MikaStars39/nano-eval huggingface dataset:
A cylindrical piston of mass $M$ slides smoothly inside a long metallic cylinder closed at one end, enclosing a certain mass of gas. The cylinder is kept with its axis horizontal. If the piston is disturbed from its equilibrium position, it oscillates simple harmonically. The period of oscillation will be

Options:
A. $$T=\pi \sqrt { (\frac { MA }{P_0h } ) } $$
B. $$T=2\pi \sqrt { (\frac { M }{P_0Ah } ) } $$
C. T=2\pi \sqrt { \left( \frac { MA }{P_0h } \right) }
D. T=2\pi \sqrt { \left( \frac { MhA }{P_0A } \right) }
E. $$T=2\pi \sqrt { (\frac { Mh }{P_0A } ) } $$
F. T=2\pi \sqrt { \left( \frac { MhA }{P_0h } \right) }
G. $$T=2\pi \sqrt { ( \( \frac { MhA }{P_0h } ) }$$
H. T=2\pi \sqrt { \left( \frac { MhA }{P_0 } \right) }
I. $$T=2\pi \sqrt { MP_0hA ) } $$
J. T=2\pi \sqrt { \left( \frac { MAh }{P_0 } \right) }
Answer: E
A bucket filled with water having a mass of $15kg$ is raised from a well of depth $12m$ with the help of a rope. If the work done to do so is $2160J$, the linear density of the rope is $(g=10 { ms }^{ -2 })$

Options:
A. 0.7 kg/m
B. 0.3 kg/m
C. 0.8 kg/m
D. $$1 kg/m$$
E. 0.6 kg/m
F. 0.9 kg/m
G. $$0.1 kg/m$$
H. $$0.2 kg/m$$
I. 0.4 kg/m
J. $$0.5 kg/m$$
Answer: J
$1 m^3$ of a gas is compressed suddenly at atmospheric pressure and temperature $27^0C$ such that its temperature becomes $627^0C$. The final pressure of gas will be ( $\gamma = 1.5$)-

Options:
A. 7.2 \times 10^4 N/ m^2
B. 2.7 \times 10^5 N/ m^2
C. 2.7 \times 10^6 N/ m^2
D. $$7.2\times 10^5 N/ m^2$$
E. $$27\times 10^6 N/ m^2$$
F. 7.2 \times 10^6 N/ m^2
G. 27 \times 10^4 N/ m^2
H. $$27\times 10^5 N/ m^2$$
Answer: E
Which of the following is/are correct about the critical condition of real gas following Vander Waal's equation of state?

Options:
A. $Z = \dfrac {1}{8}$ for every real gas at the critical point and all real gases are more compressible than ideal gases.
B. Z = \dfrac {5}{8} for every real gas at the critical point and all real gases are less compressible than ideal gases.
C. $Z = \dfrac {3}{8}$ for every real gas at the critical point and all real gases are more compressible than ideal gases.
D. Z = \dfrac {7}{8} for every real gas at the critical point and all real gases are less compressible than ideal gases.
E. $Z = \dfrac {2}{8}$ for every real gas at the critical point and all real gases are more compressible than ideal gases.
F. For the temperature less than $T_{C}$, volume has three imaginary roots.
G. $Z = \dfrac {1}{4}$ for every real gas at the critical point and all real gases are less compressible than ideal gases.
H. $Z = \dfrac {1}{3}$ for every real gas at the critical point and all real gases are more compressible than ideal gases.
Answer: C
$FAD$ is a redox-active molecule which takes part in many important biological reactions. The redox potential of $FAD$ at $pH\ 7.0$ is given below.$FAD+2H^{+}+2e^{-}\rightleftharpoons FADH_{2}$; $E_{FADH_{2}/FAD}=0.18V$. Calculate the redox potential when the media is acidified to $pH=0$.

Options:
A. $$0\ V$$
B. -0.18\ V
C. -0.16\ V
D. None of the above
E. -0.10\ V
F. -0.22\ V
G. -0.14\ V
H. -0.20\ V
I. $$-0.12\ V$$
J. $$-0.24\ V$$
Answer: A
Choose the correct option:A cylindrical tank having a cross-sectional area $A$ is resting on a smooth horizontal place. It is filled with two immiscible, non-viscous and incompressible liquids of density $\rho$ and $2\rho$ each of height $\displaystyle\frac{H}{2}$. The liquid of density $\rho$ is open to the atmosphere having pressure ${P_0}$ . A tiny hole of area of cross section $a(<A)$ is made on the right vertical side of the wall of the tank at a height $h(<H)$ for which range is maximum.

Options:
A. Range, \( R = \displaystyle\frac{4H}{3} \)
B. Range, \( R = \displaystyle\frac{5H}{3} \)
C. Range, \( R = \displaystyle\frac{4H}{5} \)
D. Range, $R = \displaystyle\frac{H}{2}$
E. Range, $R = \displaystyle\frac{3H}{2}$
F. Height, $h=\displaystyle\frac{H}{3}$
G. Range, $R = \displaystyle\frac{2H}{3}$
H. Range, \( R = \displaystyle\frac{3H}{4} \)
I. Range, \( R = \displaystyle\frac{5H}{4} \)
J. None of these
Answer: G
The equation kcosx-3 sinx=k+1 is soluble only if k belongs to the interval

Options:
A. (-4, \infty)
B. [4, \infty)
C. [-4,4]
D. None of these
E. (-\infty, 4)
F. $$(-\infty, k)$$
G. [-5,5]
H. $$(-\infty, k]$$
I. $$(k,\infty )$$
Answer: I
Let $V$ and $E$ denote the gravitational potential and gravitational field at a point, respectively. It is possible to have

Options:
A. $V
e 0$ and $E=0$
B. $V
C. $V=0$ and $E
e 0$
D. V \neq 0 \text{ and } E = -2
E. $V \neq 0 \text{ and } E = -1$
F. $V=0$ and $E=0$
G. $V \neq 0 \text{ and } E = 1$
H. $V \neq 0 \text{ and } E = 0$
I. V \neq 0 \text{ and } E \neq 0
Answer: B
In an L-R series circuit ($L-\dfrac{175}{11} mH$ and $R= 12\Omega$) , a variable emf source $( V= V_0 sin\omega t)$ of $V_{rms} = 130 \sqrt2 V$ and frequency $50$ Hz is applied. The current amplitude in the circuit and phase of current with respect to voltage are respectively ( Use $\pi = 22/7$)

Options:
A. 14.14A, tan^{-1}\dfrac{5}{11}
B. 10\sqrt2 A, 45^0
C. $$20 A, tan^{-1}\dfrac{5}{12}$$
D. 10\sqrt2 A, 30^0
E. $$10\sqrt2 A, tan^{-1}\dfrac{5}{12}$$
F. 14.14A, 45^0
G. $$14.14A, 30^0$$
H. 14.14A, tan^{-1}\dfrac{5}{12}
I. 10\sqrt2 A, tan^{-1}\dfrac{7}{12}
J. $$10 A, tan^{-1}\dfrac{5}{12}$$
Answer: G
A ray of light passing through the point $A\left( 2,3 \right)$ reflected at a point B on line $x+y=0$ and then passes through $\left( 5,3 \right)$. Then the coordinates of B are

Options:
A. $$\left( \dfrac { 2 }{ 5 } ,-\dfrac { 2 }{ 5 } \right)$$
B. \left( \dfrac { 1 }{ 5 } ,-\dfrac { 1 }{ 5 } \right)
C. \left( \dfrac { 1 }{ 4 } ,-\dfrac { 1 }{ 4 } \right)
D. \left( \dfrac { 1 }{ 2 } ,-\dfrac { 1 }{ 2 } \right)
E. \left( \dfrac { 4 }{ 15 } ,-\dfrac { 4 }{ 15 } \right)
F. $$None\ of\ these$$
G. \left( \dfrac { 3 }{ 10 } ,-\dfrac { 3 }{ 10 } \right)
H. $$\left( \dfrac { 1 }{ 3 } ,-\dfrac { 1 }{ 3 } \right)$$
I. \left( \dfrac { 1 }{ 7 } ,-\dfrac { 1 }{ 7 } \right)
J. $$\left( \dfrac { 1 }{ 13 } ,-\dfrac { 1 }{ 13 } \right)$$
Answer: H
The vapour density of a volatile chloride of a metal is 74.6. If the specific heat of the metal is 0.55, the atomic mass of the metal is

Options:
A. 7.22
B. 7.23
C. 7.35
D. 7.2
E. 10
F. 7.46
G. 7.1
H. 7.25
I. 7.3
J. 11.63
Answer: D
The acceleration of an electron in the first orbit of the hydrogen atom $(n =1)$ is :

Options:
A. $$\dfrac{h^2}{\pi^2m^2r^3}$$
B. $$\dfrac {2\pi^2kme^2Z}{\eta h}$$
C. \dfrac{h^2}{6\pi m^2r^3}
D. \dfrac{h^2}{2\pi^2m^2r^3}
E. \dfrac{h^2}{5\pi m^2r^3}
F. \dfrac{h^2}{16\pi m^2r^3}
G. \dfrac{h^2}{7\pi m^2r^3}
H. $$\dfrac{h^2}{4\pi m^2r^3}$$
I. \dfrac{h^2}{3\pi m^2r^3}
J. $$\dfrac{h^2}{8\pi^2m^2r^3}$$
Answer: H
A ray of light is coming along the line $\displaystyle x =2$ from positive direction of $\displaystyle y-$axis & strikes a concave mirror whose intersection with the $\displaystyle XOY$ plane is a parabola $\displaystyle x^{2}=4y$, then equation of the reflected ray after the second reflection is

Options:
A. None of these
B. \displaystyle y-2=0
C. $$\displaystyle x+2=0 $$
D. y-1=0
E. x-2=0
F. y-2=0
G. $$\displaystyle y+2=0 $$
H. y-3=0
I. x-3=0
J. $$\displaystyle y+1=0 $$
Answer: C
The rate of disappearance of $A$ at two temperature for the equilibrium $A \rightleftharpoons B$ is given by :                        $- \displaystyle\frac { d\left[ A \right]  }{ dt } = 2\times { 10 }^{ - 2 }\left[ A \right] - 4\times { 10 }^{ - 3 }\left[ B \right]$                      at $ 300  K$                       $- \displaystyle\frac { d\left[ A \right]  }{ dt } = 4\times { 10 }^{ - 2 }\left[ A \right] - 16\times { 10 }^{ - 4 }\left[ B \right]$                    at  $400  K$Calculate :(i)  equilibrium constants at $300  K$ and $400  K$ and (ii)  heat of reaction.

Options:
A. 0.2, 25, -3.86 kcal
B. $$ 0.2, 0.04 , -3.86 kcal $$
C. $$ 0.2, 25 , 11.56 kcal $$
D. 0.2, 5, -3.86 kcal
E. $$ 5, 25 , -3.86 kcal $$
F. 0.2, 5, 3.86 kcal
G. 5, 25, -11.56 kcal
H. $$ 5, 25 , 3.86 kcal $$
I. 0.2, 25, 3.86 kcal
Answer: H
The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position, so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $\rho$.
In equilibrium, the height H of the water column in the cylinder satisfies

Options:
A. \rho g(L_0-H)^2+P_0(L_0-H)+2L_0P_0=0
B. $$\rho g(L_0-H)^2-P_0(L_0-H)+L_0P_0=0$$
C. \rho g(L_0-H)^2+P_0(L_0-H)+L_0P_0=0
D. $$\rho g(L_0-H)^2+P_0(L_0-H)-L_0P_0=0$$
E. \rho g(L_0-H)^2-P_0(L_0-H)+2L_0P_0=0
F. \( \rho g(L_0-H)^2+P_0(L_0-H)-2L_0P_0=0 \)
G. \( \rho g(L_0-H)^2+P_0(L_0-H)+3L_0P_0=0 \)
H. $$\rho g(L_0-H)^2-P_0(L_0-H)-L_0P_0=0$$
I. \( \rho g(L_0-H)^2+P_0(L_0-H)+4L_0P_0=0 \)
Answer: D
Water is poured into an inverted conical vessel of which the radius of the base is $2$, and height $4$m, at the rate of $77$ litre/minute. The rate at which the water level is rising at the instant when the depth is $70$ cm is?(Use $\pi =22/7$)

Options:
A. $20$ cm/min
B. $50$ cm/min
C. 70 cm/min
D. $60$ cm/min
E. $30$ cm/min
F. $40$ cm/min
G. 55 cm/min
H. 45 cm/min
Answer: D
The input resistance of a common emitter transistor amplifier, if the output resistance is $500k\Omega$, the current gain $lpha=0.98$ and power gain is $6.0625\times {10}^{6}$, is :

Options:
A. 197\Omega
B. $$100\Omega$$
C. 202\Omega
D. 200\Omega
E. 195\Omega
F. $$300\Omega$$
G. 196\Omega
H. 203\Omega
I. $$198\Omega$$
J. $$400\Omega$$
Answer: I
A flat square surface with sides of length L is described by the equations $x = L,0 \le y \le L,0 \le z \le L$. the electric flux through the square due to a positive point charge $q$ located at the origin $\left( {x = 0,y = 0,z = 0} \right)$

Options:
A. \dfrac{q}{{72{\arepsilon _0}}}
B. $$\dfrac{q}{{48{arepsilon _0}}}$$
C. $$\dfrac{q}{{4{arepsilon _0}}}$$
D. $$\dfrac{q}{{24{arepsilon _0}}}$$
E. $$\dfrac{q}{{6{arepsilon _0}}}$$
F. \dfrac{q}{{48{\arepsilon _0}}}
G. \dfrac{q}{{12{\arepsilon _0}}}
H. \dfrac{q}{{32{\arepsilon _0}}}
I. \dfrac{q}{{36{\arepsilon _0}}}
J. \dfrac{q}{{8{\arepsilon _0}}}
Answer: D
Two straight long and thin parallel wires are spaced 0.1 m apart and carry a current each. Find the magnetic field at a point which is at a distance of 0.1 m from both wires in the two cases when the currents are in the (a) same and (b) opposite directions (Given= $\mu_0= 4\pi \times 10^{-7} Tm/A$).

Options:
A. (i) $3.46\times 10^{-5}T$ (ii) $2\times 10^{-5}T$
B. (i) $3.46\times 10^{-6}T$ (ii) $4\times 10^{-5}T$
C. (i) $1.46\times 10^{-5}T$ (ii) $4\times 10^{-5}T$
D. (i) $2.46 \times 10^{-5}T$ (ii) $3 \times 10^{-5}T$
E. (i) $3.46 \times 10^{-5}T$ (ii) $1.2 \times 10^{-5}T
F. (i) $4.46 \times 10^{-5}T$ (ii) $1 \times 10^{-5}T$
G. (i) $1.46 \times 10^{-5}T$ (ii) $1 \times 10^{-5}T
H. (i) $5.46\times 10^{-6}T$ (ii) $2\times 10^{-5}T$
I. (i) $2.46 \times 10^{-5}T$ (ii) $1.2 \times 10^{-5}T
Answer: A
A cubical vessel with opaque walls is so placed that the eye of an observer cannot see its bottom but can see the entire wall CD. A small object is placed at O at a distance $b=10 cm$ from corner D. What minimum depth of water $(\mu=\dfrac {4}{3})$ should be poured into the vessel which will enable the observer to see the object?

Options:
A. 25.5 cm
B. $$28.6 cm$$
C. $$22.4 cm$$
D. 24.5 cm
E. 22.5 cm
F. 25.6 cm
G. 28.5 cm
H. $$20 cm$$
I. $$26.7 cm$$
J. 26.5 cm
Answer: I
The momentum of a particle is $\overrightarrow P  = \overrightarrow A  + \overrightarrow B {t^2}$ where $\overrightarrow A \,$ and $\overrightarrow B $ are constant perpendicular vector. the force acting on the particle when its acceleration makes an angle of $45^0$ with the velocity is

Options:
A. \left( {2\sqrt {\dfrac{B}{A}} } \right)\overline B
B. \left( {2\sqrt {\dfrac{A}{B}} } \right)\overline A
C. \left( {2\sqrt {\dfrac{B}{A}} } \right)\overline B + \overline A
D. \left( {2\sqrt {\dfrac{B}{A}} } \right)\overline A
E. \left( {2\sqrt {\dfrac{B}{A}} } \right)\overline A - \overline B
F. \left( {2\sqrt {\dfrac{B}{A}} } \right)\overline B - \overline A
G. $$2\overline B $$
H. $$\left( {2\sqrt {\dfrac{A}{B}} } \right)\overline B $$
I. Zero
Answer: H
Consider the following statements concerning F.C. acacia.I. It is used for the preparation of aromatic ketones.II. In this reaction there is the formation of a carbon-carbon bondIII. For this reaction, nitrobenzene can be used as solventIV. Acylium ions,$R-C=O^{+}$ is attacking species.V. It is an electrophilic substitution reaction.Which of these statements are correct?

Options:
A. I, II, III, V
B. I, III, IV
C. I,II,III,IV,I
D. I, II, III, IV
E. I,II ,IV
F. I ,II,V
G. I,III,V
Answer: F
Arrange the following in increasing order of stability on the basis of resonance.(i) $CH_2 = CH - CH = CH - \overset{+}{CH_2}$(ii) $CH_2 = CH - \overset{+}{CH} - CH = CH_2$(iii) $CH_2 = CH - \overset{+}{CH} - \overset{-}{CH} -\overset{+}{CH_2}$(iv) $\overset{+}{CH_2} - CH = CH - \overset{-}{CH} -\overset{+}{CH_2}$.

Options:
A. (ii) $>$ (iv) $>$ (i) $>$ (iii)
B. (ii) $>$ (iii) $>$ (iv) $>$ (i)
C. (i) $>$ (iii) $>$ (ii) $>$ (iv)
D. (iv) $>$ (i) $>$ (ii) $>$ (iii)
E. (iv) $>$ (ii) $>$ (iii) $>$ (i)
F. (iii) $>$ (ii) $>$ (i) $>$ (iv)
G. (iii) $>$ (iv) $>$ (ii) $>$ (i)
H. (i) $>$ (ii) $>$ (iv) $>$ (iii)
I. (iv) $>$ (iii) $>$ (i) $>$ (ii)
J. (ii) $>$ (i) $>$ (iii) $>$ (iv)
Answer: J
Two particles execute SHM with amplitude A and 2A and angular frequency ${\omega}$ and ${2\omega}$ respectively. At t=0, they start with some initial phase difference. At $\displaystyle t=\frac{2\pi}{3\omega}$, they are in same phase. Their initial phase difference is

Options:
A. \frac{7\pi}{6}
B. \frac{5\pi}{12}
C. \frac{2\pi}{5}
D. \frac{\pi}{4}
E. $${\displaystyle\frac{\pi}{3}}$$
F. $${\displaystyle\frac{4\pi}{3}}$$
G. \frac{\pi}{6}
H. \frac{5\pi}{6}
I. $${\displaystyle\pi}$$
J. $${\displaystyle\frac{2\pi}{3}}$$
Answer: E
For the chemical reaction between mercuric chloride and potassium oxalate, the mass of ${ Hg }_{ 2 }{ Cl }_{ 2 }$ precipitated in different time intervals, at ${100}^{o}C$, is given below:
Exp.no${ \left[ Hg{ Cl }_{ 2 } \right]  }_{ 0 }\left( M \right) $${ \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right]  }_{ 0 }\left( M \right) $Time (min)${ Hg }_{ 2 }{ Cl }_{ 2 }$ formed (g)1$0.0836$$0.404$$65$$0.0068$2$0.0836$$0.202$$120$$0.0031$3$0.0418$
$0.404$$60$$0.0032$What is the rate law expression of this reaction?

Options:
A. $$r=K{ \left[ Hg{ Cl }_{ 2 } \right] }^{ 2 }\left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] $$
B. r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ 3 }
C. r=K{ \left[ Hg{ Cl }_{ 2 } \right] }^{ 3 }\left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right]
D. $$r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ 2 }\quad $$
E. $$r=K\left[ Hg{ Cl }_{ 2 } \right] \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] $$
F. r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ \frac{2}{3} }
G. r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ \frac{3}{2} }
H. r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ \frac{1}{3} }
I. r=K\left[ Hg{ Cl }_{ 2 } \right] { \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ 1/2 }
J. $$r=K{ \left[ Hg{ Cl }_{ 2 } \right] }^{ 2 }{ \left[ { K }_{ 2 }{ C }_{ 2 }{ O }_{ 4 } \right] }^{ 2 }$$
Answer: E
The capacitor is charged by closing the switch S. The switch is then opened and the capacitor is allowed to discharged. Take ${ R }_{ 1 }={ R }_{ 2 }={ R }_{ 3 }=R$ (Baterry is ideal and connecting wire has negligible resistance).
The fraction of the total heat generated, lost in ${ R }_{ 1 }$ during discharging is:

Options:
A. \dfrac{1}{9}
B. $$\dfrac { 2 }{ 3 } $$
C. $$\dfrac { 1 }{ 3 } $$
D. \dfrac{1}{7}
E. \dfrac{1}{8}
F. \dfrac{1}{4}
G. \dfrac{1}{5}
H. $$\dfrac { 1 }{ 6 } $$
I. $$\dfrac { 1 }{ 2 } $$
J. \dfrac{1}{10}
Answer: H
Consider the cell;$V^{2+}+VO^{2+}+2H^{+}\rightarrow 2V^{3+}+H_{2}O;\ E^{o}=0.616V$$V^{3+}+Ag^{+}+H_{2}O\rightarrow VO^{2+}+2H^{+}+Ag;\ E^{o}=0.439V$Potential of $E^{o}_{V^{3+}/V^{2+}}$ is :(Given that $E^{o}_{Ag^{+}/Ag}=0.799 V$)

Options:
A. 0.356\ V
B. 0.239\ V
C. -0.177\ V
D. $$1.055\ V$$
E. 0.256\ V
F. $$0.177\ V$$
G. -0.356\ V
H. 0.456\ V
I. $$-0.256\ V$$
Answer: I
A very thin copper plate is electro-plated with gold (III) using gold chloride in HCI. The current was passed for 20 min. and the increase in the weight of the plate was found to be 2g. [Au = 197]. The current passed was -

Options:
A. 2.44 amp
B. 1.81 amp
C. 1.62 amp
D. 1.21 amp
E. 0.81 amp
F. 0.92 amp
G. 1.22 amp
H. 1.163 amp
I. 3.26 amp
J. 1.63 amp
Answer: E
Morphine, $C_{17}H_{19}NO_{3}$, is administered medically to relieve pain. It is a naturally occurring base, or alkaloid. What is the $pH$ of a $0.0025 M$ solution of morphine at $25^{\circ}C$? The base-ionization constant, $K_{b}$, is $1.6 \times 10^{6}$ at $25^{\circ}C$. ($log 2 = 0.3$)

Options:
A. 10.4
B. 9.9
C. $$9.8$$
D. $$4.2$$
E. 10.5
F. $$3.7$$
G. 10.1
H. 10.0
I. 10.2
J. $$10.3$$
Answer: C
The coordinates of a particle moving in a plane are given by x(t) = acos(pt) and y(t) = bsin(pt) where a, b (<a) and p are positive constants of appropriate dimensions. Then :

Options:
A. The distance travelled by the particle in time interval t = 0 to t = \(\frac{\pi}{2p}\) is b
B. The acceleration of the particle is always directed towards a focus
C. The velocity and acceleration of the particle are normal to each other at t = $\pi/4p$
D. The velocity and acceleration of the particle are normal to each other at t = $\pi/2p$
E. The acceleration of the particle is always directed towards a vertex
F. The distance travelled by the particle in time interval t = 0 to t = $\frac{\pi}{2p}$ is a
Answer: D
One end of a metal rod of uniform cross-section and length $1.5$ m is in contact with ice at one end and the other end is in contact with steam at $100^{o}$C. At what point along its length should a temperature of $200^{o}$C be maintained so that in the steady state the mass of ice melting is equal to that of steam produced in the same interval of time? (Specific latent heat of ice = $80$ kcal kg$^{-1}$ and that of steam = $540$ kcal kg$^{-1}$

Options:
A. 0.15 m from cold end
B. 1.6 m from cold end
C. 0.104 m from cold end
D. 1.52 m from cold end
E. 1.35 m from cold end
F. 0.9 m from cold end
G. 1.3 m from cold end
H. 1.2 m from cold end
I. 1.45 m from cold end
J. 1.4 m from cold end
Answer: J
Consider the $R-L-C$ circuit given below. The circuit is driven by a $50\ Hz\ AC$ source with peak voltage $220\ V$. If $R = 400\Omega, C = 200\mu F$ and $L = 6H$, the maximum current in the circuit is closest to

Options:
A. $$0.120\ A$$
B. $$5.5\ A$$
C. 0.70\ A
D. $$0.55\ A$$
E. $$1.2\ A$$
F. 0.65\ A
G. 0.60\ A
H. 0.75\ A
I. 0.15\ A
J. 0.50\ A
Answer: D
In which of the following cell(s); $E_{cell} = E_{cell}^{\circ}$?

Options:
A. Pt(H_{2}) | pH = 1 | | Zn^{2+} (1\ M) | Zn(s)
B. $$Pt(H_{2}) | pH = 0.1 | | Zn^{2+} (0.01\ M) | Zn(s)$$
C. Pt(H_{2}) | H^{+} = 0.1\ M | | Zn^{2+} (1\ M) | Zn(s)
D. $$Pt(H_{2}) | pH = 1 | | Zn^{2} (1M) | Zn(s)$$
E. $$Pt(H_{2}) | pH = 1 | | Zn^{2+}(0.01\ M)| Zn(s)$$
F. $$Pt(H_{2}) | H^{+} = 0.01\ M | | Zn^{2+} (0.01\ M) | Zn(s)$$
Answer: E
An alloy of lead (valency = 2) and thallium (valency = 1) containing 65% $Pb$ and 35% $Tl$, by weight, can be electroplated onto a cathode from a solution. How many gram of this alloy will deposit in 9.65 hours using a constant current of 0.5 amp? [Given that only these two elements deposit simultaneously in given mass ratio at cathode] [Atomic weight $Pb = 208,\ Tl = 200$]

Options:
A. 34.5 gm
B. 26.5 gm
C. 37.5 gm
D. 38 gm
E. 24.9 gm
F. 22.5 gm
G. 3.7 gm
H. 36.5 gm
I. 35.5 gm
J. 37 gm
Answer: J
An inductor $20\ mH$, a capacitor $50\ \mu F$ and a resistor $40\ \Omega$ are connected in series across a source of emf $V=10\sin 340t$. The power loss in A.C. circuit is:

Options:
A. 0.61\ W
B. $$0.67\ W$$
C. 0.59\ W
D. $$0.89\ W$$
E. 0.58\ W
F. 0.54\ W
G. $$0.51\ W$$
H. 0.52\ W
I. 0.56\ W
J. $$0.76\ W$$
Answer: G
A potential difference of $ 10^{3} V $ is applied across an X-ray tube. The ratio of the De-Broglie wavelength of the incident electrons to the shortest wavelength of the incident electrons to the shortest wavelength of X-rays produced is {e/m = $ 1.8 \times 10 ^ {14} $ C/Kg for an electron }

Options:
A. $$\dfrac{1}{10^4}$$
B. $$1$$
C. \dfrac{1}{50}
D. $$\dfrac{1}{100}$$
E. \dfrac{1}{5000}
F. $$\dfrac{1}{20}$$
G. \dfrac{1}{200}
H. \dfrac{1}{1000}
I. \dfrac{1}{500}
J. \dfrac{1}{10}
Answer: B
A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction $ =\mu)$ with speed of centre $= u$. It collides inelastically with a smooth vertical wall at a certain moment, the coefficient of restitution being $\displaystyle \frac{1}{2}$The sphere will begin pure rolling after a time

Options:
A. $$\displaystyle \frac{3u}{7\mu g}$$
B. \frac{3u}{6\mu g}
C. \frac{2u}{6\mu g}
D. \frac{3u}{8\mu g}
E. $$\displaystyle \frac{2u}{5\mu g}$$
F. \frac{4u}{5\mu g}
G. $$\displaystyle \frac{3u}{5\mu g}$$
H. \frac{4u}{7\mu g}
I. $$\displaystyle \frac{2u}{7\mu g}$$
J. \frac{4u}{6\mu g}
Answer: A
A balloon of diameter 21 meter weight 100 kg.Calculate its pay-load, if it is filled with He at 1.0 atm and $27^oC$.Density of air is 1.2 kg $m^{-3}$(Given:R=0.082L atm $K^{-1}mol^{-1}$)

Options:
A. 4932.42 kg
B. 4942.42 kg
C. 4943.42 kg
D. 4952.41 kg
E. 4962.42 kg
F. 4952.42 kg
G. 4963.42 kg
H. 4922.42 kg
I. 493.242 kg
J. None of these
Answer: F
A non-conducting ring of radius $0.5$ m carries a total charge of 1.11 x ${ 10 }^{ -10 }$C distributed non-uniformly on its circumference producing an electric filed $\bar { E } $ every where in space. The value of the line integral $\int _{ \ell =\infty  }^{ \ell =0 }{ - } \bar { E } .d\bar { \ell  } (\ell $ = 0 being center of the ring) in volts is :

Options:
A. 4
B. 0.5
C. 1
D. +1
E. 3
F. -2
G. zero
H. -$ 1$
I. + $2$
Answer: I
An uncharged capacitor of capacitance $100 \mu F$ is connected  to a battery of emf $20 V$ at t = 0 through a resistance $10\Omega$ at what time at which the rate of energy stored the capacitors is maximum:

Options:
A. (1 ln 2) ms
B. (3 ln 2) ms
C. (8 ln 2) ms
D. (ln 2) ms
E. (9 ln 2) ms
F. (6 ln 2) ms
G. (4 ln 2) ms
H. (5 ln 2) ms
I. (2 ln 2) ms
J. (7 ln 2) ms
Answer: I
A particle is moving in a straight line whose acceleration as a function of velocity is related as a =v, where  a is  in $m/{s^2}$ and  v is in m/s. The velocity of particle at t=0 s        and x=1 m is  1 m/s , then  its velocity at x=3 m will be

Options:
A. 2 m/s
B. 4 m/s
C. 1.5 m/s
D. 3 m/s
E. 1 m/s
F. 5 m/s
G. 2.5 m/s
H. 2.2 m/s
I. 7 m/s
J. 6 m/s
Answer: A
Find the binding energy of valence electron in the ground state of a $Li$ atom if the wavelength of the sharp series is known to be $\lambda_{1}$ $= 813 nm$ and the short wave cutoff wavelength $\lambda_{2}$, $= 350 nm$

Options:
A. $$3.54 eV$$
B. $$5.32 eV$$
C. 4.54 eV
D. 5.52 eV
E. 5.22 eV
F. 5.54 eV
G. $$4.32 eV$$
H. 3.34 eV
I. $$1.5 eV$$
J. 4.52 eV
Answer: B
A long straight wire of circular cross-section is made of non -magnetic material. The wire is of radius a.The wire carries a current $I$ which is uniformly distributed over its cross -section the energy stored per unit length in the magnetic field contained within the wire is

Options:
A. $$U=\dfrac{\mu_0I^2}{8\pi}$$
B. $U=\dfrac{\mu_0I^2}{2\pi}
C. U=\dfrac{\mu_0I^2}{10\pi}
D. $U=\dfrac{\mu_0I^2}{4\pi}
E. U=\dfrac{\mu_0I^2}{14\pi}
F. $$U=\dfrac{\mu_0I^2}{12\pi}$$
G. U=\dfrac{\mu_0I^2}{6\pi}
H. $$U=\dfrac{\mu_0I^2}{16\pi}$$
I. U=\dfrac{\mu_0I^2}{18\pi}
Answer: A
The following operation can be performed on a capacitor:
X connect the capacitor to a battery of emf E.
Y disconnect the battery.
Z reconnect the battery with the polarity reversed.
W insert a dielectric slab in the capacitor.

Options:
A. The electric field in the capacitor after the action XW is four times that after WX.
B. The electric energy stored in the capacitor is greater after the action WXY than after the action XYW.
C. The electric field in the capacitor after the action XW is one-third that after WX.
D. The electric field in the capacitor after the action XW is twice that after WX.
E. The electric field in the capacitor after the action XW is the same as that after WX.
F. The charge appearing on the capacitor is greater after the action XWY than after the action XYW.
G. The electric field in the capacitor after the action XW is three times that after WX.
H. In XYZ (perform X, then Y, then Z) the stored electric energy remains unchanged and no thermal energy is developed
I. The electric field in the capacitor after the action XW is five times that after WX.
J. The electric field in the capacitor after the action XW is half that after WX.
Answer: E
Consider a hypothetical hydrogen like atom. The wavelength in $A^o$ for the spectral lines for transition from $n=p$ to $n=1$ are given by:$\lambda =\displaystyle\frac{1500p^2}{p^2-1},$ where $p > 1$Find the ionization potential of this element?

Options:
A. 20.64 \text{ eV}
B. $16.56$ eV
C. 21.4 \text{ eV}
D. $22.4$ eV
E. 21.84 \text{ eV}
F. 20.48 \text{ eV}
G. $19.28$ eV
H. $4.14$ eV
I. $8.28$ eV
J. 18.48 \text{ eV}
Answer: D
It is a data sufficiency problem in which it is to be decided on the basis of given statements whether the given question can be answered or not. No matter whether the answer is yes or no.
Question: Is the orbital of hydrogen atom $3p_x$?
Statement-1: The radial function of the orbital is $R(r)$=$\dfrac{1}{9 \sqrt 6 \, a_0^{3/2}} (4-\sigma)\sigma e^{-e/2},\sigma=\dfrac{r}{2}$
Statement-2:The orbital has 1 radial node and 0 angular node.

Options:
A. Neither is sufficient
B. Statement (1) alone is sufficient, Statement (2) alone is insufficient
C. Statement (2) alone is insufficient, Statement (1) alone is sufficient
D. Statement (2) alone is sufficient.
E. Statement (1) alone is insufficient, Statement (2) alone is insufficient
F. Statement (1) alone is insufficient
G. Statement (1) alone is sufficient
H. Statement (2) alone is sufficient
I. Both together is sufficient
J. Statement (1) alone is sufficient.
Answer: I
An electron jumps from seconds excited state of hydrogen atom to its ground state and the photon thus emitted is incident on a photo sensitive metal plate of work function 5.1 eV .The stopping potential for the plate would be (approximately)

Options:
A. 6 V
B. 7 V
C. 4 V
D. 12 V
E. 1 V
F. 3 V
G. 9 V
H. 5 V
I. 2 V
J. 8 V
Answer: F
The vapour pressure of mixture of $1$ mol volatile component $A(p^o_A = 100 \,mmHg)$ and $3$ mol of volatile component $B(p^o_B = 60 \,mmHg)$ is $75 \,mm$. For such case

Options:
A. There is a slight deviation from Raoult's law, but it is not significant enough to classify as positive or negative
B. There is no significant deviation from Raoult's law
C. Boiling point has been lowered
D. There is a slight positive deviation from Raoult's law, but it is not significant enough to classify as positive or negative
E. There is a slight negative deviation from Raoult's law, but it is not significant enough to classify as positive or negative
F. All the above statements are correct
G. Force of attraction between $A$ and $B$ is smaller than that between $A$ and $A$ or between $$ and $B$
H. There is positive deviation from Raoult's law
I. There is negative deviation from Raoult's law
J. There is no deviation from Raoult's law
Answer: H
Find the maximum $K E$ of phototoelectrons emitted from the surface of lithium $( \phi = 2.39 e V )$ when exposed with $E = E _ { 0 } \left( 1 + \cos 6 \times 10 ^ { 14 } t \right) \cos 3.6 \times 10 ^ { 15 } t$

Options:
A. 0.42 e V
B. 0.27 e V
C. 0.32 e V
D. $$0.1 e V$$
E. 0.2 e V
F. 0.49 e V
G. 0.47 e V
H. $$0.06 e V$$
I. $$0.02 e V$$
J. $$0.37 e V$$
Answer: J
A sample of $H_2O_2$ solution labelled as $28$ volume has density of $265$ g/L. Mark the correct option(s) representing concentration of same solution in other units.

Options:
A. Molality of ${H_2O_2} =13.33
B. Molality of ${H_2O_2} =12.75
C. Molality of ${H_2O_2} =13.50
D. Molality of ${H_2O_2} =14.00
E. Molality of ${H_2O_2} =13.88$
F. Percentage $w/v =17$
G. Molality of ${H_2O_2} =13.00
Answer: E
On the opposite side of a wide vertical vessel filled with water two identical holes are opened , each having the cross- sectional area $ S=0.50cm^{^2}$ . The height difference between them is equal to  $ \Delta h = 51 cm $. Find the resultant force of reaction of water flowing out of the vessel.

Options:
A. 0.25 N
B. 1.75 N
C. 2 N
D. 0.75 N
E. 1 N
F. 1.25 N
G. 0.65 N
H. 0.5 N
I. 1.5 N
J. 0.35 N
Answer: H
A $2\mu F$ capacitor is connected to an alternating voltage $V=250 \sin \ 314t$. Determine the current in the capacitor at $t=\dfrac{1}{200}\ s$, if at $t=0$, no charge is stored in the plates of the capacitor.

Options:
A. 0.11\sqrt{10}
B. 0.11\sqrt{5}
C. $$0.11\sqrt{2}$$
D. $$0.22$$
E. $$0.11$$
F. 0.11\sqrt{3}
G. 0.11\sqrt{6}
H. $$0.055$$
I. 0.11\sqrt{4}
J. 0.11\sqrt{8}
Answer: C
A fuel cell develops an electrical potential from the combustion of butane at 1 bar and 298 K
$$\begin{array}{l}{C_4}{H_{10}}\left( g \right) + 6.5{O_2}\left( g \right) \to 4C{O_2}\left( g \right) + 5{H_2}O\left( l \right)\{\Delta _r}{G^0} =  - 2746Kj/mole\end{array}$$
The $E^{0}$ of the cell is

Options:
A. 1.147
B. $$4.74$$
C. 0.647
D. $$0.547$$
E. 0.754
F. $$1.09$$
G. 1.047
H. 0.597
I. $$4.37$$
Answer: D
A large tank is filled with water (density $ \rho $), upto height h. Water is coming out from section (4). Fluid pressure at section (3) is:(Given : $ {A}_{2} = {A}_{4} = 2{A}_{3} $ and $ {A}_{2},{A}_{3},{A}_{4} << {A}_{1} $ ; atmospheric pressure = $ {P}_{0} $. Assume water to be non-viscous and incompressible.)

Options:
A. {P}_{0} - 5\rho gh
B. $$ {P}_{0} - 3\rho gh $$
C. {P}_{0} - 6\rho gh
D. $$ {P}_{0} + \rho gh $$
E. {P}_{0} - 4\rho gh
F. {P}_{0} - 2\rho gh
G. {P}_{0} - 4\_rho gh
H. $$ {P}_{0} - \rho gh $$
I. {P}_{0} - 7\rho gh
Answer: B
A sphere $ \left( \mu =1.5 \right) $ has a small bubble 6 cm from the center. Radius of the sphere is 10 cm. When seen normally from shorter side the bubble appears

Options:
A. 4.6 cm below the surface
B. 3 cm above the surface
C. 4.5 cm below the surface
D. 3 cm below the surface
E. 5 cm below the surface
F. 7 cm inside the surface
G. 2.5 cm below the surface
H. 5.6 cm below the surface
I. 4 cm below the surface
J. 4 cm above the surface
Answer: D
A bullet of mass m = 50 gm strikes a bag of mass M = 5 kg hanging from a fixed point, with a horizontal velocity $\bar{V}_p$. If bullet sticks to the sand bag then just after collision the ratio of final & initial kinetic energy of the bullet is approximately :

Options:
A. $$10^{-2}$$
B. $$10^{-4}$$
C. 10^{-5}
D. $$10^{-6}$$
E. 10^{-7}
F. 10^{-3}
G. 10^{-8}
Answer: B
What is the concentration of $Ag^+$ in a solution made by dissolving both $Ag_2CrO_4$ and $Ag_2C_2O_4$ until saturation is reached with respect to both salts?$[K_{sp}(Ag_2C_2O_4) = 2\times10^{-11}, \space K_{sp} (Ag_2CrO_4) = 2\times10^{-12}]$

Options:
A. $$6.63\times10^{-6}$$
B. 4.52 \times 10^{-4}
C. 3.62 \times 10^{-4}
D. 4.62 \times 10^{-4}
E. $$2.80\times10^{-4}$$
F. $$7.6\times10^{-5}$$
G. 3.72 \times 10^{-4}
H. 4.42 \times 10^{-4}
I. 2.92 \times 10^{-4}
J. $$3.52\times10^{-4}$$
Answer: J
Two tubes of radii $r_{1}$ and $r_{2}$ and length $l_{1}$ and $l_{2}$ respectively are connected in series and a liquid flows through each of them in streamline condition. The pressure difference across the two tubes are $P_{1}$ and $P_{2}$. If $r_{2}=\dfrac{r_{1}}{2}$ and $l_{2}=\dfrac{l_{1}}{2}$ then $P_{2}$ will be equal to

Options:
A. \dfrac{P_{1}}{16}
B. $$\dfrac{P_{1}}{2}$$
C. \dfrac{P_{1}}{8}
D. $$\dfrac{P_{1}}{4}$$
E. \dfrac{P_{1}}{32}
F. \dfrac{P_{1}}{64}
G. $$P_{1}$$
H. $$2P_{1}$$
Answer: D
The distance between an electric lamp and a screen is $d = 1\ m$. A convergent lens of focal length $f = 21\ cm$ is placed between the lamp and the lens such that a sharp image of the lamp filaments is formed on the screen.

Options:
A. Magnitude of the difference in magnification is $37/21$
B. Magnitude of the difference in magnification is $40/21$
C. Magnitude of the difference in magnification is $42/21$
D. Magnitude of the difference in magnification is $41/21$
E. Magnitude of the difference in magnification is $39/21$
F. Magnitude of the difference in magnification is $36/21$
G. The size of the lamp filament for which there are two sharp images of $4.5 cm$ and $2 cm$, is $3 cm$
H. Magnitude of the difference in magnification is $38/21$
I. The position of the lens from the lamp for which sharp images are formed on the screen are $30 cm$ and $70 cm$
J. The positions of the lens from the lamp for which sharp images are formed on the screen are $35 cm$ and $65 cm$
Answer: B
If $z=1+\cos \dfrac{10\pi}{9}+i \sin \dfrac{10\pi}{9}$, then

Options:
A. \mid{z}\mid=2\cos\dfrac{10\pi}{9}
B. \mid{z}\mid=2\cos\dfrac{6\pi}{9}
C. $$Arg(z)=\dfrac{5\pi}{9}$$
D. $$\mid{z}\mid=2\cos\dfrac{5\pi}{9}$$
E. $$\mid{z}\mid=2\cos\dfrac{4\pi}{9}$$
F. \mid{z}\mid=2\cos\dfrac{3\pi}{9}
G. \mid{z}\mid=2\cos\dfrac{8\pi}{9}
H. $$Arg(z)=-\dfrac{4\pi}{9}$$
I. \mid{z}\mid=2\cos\dfrac{2\pi}{9}
J. \mid{z}\mid=2\cos\dfrac{7\pi}{9}
Answer: D
What curvature must be given to the bounding surface of a refracting medium $(\mu =1.5)$ for the virtual image f an object in the adjacent medium $(\mu =1)$ at $10\ cm$, to be formed at a distance of $40\ cm $?

Options:
A. 11\ cm
B. 18\ cm
C. 20\ cm
D. $$8\ cm$$
E. $$10\ cm$$
F. 13\ cm
G. $$15\ cm$$
H. 16\ cm
I. $$12\ cm$$
J. 14\ cm
Answer: I
In an X-ray tube, the voltage applied is 20 kV. The energy required to remove an electron from K shell is 19.9 KeV. In the X-rays by the tube (hc = 12420 evA)

Options:
A. Minimum wavelength will be 62.4 nm
B. $L_{lpha} x$ - ray may be emitted
C. Minimum wavelength will be 62.1 nm
D. Minimum wavelength will be 62.2 nm
E. Minimum wavelength will be 62.6 nm
F. Minimum wavelength will be 62.3 nm
G. Minimum wavelength will be 62.0 nm
H. Minimum wavelength will be 62.5 nm
I. $L_{lpha} x$ - ray will have energy 19.9 KeV
J. Energy of the charcteristic x - rays will be equal to or less than 19.9 KeV
Answer: C
When there occurs a transition from $n=3$ to $n=2$ state in the hydrogen, the atom recoils. If $E_{1}-E_{2}$ = $1.9 eV$, then the ratio of $KE$ of recoil and the photon energy is of the order of

Options:
A. 10^{-14}
B. $$10^{-12}$$
C. 10^{-10}
D. $$10^{_8}$$
E. $$10^{-11}$$
F. 10^{-7}
G. $$10^{-6}$$
H. 10^{-13}
I. 10^{-8}
J. $$10^{-9}$$
Answer: J
A projectile is thrown with some initial velocity u at an angle q to the horizontal. Its speed when it is at the highest point is$\sqrt{\cfrac{2}{5}}$ times the speed $V$ when it is at height half of the maximum height. Then ratio $\cfrac{v}{u}=\sqrt{\cfrac{n}{8}}$ Find the value of $n.$

Options:
A. 5
B. \sqrt{\frac{3}{8}}
C. \sqrt{\frac{6}{8}}
D. 4
E. 3
F. \sqrt{\frac{7}{8}}
G. 2
H. 1
I. \sqrt{\frac{4}{8}}
J. \sqrt{\frac{5}{8}}
Answer: E
A right circular cylinder with radius $R$ and height $H$ contains a liquid which evaporate at a rate proportional to its surface area in contact with air (proportionally constant$=k>0$). If $T$ is time after which cylinder will be empty, then

Options:
A. $T$ is independent on $H$
B. $T$ is dependent on $R$ and $H$
C. $T$ is dependent on $H$
D. $T$ is dependent on $K$
E. T is independent on $K$
F. $T$ is dependent on $R$
G. $T$ is independent on $R$
Answer: D
50 mL of sample of hard water gave good lather with 6mL of standard soap solution (1 mL soap solutions = 1 mg CaCO$_3$). If the hardness is only due to $Mg(HCO_3)_2$, the weight of milk of lime required to remove the hardness completely from 100 kg of that sample of water is:

Options:
A. 13.5 g
B. 178 g
C. 89 g
D. 8.95 g
E. 8.5 g
F. 4.45 g
G. 17.8 g
H. 85 g
I. 44.5 g
J. 8.9 g
Answer: J
Suppose the potential energy between an electron and a proton at a distance $r$ is given by $\dfrac{Ke^2}{3r^3}$. Application of Bohr's theory to hydrogen atom in this case shows that

Options:
A. Energy in the \( n^{th} \) orbit is proportional to \( n^{-3} \)
B. Energy in the $n^{th}$ orbit is proportional to $n^{-2}$
C. Energy is proportional to \( m^{-4} \) ($m$ = mass of electron)
D. Energy is proportional to \( m^{-1} \) ($m$ = mass of electron)
E. Energy is proportional to $m^{-5}$ ($m$ = mass of electron)
F. Energy is proportional to $m^{-3}$ ($m$ = mass of electron)
G. Energy is proportional to $m^{-2}$ ($m$ = mass of electron)
H. Energy is proportional to $m^{-4}$ ($m$ = mass of electron)
I. Energy is proportional to $m^3$ ($m$ = mass of electron)
J. Energy in the $n^{th}$ orbit is proportional to $n^{-6}$
Answer: F
When a sample of ideal gas is changed from an initial state to a final state, various curves can be plotted for the process like P-V curve, V-T curve,P-T curve etc.For example, P-V curve for a fixed amount of an ideal gas at constant temperature is a rectangular hyperbola, V-T curve for a fixed amount of an ideal gas at constant volume is again a straight line. However, the shapes may vary if the constant parameters are also changed.Now, answer the questions :Which of the following statement(s) is/are correct regarding a fixed amount of ideal gas undergoing the following process?

Options:
A. Root mean square (RMS) speed of gas molecules increases during the process $A\rightarrow B$
B. Such a graph is not possible.
C. Root mean square (RMS) speed of gas molecules decreases during the process \( A \rightarrow B \)
D. Density of the gas increases during the process $A\rightarrow B$.
E. If $P_B = 3P_A$, then $V_A = 4V_B$ (Where $P_A, V_A, P_B$ & $V_B$ represent pressure and volume values at states A and B).
Answer: D
A d.c. voltage with appreciable riple expressed as $V={ V }_{ 1 }+{ V }_{ 2 }cos\omega t$ is applied to a resister R. The amount of heat generated per second is given by

Options:
A. \cfrac { { V }_{ 1 }^{ 2 }+{ 3V }_{ 2 }^{ 2 } }{ 2R }
B. \cfrac { { V }_{ 1 }^{ 2 }+{ V }_{ 2 }^{ 2 } }{ 4R }
C. $$\cfrac { { V }_{ 1 }^{ 2 }+{ 2V }_{ 2 }^{ 2 } }{ 2R } $$
D. $$None of these.$$
E. \cfrac { { V }_{ 1 }^{ 2 }+{ 2V }_{ 2 }^{ 2 } }{ 3R }
F. \cfrac { { V }_{ 1 }^{ 2 }+{ V }_{ 2 }^{ 2 } }{ 6R }
G. \cfrac { { V }_{ 1 }^{ 2 }+{ V }_{ 2 }^{ 2 } }{ 3R }
H. $$\cfrac { { V }_{ 1 }^{ 2 }+{ V }_{ 2 }^{ 2 } }{ 2R } $$
I. \cfrac { { V }_{ 1 }^{ 2 }+{ 4V }_{ 2 }^{ 2 } }{ 2R }
J. $$\cfrac { { 2V }_{ 1 }^{ 2 }+{ V }_{ 2 }^{ 2 } }{ 2R } $$
Answer: H
The uncertainity in position for a dust particle $(m={ 10 }^{ -11 }g$; diameter $={ 10 }^{ -4 }cm$ and velocity $={ 10 }^{ -4 }cm/s)$ will be (The error in measurement of velocity is 1%)

Options:
A. $$5.27\times { 10 }^{ -7 }\quad cm$$
B. $$5.27 \times { 10 }^{ -10 } \quad cm$$
C. $$5.27 \times { 10 }^{ -8 } \quad cm$$
D. $$5.27 \times { 10 }^{ -3 } \quad cm$$
E. $$5.27 \times { 10 }^{ -5 } \quad cm$$
F. $$5.27 \times { 10 }^{ -4 } \quad cm$$
G. $$5.27\times { 10 }^{ -6 }\quad cm$$
H. $$5.27 \times { 10 }^{ -9 } \quad cm$$
Answer: F
In the ionic equation, $xCH_3CH_2OH+yI_2+zOH^-\rightarrow CHI_3+{HCO_2}^-+I^-+H_2O$, the valuexs of $x,y,z$ are:

Options:
A. $$x=1, y=8, z=8$$
B. x=1, y=4, z=8
C. x=1, y=4, z=5
D. x=1, y=3, z=6
E. $$x=1, y=6, z=4$$
F. x=1, y=4, z=7
G. $$x=1, y=4, z=6$$
H. $$x=1, y=8, z=12$$
I. $$x=1, y=5, z=6$$
J. $$x=1, y=3, z=8$$
Answer: G
A dc source of emf ${E}_{1}=100V$ and internal resistance $r=0.5\Omega$ a storage battery of emf ${E}_{2}=90V$ and an external resistance $R$ are connected as shown in figure. For what value of $R$ no current will pass through the battery?

Options:
A. $$2.5\Omega$$
B. 1.5\Omega
C. 4.0\Omega
D. 6.5\Omega
E. $$3.5\Omega$$
F. $$5.5\Omega$$
G. 6.0\Omega
H. 4.5\Omega
Answer: F
The friction of the air causes a vertical retardation equal to $10\%$ of the acceleration due to gravity. Take $g =10\ m/s^{2}$ . The maximum height and time to reach the maximum height will be decreased by

Options:
A. $$11\%,\ 9\%$$
B. 10\%,\ 10\%
C. 10\%,\ 9\%
D. $$8\%,\ 8\%$$
E. $$11\%,\ 11\%$$
F. 8\%,\ 9\%
G. $$9\%,\ 9\%$$
H. $$9\%,\ 10\%$$
I. 8\%,\ 10\%
J. 10\%,\ 8\%
Answer: G
A solenoid of inductance $L$ and resistance $r$ is connected in parallel to a resistance $R$ and a battery of emf $E$. Initially if the switch is closed for a long time and at $t=0$, then the :

Options:
A. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+4r)t/L}$
B. amount of heat generated in solenoid is $\dfrac{E^2L}{2r(r+R)}$
C. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+3r)t/L}$
D. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+r)t/L}$
E. induced emf across solenoid at time $t=0$ is $\dfrac{E(R+r)}{r}$
F. potential difference across solenoid at $t=0$ is $E$
G. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R-r)t/L}$
H. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+5r)t/L}$
I. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+r/2)t/L}$
J. current through solenoid at any time $t$, after opening the switch is $\dfrac{E}{r}e^{-(R+2r)t/L}$
Answer: D
A student is performing an experiment using a resonance column and a tuning fork of frequency 244 s$^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at  which resonance occurs is (0.350 $\pm$ 0.005)m, the gas in the tube is (Useful information : $\sqrt{167RT} = 640  J^{1/2}; \sqrt{140 RT}= 590  J^{1/2}  mole^{-\frac{1}{2}}.$ The molar masses M in grams are given in the option. Take the values of $\displaystyle \sqrt{\frac{10}{M}}$ for each gas given)

Options:
A. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{19}{32})$
B. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{16}{32})$
C. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{15}{32})$
D. Oxygen $\displaystyle ( M= 32, \sqrt{\frac{10}{32}} = \frac{9}{16})$
E. Nitrogen $\displaystyle ( M = 28, \sqrt{\frac{10}{28}} = \frac{3}{5} )$
F. Argon $\displaystyle ( M = 36, \sqrt{([\frac{10}{36}}) = \frac{18}{32})$
G. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{19}{31})$
H. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{17}{32})$
I. Neon $\displaystyle ( M = 20, \sqrt{\frac{10}{20}} = \frac{7}{10})$
J. Argon $\displaystyle ( M = 36, \sqrt{\frac{10}{36}} = \frac{21}{32})$
Answer: H
Calculate the extent of hydrolysis and the $pH$ of $0.02\ M$ ${CH}_{3}COO{NH}_{4}$. $[{K}_{b}({NH}_{3})=1.8\times {10}^{-5}$, ${K}_{a}({CH}_{3}COOH)=1.8\times {10}^{-5}$]

Options:
A. $0.56$%, $pH=7$
B. $0.44$%, $pH=10$
C. 0.58%, pH=6
D. 0.64%, pH=8
E. $0.54$%, $pH=6$
F. $0.76$%, $pH=12$
G. 0.56%, pH=9
H. 0.68%, pH=6
I. 0.60%, pH=5
J. None of these
Answer: A
Consider the following amplitude modulated (AM) signal,where $f_m<B$.$x_{AM}(t)=10(1+0.5\sin{2\pi f_mt})\cos{2\pi f_ct}$The average side-band power for the AM signal given above is

Options:
A. 7.8125
B. $$3.125$$
C. $$25$$
D. 10.625
E. 15.625
F. $$12.5$$
G. 18.75
H. $$6.25$$
I. 9.375
Answer: F
The velocity of electron from a platinum surface when radiation of 200 nm falls on it will be given, the work function of platinum is 5 eV.$\left( 1eV=1.6\times { 10 }^{ -19 }J \right) $

Options:
A. 6.82 \times { 10 }^{ 2 }{ ms }^{ -1 }
B. 6.82 \times { 10 }^{ 4 }{ ms }^{ -1 }
C. 6.14 \times 10^{4} \, {ms}^{-1}
D. $$6.84\times { 10 }^{ 2 }{ ms }^{ - }$$
E. $$6.12\times { 10 }^{ 4 }{ ms }^{ -1 }$$
F. $$6.25\times { 10 }^{ 3 }{ ms }^{ -1 }$$
G. 6.82 \times { 10 }^{ 3 }{ ms }^{ -1 }
H. 6.85 \times { 10 }^{ 2 }{ ms }^{ -1 }
I. 6.54 \times 10^{4} \, {ms}^{-1}
J. $$6.52\times { 10 }^{ 5 }{ ms }^{ -1 }$$
Answer: D
Assuming the water resistance to be negligible, find the horizontal component of the force with which the man acted on the raft during the motion.

Options:
A. \displaystyle F=-\frac{mM}{4(M+m)}\frac{dv^\prime}{dt}
B. $$\displaystyle F=\frac{mM}{M+m}\frac{dv^\prime}{dt}$$
C. \displaystyle F=-\frac{3mM}{M+m}\frac{dv^\prime}{dt}
D. $$\displaystyle F=-\frac{2mM}{M+m}\frac{dv^\prime}{dt}$$
E. \displaystyle F=\frac{4mM}{M+m}\frac{dv^\prime}{dt}
F. \displaystyle F=-\frac{mM}{2(M+m)}\frac{dv^\prime}{dt}
G. $$\displaystyle F=\frac{2mM}{M+m}\frac{dv^\prime}{dt}$$
H. \displaystyle F=-\frac{5mM}{M+m}\frac{dv^\prime}{dt}
I. \displaystyle F=-\frac{mM}{3(M+m)}\frac{dv^\prime}{dt}
J. $$\displaystyle F=-\frac{mM}{M+m}\frac{dv^\prime}{dt}$$
Answer: J
Let $\lambda_{lpha}$, $\lambda_\beta$ and $\lambda_{lpha}^{'}$,  denote the wavelengths of the X-rays of the $K_lpha$, $K_\beta$ and $L_lpha$  line in the characteristic X-rays for a metal. Then

Options:
A. \displaystyle \frac{1}{\lambda_{\alpha}} = \frac{1}{\lambda_{\beta}} - \frac{1}{\lambda_{\alpha}^{'}}
B. \displaystyle \frac{1}{\lambda_{\alpha}} = \frac{1}{\lambda_{\beta}} + \frac{1}{\lambda_{\alpha}^{'}}
C. $$\lambda_{lpha}^{'} > \lambda_{lpha} > \lambda_\beta$$
D. \displaystyle \frac{1}{\lambda_{\alpha}^{'}} = \frac{1}{\lambda_{\alpha}} + \frac{1}{\lambda_{\beta}}
E. $$\displaystyle \frac{1}{\lambda_{\beta}} = \frac{1}{\lambda_{lpha}} + \frac{1}{\lambda_{lpha}^{'}}$$
F. \frac{1}{\lambda_{\alpha}} = \frac{1}{\lambda_{\beta}} + \frac{1}{\lambda_{\alpha}^{'}}
G. $$\lambda_{lpha}^{'} > \lambda_{\beta} > \lambda_lpha$$
H. \displaystyle \frac{1}{\lambda_{\beta}} = \frac{1}{\lambda_{\alpha}^{'}} + \frac{1}{\lambda_{\alpha}}
I. $$\displaystyle \frac{1}{\lambda_{lpha}} + \frac{1}{\lambda_{\beta}} = \frac{1}{\lambda_{lpha}^{'}}$$
J. \displaystyle \frac{1}{\lambda_{\alpha}^{'}} = \frac{1}{\lambda_{\beta}} + \frac{1}{\lambda_{\alpha}}
Answer: E
In the Bohr's model, for unielectronic species following symbols are used
$r_{n,z} \rightarrow$ Radius of $n^{th}$ orbit with atomic number "z"
$U_{n,z} \rightarrow$ Potential energy of electron in $n^{th}$ orbit with atomic number "z"
$K_{n,z} \rightarrow$ Kinetic energy of electron in $n^{th}$ orbit with atomic number "z"
$v_{n,z} \rightarrow$ Velocity of electron in $n^{th}$ orbit with atomic number "z"
$T_{n,z} \rightarrow$ Time period of revolution of electron in $n^{th}$ orbit with atomic number "z"
Calculate z in all in cases.

Options:
A. U_{1,2} : K_{1,z} = -5 : 1
B. U_{1,2} : K_{1,z} = -6 : 1
C. U_{1,2} : K_{1,z} = -10 : 1
D. $$v_{1,z} : v_{3,1} = 9 : 1$$
E. $$U_{1,2} : K_{1,z} = -8 : 1$$
F. U_{1,2} : K_{1,z} = -12 : 1
G. U_{1,2} : K_{1,z} = -7 : 1
H. U_{1,2} : K_{1,z} = -9 : 1
Answer: E
Two cylinder A and B having piston connected by massless rod (as shown in fig). The cross-section are of two cylinder are same and equal to 's'. The cylinder A contains m gm of an ideal gas at pressure $P_0$ and Temperature $T_0$. the cylinder B contain identical gas at same temperature $T_0$ but has different mass. The piston is held at the stare in the position so that volume of gas in cylinder A and cylinder B are same and is equal to $V_0$..The walls and piston of cylinder A are thermally insulated, whereas cylinder B is maintained at temperature $T_0$ reservoir. The whole system is vacume. Now the piston is slowly released and it moves towards left and mechanical equilibrium is reached at the state when the volume of gas in cylinder A becomes $\frac {V_0}{2}$. then (here $\gamma $ for the gas=1.5)
The mass of gas in cylinder B:

Options:
A. 2\sqrt 2
B. 5\sqrt 2
C. $$7\sqrt 2$$
D. 6\sqrt 2
E. 8\sqrt 2
F. $$\sqrt 2$$
G. none of these
H. $$3\sqrt 2$$
I. 4\sqrt 2
Answer: H
CsBr crystallises in a body centred cubic lattice.The until cell length is 436.6pm.Given that the atomic mass of Cs=133 and that of Br=80 amu and Avogadro number being $ 6.02\times { 10 }^{ 23 } { mol }^{ -1 }$,the density of $CsBr$ is:

Options:
A. 8.15{ g }/{ { cm }^{ 3 } }
B. $$42.5{ g }/{ { cm }^{ 3 } }$$
C. $$8.25{ g }/{ { cm }^{ 3 } }$$
D. 8.05{ g }/{ { cm }^{ 3 } }
E. 8.20{ g }/{ { cm }^{ 3 } }
F. 8.45{ g }/{ { cm }^{ 3 } }
G. $$0.425{ g }/{ { cm }^{ 3 } }$$
H. $$4.55{ g }/{ { cm }^{ 3 } }$$
I. $$4.25{ g }/{ { cm }^{ 3 } }$$
Answer: I
An athlete takes 20 breathes per minute at room temperature. The air inhaled in each breath is 200 mL which contains 20% oxygen by volume, while exhaled air contains 10% oxygen by volume. Assuming that all the oxygen consumed is used for converting glucose into $CO_2$ and $H_2O(l)$, how much glucose will be burnt in the body in 1 hour and what is the heat produced? (Room temperature $= 27^{\circ}\! \ C$ and enthalpy of combustion of glucose is $-2822.5 \: kJ \: mol^{-1} \: at \: 0^{\circ}\! \ C$)

Options:
A. a) $280\ g$   b) $= 478.66 \: kJ \: heat$
B. a) $180\ g$   b) $= 458.66 \: kJ \:heat$
C. a) $270\ g$   b) $= 448.66 \: kJ \:heat$
D. a) $200\ g$   b) $= 468.66 \: kJ \: heat$
E. a) $360\ g$   b) $= 358.66 \: kJ \: heat$
F. None of the above
G. a) $190\ g$   b) $= 455.66 \: kJ \:heat$
H. a) $190\ g$   b) $= 458.66 \: kJ \:heat$
I. a) $180\ g$   b) $= 455.66 \: kJ \:heat$
J. a) $210\ g$   b) $= 468.66 \: kJ \: heat$
Answer: B