
I. x=-\frac{a}{2}
Answer: B
Air is filled in a tube of the wheel of a car at $27^{\circ } C$ and 2 atm pressure if the tube is suddenly bursts, the final temperature of air will be-
$$(\gamma =1.5, 2^{1/3}=1.251)$$

Options:
A. 260^{\circ } C
B. $$240^{\circ } C$$
C. 180^{\circ } C
D. $$-33^{\circ } C$$
E. 250^{\circ } C
F. 230^{\circ } C
G. 270^{\circ } C
H. $$0^{\circ } C$$
I. $$21.6^{\circ } C$$
J. 27^{\circ } C
Answer: B
The relative density of the liquid at the bottom of the U-tube is $11$. Water is filled over it as shown. The difference in the liquid level in the U-tube is:$P_1-P_2=10^5 Pa$

Options:
A. $$\Delta h = 40 cm$$
B. \Delta h = 50 cm
C. \Delta h = 15 cm
D. $$\Delta h = 20 cm$$
E. $$\Delta h = 30 cm$$
F. \Delta h = 3 cm
G. $$\Delta h = 1 cm$$
H. \Delta h = 10 cm
I. \Delta h = 2 cm
J. \Delta h = 5 cm
Answer: G
The heat evolved on combustion of 1 g starch $(C_6H_{10}O_5)_n$ into $CO_2$ and $H2O(l)$ is $17.49 \: kJ \: g^{-1}$. Then the enthalpy of formation of 1 g starch is:$[Given \: \Delta _fH \: of \: H_2O(l)=-285.85\: kJ \: mol^{-1} . \Delta _fH \: of \: CO_2=- 293.7 \: kJ \: mol^{-1}]$

Options:
A. $$ -4.21 \: kJ$$
B. $$ -1.22\: kJ$$
C. -3.23 \: kJ
D. -2.31 \: kJ
E. $$ -2.21 \: kJ$$
F. -2.72 \: kJ
G. -3.22 \: kJ
H. -3.21 \: kJ
I. $$ -3.71 \: kJ$$
J. -2.71 \: kJ
Answer: E
A current source sends a current $I - i_0\cos(\omega t)$. when connected across an unknown load, it gives a voltage output of $v = v_0\sin[\omega t + (\pi/4)]$ across that load. then the voltage across the current source may be brought in phase with the current through it by

Options:
A. Connecting a resistor in parallel with the load
B. Connecting a capacitor in series with the load
C. Connecting an inductor in parallel with the load
D. Connecting an inductor in series with the load
E. Connecting a resistor in series with the load
F. Connecting an inductor in parallel with the resistor
G. Connecting a capacitor in series with the inductor
H. Connecting a capacitor in parallel with the load
I. Connecting a resistor in parallel with the inductor
J. Connecting a resistor in series with the inductor
Answer: D
If the potential energy of two molecules is give by, $U=\dfrac{A}{r^{12}}-\dfrac{B}{r^6}$ then at equilibrium position, its potential energy is equal to?

Options:
A. \dfrac{A^2}{8B}
B. $$-\dfrac{B^2}{4A}$$
C. \(\dfrac{A^2}{14B}\)
D. $$\dfrac{A^2}{4B}$$
E. \(\dfrac{A^2}{12B}\)
F. \(\dfrac{A^2}{2B}\)
G. \dfrac{A^2}{6B}
H. $$3A$$
I. $$(\dfrac{2A}{B})^\frac{1}{6}$$
J. \(\dfrac{A^2}{10B}\)
Answer: I
A particle is moving along a line so that$s = 3 t ^ { 3 } + 8 t + 1 .$ The instant at which velocity and acceleration are equal are given by

Options:
A. $$t = 0,2 / 3$$
B. $$t = 2 / 3,4 / 3$$
C. t = 1 / 3,1 / 3
D. $$t = 0,5 / 3$$
E. t = 1 / 3,5 / 3
F. $$t = 1 / 3,4 / 3$$
G. t = 1 / 3, 2 / 3
H. t = 2 / 3, 1 / 3
Answer: A
The sound from a very high burst of fireworks takes $ 5\,s $ to arrive at the observer. The burst occurs $ 1662\,m $ above the observer and travels vertically through two stratifier layers of air, the top one of thickness $ d_1 $ at $ 0^{\circ}\,C $  and the bottom one of thickness $ d_2 $ at $ 20^{\circ} \,C $ . Then (assume velocity of sound at $ 0^{\circ}\,C $ is $ 330\,m/s $)

Options:
A. d_2 = 335\,m
B. d_2 = 345\,m
C. $$ d_1 = 342\,m $$
D. d_2 = 340\,m
E. d_2 = 330\,m
F. $$ d_2 = 1320\,m $$
G. d_2 = 333\,m
H. $$ d_2 = 342\,m $$
I. $$ d_1 = 1485 \,m $$
J. d_2 = 337\,m
Answer: H
The emf of a thermocouple, cold junction of which is kept at $- 300 ^ { \circ } \mathrm { C }$ is given by $E = 40 t + \frac { 1 } { 10 } t ^ { 2 }$ . The temperature of inversion of thermocouple will be

Options:
A. 10 ^ { \circ } \mathrm { C }
B. 40 ^ { \circ } \mathrm { C }
C. $$- 200 ^ { \circ } \mathrm { C }$$
D. $$20 ^ { \circ } \mathrm { C }$$
E. 300 ^ { \circ } \mathrm { C }
F. 120 ^ { \circ } \mathrm { C }
G. $$400 ^ { \circ } \mathrm { C }$$
H. 100 ^ { \circ } \mathrm { C }
I. 60 ^ { \circ } \mathrm { C }
J. $$- 100 ^ { \circ } \mathrm { C }$$
Answer: D
A right angled tube is fixed horizontally on a horizontal surface and an ideal liquid of density $\rho $ is flowing into the tube at the rate of $q=4\ m^{3}/s$. Cross sectional are of the tube at in take and outlet positions are $A=2\ m^{2}$ and $S=1\ m^{2}$ respectively. The magnitude of net force exerted by liquid on the tube (Given that the value of atmospheric pressure $P_{0}=4\rho\ N/m^{2}$)

Options:
A. $$4\sqrt{41\rho}$$
B. 4\sqrt{42\rho}
C. 4\sqrt{40\rho}
D. $$5\sqrt{41\rho}$$
E. $$5\sqrt{21\rho}$$
F. $$3\sqrt{12\rho}$$
G. None of these
H. 3\sqrt{41\rho}
I. 4\sqrt{21\rho}
Answer: A
Piston cylinder device initially contains $0.5\:m^3$ of nitrogen gas at $400\:kPa$ and $27^\circ C$. An electric heater within the device is turned on and is allowed to pass a current of $2\:A$ for $5\:min$ from a $120\:V$ source. Nitrogen expands at constant pressure and a heat loss of $2800\:J$ occurs during the process. $\displaystyle R=\frac{25}{3}\:kJ/kmol K$ . The final temperature of nitrogen is

Options:
A. 52.6^\circ C
B. 51.6^\circ C
C. $$29.6^\circ C$$
D. 54.6^\circ C
E. $$2.6^\circ C$$
F. 26.6^\circ C
G. 53.6^\circ C
H. $$56.6^\circ C$$
I. 55.6^\circ C
J. $$5.67^\circ C$$
Answer: H
A plane wave of wavelength $\lambda$ is incident at an angle $\theta$ on a plane mirror. Maximum intensity will be observed at $P$, when

Options:
A. \sec \theta - \cos \theta = 2\lambda / 4d
B. $$\cos \theta = \lambda / 4d$$
C. \sec \theta - \cos \theta = \lambda / 2d
D. \cos \theta = \lambda / 5d
E. \cos \theta = \lambda / 3d
F. \cos \theta = 3\lambda / 4d
G. $$\cos \theta = 3\lambda / 2d$$
H. \cos \theta = \lambda / 2d
I. $$\sec \theta - \cos \theta = 3\lambda / 4d$$
J. $$\sec \theta - \cos \theta = \lambda / 4d$$
Answer: B
XY crystallises in bcc lattice .The unit cell edge  length is 400 pm . Molar mass of XY is 200. The density of crystal in gm/cc is $\left( N_{ A }=6\times 10^{ 23 } \right) $

Options:
A. 2.6 \times 10^{6} \text{ gm/cc}
B. 2.6 \times 10^{-3} \text{ gm/cc}
C. $10.4\times 10^{6 }$ gm/cc
D. 10.4 \times 10^{-3} \text{ gm/cc}
E. 5.2 gm/cc
F. 5.2 \times 10^{-3} \text{ gm/cc}
G. 10.4 gm/cc
H. $5.2\times 10^{ 6 }$ gm/cc
I. 2.6 \times 10^{-6} \text{ gm/cc}
J. 10.4 \times 10^{-6} \text{ gm/cc}
Answer: E
Consider a parallel plate of thickness $d$ as shown in figure, whose refractive index varies as $\mu=\dfrac{\mu_0}{1 -\dfrac{x}{R}}$ ; where $\mu_0=1.2$ and $R=13 cm$ A light beam enters at $l=90^o$ from $(x_A=0)$ and emerges fro the point $B$ at an angle $lpha=30^o$ The thickness of the slab is

Options:
A. $$5.53\ cm$$
B. $$4.24\ cm$$
C. 7.75\ cm
D. 7.24\ cm
E. $$6.75\ cm$$
F. 9.75\ cm
G. $$8.75\ cm$$
H. 7.53\ cm
I. 8.25\ cm
J. 7.55\ cm
Answer: G
The number of atoms in $100 \mathrm { g }$ of an FCC crystal with density $d = 10 \mathrm { g } \mathrm { cm } ^ { - 3 }$ and cell edge as $200 \mathrm { pm }$ is equal to

Options:
A. 4 \times 10 ^ { 23}
B. 5 \times 10 ^ { 25}
C. 4 \times 10 ^ { 24}
D. $$1 \times 10 ^ { 25 }$$
E. $$2 \times 10 ^ { 25 }$$
F. $$3 \times 10 ^ { 25 }$$
G. $$0.5 \times 10 ^ { 25 }$$
H. $$2 \times 10 ^ { 24 }$$
I. 4 \times 10 ^ { 25 }
Answer: F
A uniform cylinder of steel of mass $M$, radius $R$ is palced  on frictionless bearing and set to rotate about its vertical axis with angular velocity $\omega_0$.After the cylinder has reached the specified state of rotation it is heated, without any mechanical contact, from temperature $T_0$ to $T_0+ \Delta T$. If $\dfrac{\Delta I}{I}$ is the fractional change in moment of inertia of the cylinder and $\dfrac{\Delta \omega}{\omega _0}$ be the frictional charge in the angular velocity of the cylinder and $a$ be the coefficient of linear expansion, then

Options:
A. \dfrac{\Delta I}{I}=\dfrac{\Delta R}{2R}
B. $$\dfrac {\Delta I}{I}= - \dfrac{2 \Delta R}{R}$$
C. $$\dfrac{\Delta I}{I}=\dfrac{2 \Delta R}{R}$$
D. $$\dfrac{\Delta \omega }{\omega_0}= -2 lpha \Delta T$$
E. \dfrac{\Delta I}{I}=\dfrac{4 \Delta R}{R}
F. \dfrac{\Delta I}{I}=\dfrac{\Delta R}{R}
G. \dfrac{\Delta I}{I}=\dfrac{\Delta R}{3R}
H. \dfrac{\Delta I}{I}=\dfrac{3 \Delta R}{R}
I. $$\dfrac{\Delta I}{I}=\dfrac {\Delta \omega }{\omega _0}$$
Answer: C
A small body of mass $m$ is located on a horizontal plane at the point $O$. The body acquires a horizontal velocity $v_0$. Find the mean power developed by the friction force during the whole time of motion, if the friction coefficient $k=0.27$, $m=1.0\:kg$, and $v_0=1.5\:m/s$.

Options:
A. $$4\:W$$
B. 1.5\:W
C. $$-3\:W$$
D. $$1\:W$$
E. 3\:W
F. 3.5\:W
G. 2.2\:W
H. $$2\:W$$
I. $$-4\:W$$
J. 2.5\:W
Answer: H
A manufacturer plans to construct a cylindrical can to hold one cubic metre of liquid. If the cost of constructing the top and bottom is twice the cost of constructing the sides, what are the dimensions of the most economical can?

Options:
A. $$\displaystyle r=\dfrac{1}{\left ( \pi \right )^{1/3}},h=\left ( \dfrac{1}{\pi } \right )^{1/3}$$
B. \displaystyle r=\dfrac{1}{\left ( 4\pi \right )^{1/3}},h=\left ( \dfrac{8}{\pi } \right )^{1/3}
C. \displaystyle r=\dfrac{1}{\left ( 4\pi \right )^{1/3}},h=\left ( \dfrac{64}{\pi } \right )^{1/3}
D. \displaystyle r=\dfrac{1}{\left ( 4\pi \right )^{1/3}},h=\left ( \dfrac{2}{\pi } \right )^{1/3}
E. \displaystyle r=\dfrac{1}{\left ( 8\pi \right )^{1/3}},h=\left ( \dfrac{32}{\pi } \right )^{1/3}
F. $$\displaystyle r=\dfrac{1}{\left ( 4\pi \right )^{1/3}},h=\left ( \dfrac{16}{\pi } \right )^{1/3}$$
G. r=\dfrac{1}{\left ( 2\pi \right )^{1/3}},h=\left ( \dfrac{8}{\pi } \right )^{1/3}
H. $$\displaystyle r=\dfrac{1}{\left ( 4\pi \right )^{1/3}},h=\left ( \dfrac{4}{\pi } \right )^{1/3}$$
I. $$\displaystyle r=\dfrac{1}{\left ( 2\pi \right )^{1/3}},h=\left ( \dfrac{4}{\pi } \right )^{1/3}$$
J. r=\dfrac{1}{\left ( 2\pi \right )^{1/3}},h=\left ( \dfrac{1}{\pi } \right )^{1/3}
Answer: F
A $20$g bullet pierces through a plate of mass $M_1=1$kg and then comes to rest inside a second plate of mass $M_2=2.98$kg as shown in Fig. It is found that the two plates, initially at rest, now move with equal velocities. Find the percentage loss in the initial velocity of the bullet when it is between $M_1$ and $M_2$. Neglect any loss of material of the plates due to the action of bullet.

Options:
A. 35\%
B. 50\%
C. 70\%
D. $$100\%$$
E. $$25\%$$
F. 45\%
G. 30\%
H. 40\%
I. $$75\%$$
Answer: E
The water equivalent of a copper calorimeter is $4.5$ g. If specific heat of copper is $0.09 cal / g / ^0C$, then ($L_f = 80 cal / gm$)

Options:
A. 40 cal
B. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $38 $ cal.
C. Mass of the calorimeter is $0.5$ kg
D. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $32 $ cal.
E. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $48 $ cal.
F. Thermal capacity of the calorimeter is $4.5 cal ^0 / C$
G. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $36 $ cal.
H. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $40$ cal.
I. The heat required to raise the temperature of the calorimeter by $8^0 C$ will be $44 $ cal.
J. Heat required to melt $15$ gm of ice at $0^o C$ Placed in the calorimeter will be $1200$ cal
Answer: G
Two fine steel wires, fastened between the projections of a heavy brass bar, are just taut when the whole system is at $0^{\circ}C$. What is the tensile stress in the steel wires when the temperature of the system is raised by $200^{\circ}C$?($lpha_{brass}=2\times 10^{-5}\ C^{-1},lpha_{steel}=1.2\times 10^{-5}\ C^{-1},Y_{steel}=200\ GNm^{-2}$)

Options:
A. 32 \times 10^{6} Nm^{-2}
B. $$32\times 10^{-8}\ Nm^{-2}$$
C. 3.2 \times 10^{5}\ Nm^{-2}
D. $$3.2\ Nm^{-2}$$
E. 0.32 \times 10^{8} Nm^{-2}
F. $$0.48\ Nm^{-2}$$
G. 0.32 \times 10^{8}\ Nm^{-2}
H. 3.2 \times 10^{7} Nm^{-2
I. $$3.2\times 10^{8}\ Nm^{-2}$$
J. 3.2 \times 10^{6} Nm^{-2
Answer: D
The loop $ABCD$ is moving with velocity $v$ towards right. The magnetic field is $4\ T$. The loop is connected to a resistance of $8\ ohm$. If steady current of $2\ A$ flow in the loop then value of $v$ if has a resistance of $4\ ohm$, is: (Given $AB=30\ cm, AD=30\ cm$)

Options:
A. $$20\ m/s$$
B. \dfrac{150}{3}\ m/s
C. \dfrac{125}{4}\ m/s
D. $$\dfrac{100}{3}\ m/s$$
E. $$\dfrac{50}{3}m/s$$
F. \dfrac{75}{3}\ m/s
G. $$10\ m/s$$
H. \dfrac{110}{3}\ m/s
I. \dfrac{125}{3}\ m/s
J. \dfrac{120}{3}\ m/s
Answer: D
A neon gas tube is connected in parallel to a 1 $\mathrm{m}\mathrm{F}$ capacitor, which is charged by a source of emf 15 V through a 1 $\mathrm{k}\Omega$ resistor as shown. The switch is closed at $\mathrm{t}=0  \mathrm{s}$. When the potential difference across the tube reaches the firing value $\displaystyle V_{\mathrm{F}}=10  V$, neon gas starts conducting with almost zero resistance and emits a flash of light. The capacitor then discharges rapidly and when the potential drops to extinction V$ _{\mathrm{E}}=5ee$, the gas becomes an insulator, and the capacitor again starts charging. The period of flashing $\tau$ is about

Options:
A. $$500 ms$$
B. 800 ms
C. 650 ms
D. 850 ms
E. 400 ms
F. $$100 ms$$
G. $$700 ms$$
H. 900 ms
I. $$300 ms$$
J. 600 ms
Answer: G
If temperature of Sun $=6000$K, radius of Sun is $7.2\times 10^5$ Km, radius of Earth $=6000$km & distance between earth and Sun $=15\times 10^7$ Km. Find intensity of light on Earth.

Options:
A. $$18.3\times 10^{16}$$
B. $$19.2\times 10^{16}$$
C. $$12.2\times 10^{16}$$
D. 18.2 \times 10^{16}
E. 16.2 \times 10^{16}
F. $$9.2\times 10^{16}$$
G. 19.2 \times 10^{15}
H. 18.5 \times 10^{16}
I. 17.2 \times 10^{16}
J. 20.2 \times 10^{16}
Answer: B
A long tube of length $l=25\ cm$ and diameter equal to $2\ cm$ is taken and at its mouth air is blown as shown in figure. The sound emitted by tube will have all the frequencies of the group: ( velocity of sound $=330\ m/s$)

Options:
A. $$660, 1000, 3300\ Hz$$
B. 660, 1320, 1950\ Hz
C. $$302, 684, 1320\ Hz$$
D. 660, 1320, 1960\ Hz
E. 660, 1320, 2040\ Hz
F. 660, 1320, 1970\ Hz
G. $$330, 990, 1690\ Hz$$
H. $$660, 1320, 1980\ Hz$$
I. 660, 1320, 1990\ Hz
J. 660, 1320, 2000\ Hz
Answer: H
A (75 - j40 ) $\Omega $ load is the connected to a coaxial line of $z _ { 0 } = 75 \Omega$ The load matching on the line can be accomplished by connecting

Options:
A. An open-circuit stub at the load
B. An open-circuit stub at a specific distance from the load
C. A capacitance at a specific distance from the load
D. A short circuited stub at a specific distance from the load
E. An inductance at a specific distance from the load
F. A short-circuit stub at the load
G. A short-circuit stub at a specific distance from the load
H. An inductance at the load
I. A capacitance at the load
Answer: F
When transition of electron in ${ He }^{ + }$ takes place from ${ n }_{ 2 }$ to ${ n }_{ 1 }$ then wave number in terms of Rydberg constant R will be : (Given : ${ n }_{ 1 }+{ n }_{ 2 }=4$, ${ n }_{ 1 }-{ n }_{ 2 }=2$)

Options:
A. $$\cfrac { 24R }{ 9 } $$
B. \cfrac{ 24R }{ 16 }
C. $$\cfrac { 3R }{ 4 } $$
D. $$\cfrac { 32R }{ 9 } $$
E. \cfrac{ 27R }{ 16 }
F. \cfrac { 3R }{ 16 }
G. \cfrac{ 3R }{ 32 }
H. \cfrac{ 3R }{ 8 }
I. \cfrac { 9R }{ 16 }
J. $$\cfrac { 8R }{ 9 } $$
Answer: C
A solenoid with $600$ turns per metre and a radius of $2$ $cm$, carries a time varying current $i(t) = (6 + 4t^{2}$)

Options:
A. 70
B. 52
C. 58
D. $$68$$
E. $$40$$
F. $$48$$
G. $$38$$
H. $$50$$
I. $$60$$
Answer: I
Consider a circular turn on a highway, where the angle of banking is more than the angle of response. A car on this turn can move with a constant speed $ v_o $ without the help of friction. Taking advantage of friction, it can achieve a maximum speed but cannot reduce its speed lower than a minimum speed $ v_{min} $.Which of the following conclusions can you draw from the given information?

Options:
A. It depends on coefficient of static friction.
B. $$ v_o < 0.5 (v_{max} + v_{min} ) $$
C. v_o > 0.5 (v_{max} + v_{min} )
D. $$ v_o = 0.75 (v_{max} + v_{min} ) $$
E. v_o = 0.45 (v_{max} + v_{min} )
F. $$ v_o = 0.6 (v_{max} + v_{min} ) $$
G. $$ v_o = 0.55 (v_{max} + v_{min} ) $$
H. v_o > 0.75 (v_{max} + v_{min} )
I. $$ v_0 = 0.5 (v_{max} + v_{min} ) $$
Answer: B
A steel ring of $3.000$ inch inside diameter at $20^oC$ is to heated and slipped over a brass shaft measuring $3.002$ inch in diameter at $20^oC.$ The ring should be heated to a temperature of $(a_{steel}=1.1\times10^{-5}PC)$

Options:
A. 71.6^oC
B. 68.6^oC
C. $$80.6^oC$$
D. 73.6^oC
E. $$75.6^oC$$
F. $$78.6^oC$$
G. 77.6^oC
H. 72.6^oC
I. 69.6^oC
J. $$70.6^oC$$
Answer: J
A charge particle of charge $q$ and mass $m$ is clamped rigidly at the circumference of a ring with mass $m$ and radius $R$. Initially ring is in vertical plane resting on a sufficiently rough horizontal surface with charge $q$ at the same horizontal level as that of the center of the ring. There exist uniform horizontal electric fields as shown. At  $ t = 0$ the system is let free. Given that $(qE = mg)$. Using the above information answer the following. (Assume there is no sliding at point of contact at any moment of time during motion).Work done by the electric field when the ring has rotated through $90^{\circ}$ (use $ \pi = \frac{22}{7}$)

Options:
A. $$ \dfrac{4}{7} mgR$$
B. $$ -mgR$$
C. \dfrac{8}{7} mgR
D. \dfrac{3}{7} mgR
E. $$ mg \sqrt{2}R$$
F. $$ \dfrac{2}{7} mgR$$
G. \dfrac{5}{7} mgR
H. \dfrac{6}{7} mgR
I. \dfrac{1}{7} mgR
J. \dfrac{9}{7} mgR
Answer: A
A particle of mass m is held is circular orbits around origin by an attraction force $ F(r)= -D \times r$. Where  is a positive constant. Assuming particle obeys Bohr's quantization principle and taking potential energy to be zero at $r = 0$, what is the value of energy of the particle in n^th orbit?

Options:
A. $$\dfrac { nh }{ \pi } \dfrac { \sqrt { D } }{ m } $$
B. \left(\dfrac{n^2h^2D}{3\pi^2}\right)^{\dfrac{1}{4}}
C. \left(\dfrac{n^2h^2D}{4\pi^2}\right)^{\dfrac{1}{4}}
D. $$({\dfrac{n^2h^2D}{\pi^2}})^{\dfrac{1}{4}}$$
E. $$({\dfrac{n^2h^2D}{\pi^2}})^{\dfrac{1}{5}}$$
F. $$\left(\dfrac{n^2h^2D}{2\pi^2}\right)^{\dfrac{1}{4}}$$
G. $$({\dfrac{n^2h^2D}{\pi^2}})^{\dfrac{1}{3}}$$
H. $$\dfrac { nh }{ 2 \pi } \frac { \sqrt { D } }{ m } $$
I. \left(\dfrac{n^2h^2D}{6\pi^2}\right)^{\dfrac{1}{4}}
J. none of these
Answer: D
The cured wall of a dam is described by the equation $x^2= 2y$
The coordinates of point $A$ are $(4m,8m)$ The width of the dam is $2m$ and the fluid is water of density $1\times 10^3 \, kg/m^3$. Atmospheric pressure is $1.0 \times 10^5$ pa.
The horizontal component of the force applied by  the liquid on the surface $AB$ is $(g = 10\,ms^{-2})$

Options:
A. 5.3 \times 10^5 \, N
B. 6.3 \times 10^5 \, N
C. $$4.3 \times 10^5 \, N$$
D. 5.4 \times 10^5 \, N
E. 5.2 \times 10^5 \, N
F. 3.3 \times 10^5 \, N
G. $$22.4 \times 10^5 \, N$$
H. $$7.2 \times 10^5 \, N$$
I. $$6.4 \times 10^5 \, N$$
Answer: C
The ratio of maximum to minimum number of electrons that have magnetic quantum number m = +1, spin quantum number s = +$\frac{1}{2}$ in Cr atom:

Options:
A. \frac{7}{3}
B. \frac{7}{4}
C. $$\frac{4}{1}$$
D. $$\frac{5}{2}$$
E. $$\frac{3}{2}$$
F. \frac{5}{3}
G. \frac{5}{4}
H. $$\frac{2}{1}$$
I. \frac{4}{3}
J. \frac{3}{1}
Answer: E
For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then find the angle of inclination of the inclined plane.

Options:
A. $$lpha=30^o$$
B. \alpha=45^o
C. \alpha=35^o
D. \alpha=32^o
E. $$\alpha=37^o$$
F. $$lpha=40^o$$
G. \alpha=25^o
H. \alpha=50^o
I. $$lpha=60^o$$
J. $$lpha=20^o$$
Answer: A
An adiabatic cylinder has 8 grams of helium. A light smooth adiabatic piston is connected to a light spring of force constant 300 N/m. The other end of the spring is connected with a block of mass 10 kg kept on a rough horizontal surface of coefficient of friction $\mu =0.3$. Area of cross-section of cylinder is A=25$ cm ^ { 2 }$. Initially, the spring is in a relaxed position and the temperature of the gas is 400 K.The gas is heated slowly for some time by means of an electric heater so as to bring the block M on the verge of motion. (Take ${ P }_{ atm }={ 10 }^{ 5 }\dfrac { N }{ { m }^{ 2 } }$ and $g=10ms^{-2}$. Find the work done by the gas:

Options:
A. 30 J
B. 328 J
C. 278 J
D. 308 J
E. 348 J
F. 288 J
G. 298 J
H. None of these
I. 318 J
J. 338 J
Answer: I
Length of the latus rectum of the parabola $25\left[ { \left( x-2 \right)  }^{ 2 }+{ \left( y-3 \right)  }^{ 2 } \right] ={ \left( 3x-4y+7 \right)  }^{ 2 }$ is

Options:
A. 1/4
B. 1/5
C. 3
D. 4
E. 8
F. 2
G. 1/2
H. 3/4
I. 2/5
J. 5
Answer: D
Two shots are projected from a gun at the top of a hill with the same velocity $u$ at angles of projection $ lpha$ and $ \beta$ respectively. If the shots strike the horizontal ground through the foot of the hill at the same point, find the height h of the hill above the plane is

Options:
A. h=2{ u }^{ 2 }\left( \frac { 1-tan\alpha \ tan \beta }{ g (tan\alpha - 3tan\beta)^2 } \right)
B. $$h={ u }^{ 2 }\left( \frac { 1-tanlpha \ tan \beta  }{ g (tanlpha + tan\beta)^2  } \right) $$
C. $$h=2{ u }^{ 2 }\left( \frac { 1-tanlpha \ tan \beta  }{ g (tanlpha + tan\beta)^2  } \right) $$
D. $$h=2{ u }^{ 2 }\left( \frac { 1-tanlpha \ tan \beta  }{ g (tanlpha - tan\beta)^2  } \right) $$
E. h=2{ u }^{ 2 }\left( \frac { 1+tan\alpha \ tan \beta }{ g (tan\alpha - tan\beta)^2 } \right)
F. h=2{ u }^{ 2 }\left( \frac { 1-tan\alpha \ tan \beta }{ g (tan\alpha + 3tan\beta)^2 } \right)
G. $$h=2{ u }^{ 2 }\left( \frac { 1+tanlpha \ tan \beta  }{ g (tanlpha + tan\beta)^2  } \right) $$
H. h=2{ u }^{ 2 }\left( \frac { 1-tanlpha \ tan \beta  }{ g (tanlpha + tan\beta)  } \right)
I. h=2{ u }^{ 2 }\left( \frac { 1-tanlpha \ tan \beta  }{ g (2tanlpha + tan\beta)^2  } \right)
J. h=2{ u }^{ 2 }\left( \frac { 1-tan\alpha \ tan \beta }{ g (tan\alpha + 2tan\beta)^2 } \right)
Answer: C
An angiosperm 'A' and a gymnosperm 'G' have 100 chromosomes in the cells of their meristem. What would be the correct number of chromosomes in the endosperms of the seeds of A and G?

Options:
A. A = 300; G = 200
B. A = 100; G = 100
C. A = 100; G = 200
D. A = 200; G = 300
E. A = 200; G = 100
F. A = 300; G = 100
G. A = 100; G = 300
H. A = 300; G = 300
I. A = 200; G =200
J. A = 150; G = 250
Answer: I
A sample containing 1.0 mole of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at 300K and at 600K respectively. Choose the correct option(s).

Options:
A. Work done at 300K is twice the work done at 600K.
B. Work done at 600K is 5 times the work done at 300K.
C. Work done at 600K is the same as the work done at 300K.
D. Work done at 600K is 4 times the work done at 300K.
E. Work done at 600K is 3 times the work done at 300K.
F. Work done at 600K is 20 times the work done at 300K.
G. $ \Delta U$ = 0 in both cases.
H. Work done at 600K is half the work done at 300K.
I. Work done at 600K is 10 times the work done at 300K.
Answer: G
A light source, which emits two wavelengths $\lambda_1 = 400$nm and $\lambda_2 = 600$nm, is used in a Young's double slit experiment. If recorded fringe widths for $\lambda_1$ and $\lambda_2$ are $\beta_1$ and $\beta_2$ and the number of fringes for them within a distance y on one side of the central maximum are m$_1$ and m$_2$, respectively, then

Options:
A. From the central maximum, 4$^{th}$ maximum of $\lambda_2$ overlaps with 6$^{th}$ minimum of $\lambda_1$
B. From the central maximum, 3$^{rd}$ maximum of $\lambda_2$ overlaps with 6$^{th}$ minimum of $\lambda_1
C. From the central maximum, 3$^{rd}$ maximum of $\lambda_2$ overlaps with 5$^{th}$ minimum of $\lambda_1$
D. The angular separation of fringes for $\lambda_1$ is greater than $\lambda_2$
E. $$\beta_2 > \beta_1$$
F. $$m_1 > m_2$$
G. From the central maximum, 4$^{th}$ maximum of $\lambda_2$ overlaps with 5$^{th}$ minimum of $\lambda_1
H. From the central maximum, 3$^{rd}$ maximum of $\lambda_2$ overlaps with 4$^{th}$ minimum of $\lambda_1
Answer: C
The length of the latus rectum of the parabola whose focus is (3,0) and directrix is 3x-4y-2=0 is

Options:
A. 1
B. 4
C. 20
D. 6
E. 12
F. 24
G. 8
H. 16
I. none of these
J. 18
Answer: E
A particular atom has the 4th shell as its valence shell. If the difference between the number of electrons between K and N shell and L and M shell is zero, find the electronic configuration of its stable ion.

Options:
A. 2, 8, 18
B. 2, 8, 10
C. 2, 8, 7
D. 2, 8, 8, 2
E. 2, 8, 9
F. 2, 8, 10, 2
G. 2, 8, 18, 8
H. 2, 8, 8, 1
I. 2, 8
J. 2, 8, 8
Answer: J
The correct information regarding a solid element (atomic radius $=r$) having $ABCABC....$ type packing (FCC unit cell edge length $=a$) is:

Options:
A. the distance between successive A and B layers is \( 2r.\sqrt { \cfrac { 3 }{ 2 } } \)
B. the distance between two nearest octahedral void is $\cfrac { a }{ \sqrt { 2 } } $
C. the distance between successive A and B layers is \( 2r.\sqrt { \cfrac { 5 }{ 3 } } \)
D. the distance between tow nearest tetrahedral void is $\cfrac { \sqrt { 3 } }{ 2 } a$
E. the distance between successive A and B layers is \( 2r.\sqrt { \cfrac { 1 }{ 6 } } \)
F. the distance between successive A and B layers is $2r.\sqrt { \cfrac { 2 }{ 3 } } $
G. the distance between successive A and B layers is $2r.\sqrt { \cfrac { 1 }{ 3 } } $
H. the distance between successive A and B layers is \( 2r.\sqrt { \cfrac { 1 }{ 2 } } \)
I. the distance between the nearest octahedral and tetrahedral void is $\cfrac { \sqrt { 3 } }{ 4 } a$
J. the distance between successive A and B layers is \( 2r.\sqrt { \cfrac { 3 }{ 4 } } \)
Answer: F
A frame $CDEF$ is laced in a region where a magnetic field $ec {B}$ is present. A rod of length one metre moves with constant velocity $20\ m/s$ and strength of magnitude field is one tesia. The power spent in the process is (take $R=0.2 \Omega$ and all other wires and rod have zero resistance)

Options:
A. $$3\ kW$$
B. 5\ kW
C. 0.75\ kW
D. $$1\ kW$$
E. 0.5\ kW
F. $$1.5\ kW$$
G. 0.25\ kW
H. 2.5\ kW
I. $$2\ kW$$
J. $$4\ kW$$
Answer: D
In the shown figure, there are two long fixed parallel conducting rails having negligible resistance) and are separated by distance $L$ . A uniform rod(cd) of resistance $R$ and $\operatorname { mass } M$ is placed at rest on frictionless rail. Now at time $t = 0 ,$ a capacitor having charge $Q _ { 0 }$ and capacitance $C$ is connected across rails at ends a and b such that current in rod(cd) is from $c$ towards $d$ and the rod is released. A uniform and constant magnetic ficld having magnitude $B$ exists normal to plane of paper as shown. (Neglect acceleration due to gravity) . When the acceleration of rod is zero, the speed of rod is

Options:
A. \frac { Q _ { 0 } L B } { M + B ^ { 2 } L ^ { 2 } R }
B. \frac { Q _ { 0 } L B } { M + B ^ { 2 } R C }
C. \frac { Q _ { 0 } L B } { M + B ^ { 2 } R ^ { 2 } C ^ { 2 } }
D. \frac { Q _ { 0 } L B } { M + B ^ { 2 } R ^ { 2 } C }
E. $$\frac { Q _ { 0 } L B } { M + B ^ { 2 } L ^ { 2 } C ^ { 2 } }$$
F. $$\frac { Q _ { 0 } L B } { M + B ^ { 2 } R ^ { 4 } C ^ { 4 } }$$
G. \frac { Q _ { 0 } L B } { M + B ^ { 2 } L R }
H. $$\frac { Q _ { 0 } L B } { M + B ^ { 2 } L ^ { 2 } C }$$
I. \frac { Q _ { 0 } L B } { M + B ^ { 2 } R L C }
J. $$\frac { Q _ { 0 } R ^ { 2 } B C } { M + B ^ { 2 } L ^ { 2 } C ^ { 2 } }$$
Answer: H
The volume of the largest cone that can be inscribed in a sphere of radius = $9$ cm is

Options:
A. \dfrac{128}{3}\pi c.c
B. $$288\pi c.c$$
C. \dfrac{144}{3}\pi c.c
D. $$\dfrac{288}{3}\pi c.c$$
E. \dfrac{64}{3}\pi c.c
F. $$\dfrac{32}{3}\pi c.c$$
G. \dfrac{96}{3}\pi c.c
H. \dfrac{16}{3}\pi c.c
I. \dfrac{256}{3}\pi c.c
J. $$72\pi c.c$$
Answer: F
A radio transmitter at position A operates at a wavelength of 20 m. A second, identical transmitter is located at a distance x from the first transmitter, at position B. The transmitters are phase locked together such that the second transmitter is lagging $\pi/2$ out of phase with the first. For which of the following values of BC - CA will the intensity at C be maximum.

Options:
A. BC - CA = 70 m
B. BC - CA = 77.5 m
C. BC - CA = 62.5 m
D. BC - CA = 55 m
E. BC - CA = 67.5 m
F. BC - CA = 72.5 m
G. BC - CA = 60 m
H. BC - CA = 65 m
I. BC - CA = 80 m
J. BC - CA = 75 m
Answer: J
A solid cube of mass 5 kg is placed on a rough horizontal surface, in xy-plane as shown. The friction coefficient between the surface and the cube is 0.4. An external force $ec{F}=3 \hat{i}+4\hat{j}+20 \hat{k}$ N is applied on the cube. (use $g = 10 m/s^2$)

Options:
A. The contact force exerted by the surface on the cube is $\sqrt{945}N$
B. The contact force exerted by the surface on the cube is $\sqrt{875}N$
C. The contact force exerted by the surface on the cube is $\sqrt{915}N$
D. The contact force exerted by the surface on the cube is $\sqrt{845}N$
E. The block starts slipping over the surface
F. The contact force exerted by the surface on the cube is $\sqrt{925}N$
G. The friction force on the cube by the surface is 5 N.
H. The contact force exerted by the surface on the cube is $\sqrt{905}N$
I. The friction force acts in xy-plane at angle 127 with the positive x-axis in clockwise direction.
J. The contact force exerted by the surface on the cube is $\sqrt{935}N$
Answer: F
A hydrogen electrode is immersed in a solution with pH = 0 (HCl). By how much will the potential (reduction) change if an equivalent amount of NaOH is added to the solution? (Take $p_{H_{2}} = 1$ atm, T = 298 K)

Options:
A. Decrease by 0.31 V
B. Decrease by 0.59 V
C. Decrease by 41 mV
D. Increase by 59 mV
E. Increase by 0.59 V
F. Increase by 0.31 V
G. Increase by 0.41 V
H. Decrease by 0.51 V
I. Decrease by 59 mV
J. Decrease by 0.41 V
Answer: J
An insect jumps from ball A onto ball B, which are suspended from inextensible light strings each of length L = 8 cm. The mass of each ball and insect is same. What should be the minimum relative velocity (in $ms^{-1}$) of jump of insect w.r.t. ball A,  if both the balls manage to complete the full circle?

Options:
A. 12
B. 15
C. 13
D. 7
E. 9
F. 14
G. 20
H. 11
I. 10
J. 8
Answer: J
$AB$ has $NaCl$ structure while $XB$ has $CsCl$ structure if ${ r }_{ A }|{ r }_{ B }=\ 5$ and ${ r }_{ X }|{ r }_{ B }= 0.75$ then what is the ratio of edge length of unit cell of $AB$ and $XB$.

Options:
A. 1.44
B. 1.42
C. $$1.43$$
D. $$1.50$$
E. $$1.45$$
F. 1.52
G. $$0.85$$
H. $$1.40$$
Answer: H
In the circuit shown, the resistance $r$ is a variable resistance. If for $r=fR$, the heat generation in $r$ is maximum then the value of $f$ is:

Options:
A. \dfrac{1}{6}
B. \dfrac{2}{3}
C. $$\dfrac{1}{2}$$
D. \dfrac{1}{5}
E. \dfrac{1}{3}
F. $$1$$
G. \dfrac{2}{5}
H. $$\dfrac{1}{4}$$
I. \dfrac{1}{7}
J. $$\dfrac{3}{4}$$
Answer: C
The wavelength of very fast moving electron $ ( v pprox  c) $ is :

Options:
A. \lambda = \cfrac {h}{2m_0v}
B. \lambda = \cfrac {h \sqrt { 1-\cfrac { v^2 }{ c^2 } } }{ 2m_0v }
C. $$ \lambda^3 = \cfrac {h^2}{2mE} $$
D. $$ \lambda = \cfrac {h}{m_0v} $$
E. $$ \lambda =\cfrac {h \sqrt { 1-\cfrac { v^2 }{ c^2 } } }{ m_0v } $$
F. \lambda = \cfrac {h \sqrt { 1+\cfrac { v^2 }{ c^2 } } }{ m_0v }
G. $$ \lambda = \cfrac {h}{2mE} $$
H. \lambda = \cfrac {h}{m_0v^2}
I. \lambda = \cfrac {h \sqrt { 1-\cfrac { v^2 }{ c^2 } } }{ 2m_0v^2 }
J. \lambda = \cfrac {h \sqrt { 1-\cfrac { v^2 }{ c^2 } } }{ m_0v^2 }
Answer: D
The magnetic field associated with a light wave is given, at the origin, by  $B = B_0 [sin (3.14 \times 10^7) ct + sin (6.28 \times 10^7) ct]$. If this light falls on a silver plate having a work function of $4.7 eV$, what will be the maximum kinetic energy of the photo electrons ?
$$(c = 3 \times 10^8 ms^{-1}. \, h = 6.6 \times 10^{-34} J-s)$$

Options:
A. 7.52 eV
B. 6.82 eV
C. 7.22 eV
D. 7.92 eV
E. 12.5 eV
F. 7.72 eV
G. 8.72 eV
H. 8.22 eV
I. 7.82 eV
J. 8.52 eV
Answer: F
For the decomposition of $  \mathrm{N}_{2} \mathrm{O}_{5}  $ at a particular temperature, according to the equations
$$ 2 \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 4 \mathrm{NO}_{2}+\mathrm{O}_{2} $$
$$ \mathrm{N}_{2} \mathrm{O}_{5} \rightarrow 2 \mathrm{NO}_{2}+1 / 2 \mathrm{O}_{2} $$
the activation energies are $  E_{1}  $ and $  E_{2},  $ respectively. Then

Options:
A. $$ E_{1}=E_{2} $$
B. E_{1} = \frac{5}{4} E_{2}
C. E_{1} < \frac{1}{2}E_{2}
D. $$ E_{1}=2 E_{2} $$
E. E_{1} > 2E_{2}
F. $$ E_{1}>E_{2} $$
G. E_{1} < \frac{3}{4}E_{2}
H. $$ E_{1}<E_{2} $$
I. E_{1} = \frac{1}{2}E_{2}
J. E_{1} < 2E_{2}
Answer: F
A container has a hole at a height of $2m$ If the time taken by the efflux to strike the inclined plane perpendicularly is $1$sec. Then the height of liquid level initially is (Take $g=10m/s^2$).

Options:
A. $3$m
B. $8$m
C. $5$m
D. $7$m
E. 4m
F. $2$m
G. $6$m
Answer: C
$5\ g$ of steam at $100^{\circ}C$ is mixed with $10\ g$ of ice at $0^{\circ}C$. Choose correct alternative/s. Given: $s_{water}=1\ cal/g^{\circ}C,L_F=80\ cal/g,L_V=540\ cal/g$

Options:
A. At equilibrium, mixture contains $1\dfrac{1}{6}\ g$ of steam
B. At equilibrium, mixture contains $1\dfrac{2}{3}\ g$ of steam
C. At equilibrium, mixture contains $14\dfrac{1}{3}\ g$ of water
D. At equilibrium, mixture contains $1\dfrac{1}{4}\ g$ of steam
E. At equilibrium, mixture contains $1\dfrac{1}{12}\ g$ of steam
F. Equilibrium temperature of mixture is $160^{\circ}C$
G. At equilibrium, mixture contains $1\dfrac{1}{9}\ g$ of steam
H. At equilibrium, mixture contains $1\dfrac{1}{3}\ g$ of steam
Answer: B
Gold crystallizes in the face-centred cubic lattice. The number of unit cells in $1\ g$ of gold (atomic mass =$197\ u$) will be

Options:
A. 5.24 \times 10^{23}
B. $$15.28\times 10^{20}$$
C. $$6.02\times 10^{23}$$
D. 6.20 \times 10^{23}
E. 4.52 \times 10^{20}
F. 9.02 \times 10^{20}
G. 4.82 \times 10^{20}
H. 3.02 \times 10^{23}
I. $$3.82\times 10^{20}$$
J. $$7.64\times 10^{20}$$
Answer: C
In Fig. key K is closed at $t=0$. After a long time, the potential difference between A and B is zero, the value of R will be $[r_1=r_2=1\Omega, E_1=3V$ and $E_2=7V, C=2\mu F, L=4 mH$, where $r_1$ and $r_2$ are the internal resistance of cells $E_1$ and $E_2$, respectively]:

Options:
A. \dfrac{4}{5}\Omega
B. $$4\Omega$$
C. \dfrac{5}{9}\Omega
D. \dfrac{16}{9}\Omega
E. $$\dfrac {4}{3}\Omega$$
F. $$\dfrac {2}{3}\Omega$$
G. \dfrac {8}{9}\Omega
H. $$\dfrac {4}{9}\Omega$$
I. \dfrac{2}{9}\Omega
Answer: H
The first Lyman transition in the hydrogen spectrum has $\triangle E=10.2\quad eV$. The same energy change is observed in the second Balmer transition of :-

Options:
A. { Be }^{ 2+ }
B. { Li }^{ + }
C. { Li }^{ 3+ }
D. $${ Be }^{ 3+ }$$
E. $${ Li }^{ 2+ }$$
F. { Be }^{ 1+ }
G. $${ He }^{ + }$$
H. { He }^{ 2+ }
I. { Li }^{ 1+ }
Answer: E
A solid cone is placed on a horizontal surface with height 'h' and radius 'R' and apex angle is $\theta$. If gravitational potential energy of the cone does not change as position of the cone is changed from fig. (A) to fig. (B), then,

Options:
A. \theta = \sin^{-1}\left(\frac{3}{4}\right)
B. \theta = \sin^{-1}\left(\frac{1}{5}\right)
C. \theta = sin^{-1}\left(\frac{1}{4}\right)
D. $$\frac{h}{R} = 2\sqrt 2$$
E. \theta = \sin^{-1}\left(\frac{1}{2}\right)
F. $$\theta = \frac{\pi}{4}$$
G. $$\frac{h}{R} = 4$$
H. \theta = \sin^{-1}\left(\frac{1}{3}\right)
I. \theta = \sin^{-1}\left(\frac{4}{5}\right)
J. $$\theta = sin^{-1}(\frac{2}{3})$$
Answer: J
A slab of thickness 10 cm is kept on x-y (z=0) and its refractive index varies as $ \mu=1.63 (1+ \frac  {Z}{20} ) $ where Z is in cm. if it is viwed from top its apparent thickness will be (in cm)

Options:
A. 3
B. 3.5
C. 3.75
D. 4.75
E. 5
F. 6
G. 4.15
H. 4.25
I. 4.5
J. 4
Answer: J
In biological cells, the energy released by the oxidation of foods is stored in adenosinetriphosphate (ATP or $ATP^{4-}$) The essence of ATP's action is its ability to lose it terminal phosphate group by hydrolysis and to form ADP.:
$$ATP^{4-}(aq)+ H_2O(l) \to ADP^{3-}(aq)+ HPO_4^{2-}(aq)+ H_3O^+$$
At pH= 7 and $37^C$, the $\Delta H$ and $\Delta G$ of hydrolysis are $-20$ kJ/mol and $-31$ kJ/mol respectively. Answer the given questions under these conditions.
The formation of glutamin from glutamate and ammonium ions requires $62 kJ/mol^{-1}$ of energy input. It is driven by the hydrolysis of ATP to ADP. How many moles of ATP must be hydrolysis to form $1$ mol glutamine:

Options:
A. 0.75 mol
B. $2$ mol
C. 0.5 mol
D. $4$ mol
E. $1.5$ mol
F. $1$ mol
G. 3 mol
Answer: F
The switch $ S $ in the circuit diagram (Fig.) is closed at $ t=0 . $ The charge on capacitors at any time $ t $ is

Options:
A. q_{(t)}=E C\left(1-e^{-2 t / 5 R C} \right)
B. $$ q_{(t)}=E C\left(1-e^{-t / 2 R C}\right) $$
C. q_{(t)}=E C\left(1-e^{-t / 5 R C} \right)
D. $$ q_{(t)}=E C\left(1-e^{-t / 3 R C}\right) $$
E. q_{(t)}=E C\left(1-e^{-t / 7 R C} \right)
F. q_{(t)}=E C\left(1-e^{-t / 8 R C} \right)
G. q_{(t)}=E C\left(1-e^{-t / 6 R C} görmek록 \right)
H. $$ q_{(t)}=E C\left(1-e^{-2 t / 3 R C}\right) $$
I. q_{(t)}=E C\left(1-e^{-t / 4 R C} \right)
J. $$ q_{(t)}=E C\left(1-e^{-3 t / 2 R C}\right) $$
Answer: D
Cell equation : $A + 2B^{+}\rightarrow A^{2+} + 2B$
$$A^{2+} + 2e \rightarrow A\ E^{\circ} = +0.34\ V$$
and $\log_{10} K = 15.6$ at $300\ K$ for cell reactions
Find $E^{\circ}$ for $B^{+} + e\rightarrow B$
Given $\left [\dfrac {2.303\ RT}{nF} = 0.059\right ]_{at\ 300\ K}$.

Options:
A. $$0.80$$
B. 0.89
C. 1.06
D. 1.04
E. $$1.26$$
F. 0.82
G. $$-0.54$$
H. $$+0.94$$
I. 0.81
J. 0.90
Answer: A
Find the quantam number $n$ corresponding to the excited state of He' ion if on transition to the ground state that ion emits two photons in succession with wavelength 1026.7$\mathrm { A }$ and 304$\mathrm { A }$ . $R = 1.097 \times 10 ^ { 7 } \mathrm { m }$

Options:
A. n=8
B. $$n=5$$
C. n=7
D. $$n=4$$
E. n=11
F. $$n=10$$
G. $$n=6$$
H. n=12
I. $$n=3$$
J. n=9
Answer: G
A metal having atomic mass $60.22g/mole$ crystallizes in $ABCABC.....$ type packing. The density of each metal atom if the edge length of unit cell is $10\mathring { A } $, is:$\left( { N }_{ A }=6.022\times { 10 }^{ 23 } \right) $

Options:
A. $$0.54g/{ cm }^{ 3 }$$
B. $$0.4g/{ cm }^{ 3 }$$
C. 0.054g/{ cm }^{ 3 }
D. $$40g/{ cm }^{ 3 }$$
E. $$5.4g/{ cm }^{ 3 }$$
F. 0.45g/{ cm }^{ 3 }
G. 0.504g/{ cm }^{ 3 }
H. $$54g/{ cm }^{ 3 }$$
Answer: A
A copper rod is bent into a semi-circle of radius $a$ and at straight parts are bent along diameter of the semicircle and are passed through fixed, smooth and conducting ring $O$ $O'$ as shown in figure. A capacitor having capacitance $C$ is connected to the rings. The system is located in a uniform magnetic field on induction $B$ such that axis of rotation $OO'$ is perpendicular to the field direction. At initial moment of time $(t=0)$, plane of semi-circle was normal to the field direction and the semi-circle is set in rotation with constant angular velocity $\omega$. Neglect the resistance and inductance of the circuit. The current flowing through the circuit as function of time is

Options:
A. \cfrac { 1 }{ 2 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\cos { \omega t + \frac{\pi}{2} }
B. $$\cfrac { 1 }{ 4 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\sin { \omega t } $$
C. \cfrac { 1 }{ 3 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\cos { \omega t }
D. \cfrac { 1 }{ 4 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\cos { 2\omega t }
E. \cfrac { 1 }{ 2 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\sin { 2\omega t }
F. $$\cfrac { 1 }{ 2 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\cos { \omega t } $$
G. $$\cfrac { 1 }{ 2 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\sin { \omega t } $$
H. \cfrac { 1 }{ 3 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\sin { \omega t }
I. $$\cfrac { 1 }{ 4 } \pi { \omega }^{ 2 }{ a }^{ 2 }CN\cos { \omega t } $$
Answer: F
Breaking stress for a material is $2 \times 10^8 \ N/m^2$ . What maximum length of the wire of this material can be taken so that the wire does not break by own weight ? [Density of material = $5 \times 10^3 \ kg/m^3$]

Options:
A. 1.5 km
B. 4 km
C. 2.5 km
D. 3 km
E. 3.5 km
F. 1.8 km
G. 2 km
H. 2.2 km
I. 2.1 km
J. 1 km
Answer: G