Q. Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

1. $\frac{11}{10\lambda }$
2. $\frac{1}{9\lambda }$
3. $\frac{1}{10\lambda }$
4. $\frac{11}{11\lambda }$

Q. A ball is thrown upward with an initial velocity $V_0$ from the surface of the earth. The motion of the ball is affected by a drag force equal to $m\gamma v^2$ (where m is mass of the ball, $v$ is its instantaneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is:

1. $\frac{1}{\sqrt{\gamma g}}si{n}^{-1}\left(\sqrt{\frac{\gamma }{g}}\right)V_0$
2. $\frac{1}{\sqrt{\gamma g}}ta{n}^{-1}\left(\sqrt{\frac{\gamma }{g}}\right)V_0$
3. $\frac{1}{\sqrt{\gamma g}}1n(1+\sqrt{\frac{\gamma }{g}})V_0$
4. $\frac{1}{\sqrt{2\gamma g}}ta{n}^{-1}\left(\sqrt{\frac{2\gamma }{g}}\right)V_0$

Q. The electric field of a plane electromagnetic wave is given by
$\overrightarrow{y}=E_0\hat{i}cos\left(kz\right)\left(\omega t\right)$
The corresponding magnetic field $\overrightarrow{B}$ is then given by:

1. $\overrightarrow{B}=\frac{E_0}{c}\hat{i}sin\left(kz\right)cos\left(\omega t\right)$
2. $\overrightarrow{B}=\frac{E_0}{c}\hat{j}sin\left(kz\right)cos\left(\omega t\right)$
3. $\overrightarrow{B}=\frac{E_0}{c}\hat{k}sin\left(kz\right)cos\left(\omega t\right)$
4. $\overrightarrow{B}=\frac{E_0}{c}\hat{j}cos\left(kz\right)sin\left(\omega t\right)$

Q. in a photoelectric effect experiment the threshold wavelength of the light is $380nm$. If the wavelength of incident light is $260nm$, the maximum kinetic energy electrons will be:
Given $E\left(ineV\right)=\frac{1237}{\lambda \left(innm\right)}$

1. $15.1eV$
2. $4.5eV$
3. $1.5eV$
4. $3.0eV$

Q. Two coaxial disc, having moments if inertia $I_1$ and $\frac{I_1}{2}$, are roatating with respective angular velocities ${\omega }_1$ and $\frac{{\omega }_1}{2}$, about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If $E_f$ and $E_i$ the final and initial total energies, then $(E_f-E_i)$ is :

1. $\frac{I_1{\omega }_1^2}{12}$
2. $\frac{3}{8}{I}_1{\omega }_1^2$
3. $\frac{I_1{\omega }_1^2}{6}$
4. $\frac{-I_1{\omega }_1^2}{24}$

Q. A moving coil galvanometer allows a full scale current of ${10}^{-4}A$. A series resistance of $2M\Omega$ is required to convert the above galvanometer into a voltmeter of range $0-5V$. therefore the value of shunt resistance required to convert the above galvanometer into an ammeter of range $0-10mA$ is:

1. $40\Omega$
2. $100\Omega$
3. $10\Omega$
4. $500\Omega$

Q. In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure.

SI.No.	R(\Omega|)	$l\left(cm\right)$
1.	1000	60
2.	100	13
3.	10	1.5
4.	1	1.0

Which of the readings is inconsistent?

1. $3$
2. $4$
3. $1$
4. $2$

Q. The displacement of a damped harmonic oscillator is given by $x\left(t\right)=e^{-01.1t}cos(10\pi t+\Phi ).$ Here $t$ is in seconds. The time taken for its amplitude of vibration to drop to half for its initial value is close to :

1. $4s$
2. $7s$
3. $13s$
4. $27s$

Q. A cylinder with fixed capacity of $67.2$ lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by ${20}^{0}C$ is :

1. $374J$
2. $350J$`
3. $700J$
4. $748J$

Q. A thin disc of mass M and radius R has per unit area $\sigma \left(r\right)=k{r}^2$ where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular ti its plane is :

1. $2\frac{M{R}^2}{6}$
2. $2\frac{M{R}^2}{3}$
3. $2\frac{M{R}^2}{2}$
4. $2\frac{2M{R}^2}{3}$

Q. One plano-convex and one plano-concave lens of same radius of curvature ${}^{\prime }{R}^{\prime }$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is ${\mu }_1$ and that of $2$ is ${\mu }_2$ is:

1. $\frac{R}{2({\mu }_1-{\mu }_2)}$
2. $\frac{R}{{\mu }_1-{\mu }_2}$
3. $\frac{R}{2-({\mu }_1-{\mu }_2)}$
4. $\frac{2R}{{\mu }_1-{\mu }_2}$

Q. An npn transistor operates as a common emitter amplifier, with a power gain of $60dB$. The input circuit resistance is $100\Omega$ and the output load resistance is $10k\Omega$. The common emitter current gain $\beta$ is :

1. $60$
2. ${10}^4$
3. $6\times {10}^2$
4. ${10}^2$

Q. Figure shows charge $\left(q\right)$ versus voltage $\left(V\right)$ graph fro series and parallel combination of two given capacitors. The capacitances are :

1. $40\mu F$ and $10/muF$
2. $60\mu F$ and $40/muF$
3. $50\mu F$ and $30/muF$
4. $20\mu F$ and $30/muF$

Q. A stationary source emits sound wave of frequency $500Hz$. Two observers moving along a line passing through the source detect sound to be of frequencies $480Hz$ and $530Hz$, Their respective speeds are, in $m{s}^{-1}$
(Given speed of sound$=300ms)$

1. $12,18$
2. $16,14$
3. $8,18$
4. $12,16$

Q. A current of $5A$ passes through a copper conductor $(resistivity=1.7\times {10}^{-8}\Omega m$) of radius of cross-section $5mm$. Find the mobility of the charges if their drift velocity is $1.1\times {10}^{-3}m/s$

1. $1.3m^2/Vs$
2. $1.8m^2/Vs$
3. $1.5m^2/Vs$
4. $1.0m^2/Vs$

Q. A transformer consisting of $300$ turns in the primary and $150$ turns in the secondary gives output power of $2.2kW$.If the current in the secondary coil is $10A$, then the input voltage and current in the primary coil are :

1. $220V$ and $10A$
2. $440V$ and $5A$
3. $440V$ and $20A$
4. $220V$ and $20A$

Q. In the given circuit, an ideal voltmeter connected across the $10\Omega$ resistance reads $2V$. The internal resistance $r$, of each cell is :

1. $1.5\Omega$
2. $0\Omega$
3. $1\Omega$
4. $0.5\Omega$

Q. A particle of mass m is moving along a trajectory give by
$x=x_0+acos{\omega }_{1}t$
$y=y_0+bsin{\omega }_{2}t$
The torque, acting on the particle about the origin, at $t=0$ is:

Q. A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicular to the plane. let $r_p$, $r_e$ and $r_{He}$ be their respectively radii, then ,

Q. Two wires $A$ and $B$ are carrying currents $I_1$ and $I_2$ as shown in the figure. The separation between them is $d$. A third
wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from $A$ such that the net force acting on it is
zero. The possible values of $x$ are

Q. A message signal of frequency $100MHz$ and peak voltage $100V$ is used to execute amplitude modulation on a carrier wave of frequency $300GHz$ and peak voltage $400V$. The modulation index and difference between the two side band frequency are :

Q. In an experiment, the resistance of a material is plotted as a function of temperature (in some range). As shown in the figure, it is a straight line. One may conclude that :

Q. A ray light $AO$ in vacuum is incident on a glass slab at angle ${60}^0$ and refracted at angle ${30}^0$ along $OB$ as shown in the figure. The optical path length of light ray from A to B is :

Q. A $25\times {10}^{-3}$ volume cylinder is filled with $1mol$ of $O_2$ gas at room temperature $\left(3ooK\right)$. The molecular diameter of $O_2$, and its root mean square speed, are found to be $0.3nm$, and $200m/s$, respectively. What is the average collision rate (per second) for an $O_2$ molecule ?

Q. N mole of an idelal gas with constant volume heat capacity $C_V$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is :

Q. A uniformly charged ring of radius $3a$ and total charge $q$ is placed in xy-plane centred at origin. A point charge $q$ is moving towards the ring along the z-axis and has speed $u$ at $z-4a$. The minimum value of $u$ such that it crosses the origin is :

Q. The value of acceleration due to gravity at Earth's surface is $9.8m{s}^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to $4.9m{s}^{-2}$, is close to :
(Radius o f earth =$6.4\times {10}^{6}m)$

Q. Given below in the left column are different modes of communication using the kinds of waves given the right column.

A.	Optical Fibre communication	P.	Ultrasound
B.	Radar	Q.	Infrared Light
C.	Sonar	R.	Microwaves
D.	Mobile phones	S.	Radio Waves

Q. The ratio of surface tensions of mercury and water is given to be $7.5$ while the ratio of their densities is $13.6$. Their contact angles, with glass, are close to ${135}^0$ and $0^0$, respectively. It is observed that mercury gets depressed by an amount $h$ in a capillary tube of radius $r_1$, while water rises by the same amount h in a capillary tube of radius $r_2$. The ratio, $\left(r_2/r_1\right)$, is then close to :

Q. Two particle, of masses $M$ and $2M$, moving, ash shown , with speeds of $10m/s$ and $5m/s$, collide elastically at the origin. After the collision, they move along the indicated directions with speeds $v_1$ and $v_2$, respectively. the values of $v_1$ and $v_2$ are nearly: