Q. A heating element has a resistance of $100\Omega$ at room temperature. When it is connected to a supply of $220V$, a steady current of $2A$ passes in it and temperature is ${500}^{\circ }C$ more than room temperature. What is the temperature coefficient of resistance of the heating element?

1. $1\times {10}^{-4}{}^{\circ }{C}^{-1}$
2. $5\times {10}^{-4}{}^{\circ }{C}^{-1}$
3. $2\times {10}^{-4}{}^{\circ }{C}^{-1}$
4. $0.5\times {10}^{-4}{}^{\circ }{C}^{-1}$

Q. In a circuit for finding the resistance of a galvanometer by half deflection method, a $6V$ battery and a high resistance of $11k\Omega$ are used. The figure of merit of the galvanometer $60\mu A/division$. In the absence of shunt resistance, the galvanometer produces a deflection of $\theta =9$ divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of $\theta /2$, is closest to

1. $55\Omega$
2. $110\Omega$
3. $220\Omega$
4. $550\Omega$

Q. A power transmission line feeds input power at $2300V$ to a step down transformer with its primary windings having $4000$ turns, giving the output power at $230V$. If the current in the primary of the transformer is $5A$, and its efficiency is $90\%$, the output current would be:

1. $20A$
2. $50A$
3. $45A$
4. $25A$

Q. One mole of an ideal monoatomic gas is taken along the path $ABCA$ as shown in the $PV$ diagram. The maximum temperature attained by the gas along the path $BC$ is given by :-

1. $\frac{25}{8}\frac{P_0{V}_0}{R}$
2. $\frac{25}{4}\frac{P_0{V}_0}{R}$
3. $\frac{25}{16}\frac{P_0{V}_0}{R}$
4. $\frac{5}{8}\frac{P_0{V}_0}{R}$

Q. A galvanometer with its coil resistance $25\Omega$ requires a current of $1mA$ for its full deflection. In order to construct an ammeter to read up to a current of $2A$, the approximate value of the shunt resistance should be

1. $2.5\times {10}^{-2}\Omega$
2. $1.25\times {10}^{-3}\Omega$
3. $2.5\times {10}^{-3}\Omega$
4. $1.25\times {10}^{-2}\Omega$

Q. Two identical conducting spheres $A$ and $B$, carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is $F$. A third identical conducting sphere, $C$, is uncharged. Sphere $C$ is first touched to $A$, then to $B$, and the removed. As a result, the force between $A$ and $B$ would be equal to

1. $\frac{F}{2}$
2. $\frac{3F}{4}$
3. $F$
4. $\frac{3F}{8}$

Q. An oscillator of mass $M$ is at rest in its equilibrium position in a potential $V=\frac{1}{2}k(x-X{)}^2$. A particle of mass $m$ comes from right with speed $u$ and collides completely inelastically with $M$ and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after $13$ collisions is: $(M=10,m=5,u=1,k=1)$.

1. $\frac{1}{2}$
2. $\frac{2}{3}$
3. $\frac{1}{\sqrt{3}}$
4. $\sqrt{\frac{3}{5}}$

Q. A coil of cross-sectional area $A$ having $n$ turns is placed in a uniform magnetic field $B$. When it is rotated with an angular velocity $\omega$, the maximum e.m.f. induced in the coil will be

1. $nBA\omega$
2. $\frac{3}{2}nBA\omega$
3. $3nBA\omega$
4. $\frac{1}{2}nBA\omega$

Q. At some instant, a radioactive sample $S_1$ having an activity $5\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\mu Ci$. The half lives of $S_1$ and $S_2$ are

1. $20$ years and $5$ years, respectively
2. $20$ years and $10$ years, respectively
3. $10$ year each
4. $5$ year each

Q. Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence.

1. Weight of the object, everywhere on the earth, will decrease
2. There will be no change in weight anywhere on the earth
3. Weight of the object, everywhere on the earth, will increase
4. Except at poles, weight of the object on the earth will decrease

Q. Two moles of helium are mixed with $n$ moles of hydrogen. If $\frac{C_P}{C_V}=\frac{3}{2}$ for the mixture, then the value of $n$ is

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

Q. Two sitar strings, $A$ and $B$, playing the note 'Dha' are slightly out of tune and produce beats and frequency $5Hz$. The tension of the string $B$ is slightly increased and the beat frequency is found to decrease by $3Hz$. If the frequency of $A$ is $425Hz$, the original frequency of $B$ is

1. $430Hz$
2. $428Hz$
3. $422Hz$
4. $420Hz$

Q. A body of mass starts moving from rest along x-axis so that its velocity varies as $v=a\sqrt{s}$ where $a$ is a constant and $s$ is the distance covered by the body. The total work done by all the forces acting on the body in the first seconds after the start of the motion is:

1. $\frac{1}{8}m{a}^4{t}^2$
2. $4m{a}^4{t}^2$
3. $8m{a}^4{t}^2$
4. $\frac{1}{4}m{a}^4{t}^2$

Q. The end correction of a resonance column is $1cm$. If the shortest length resonating with the tuning fork is $10cm$, the next resonating length should be

1. $32cm$
2. $40cm$
3. $28cm$
4. $36cm$

Q. Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths ${\lambda }_N,{\lambda }_A$ respectively. The ratio $\frac{{\lambda }_N}{{\lambda }_A}$ is closest to

1. ${10}^{-10}$
2. ${10}^{-1}$
3. ${10}^{-6}$
4. $10$

Q. A thin circular disk is in the $xy$ plane as shown in the figure. The ratio of its moment of inertia about $z$ and $z^{\prime }$ axes will be

1. $1:2$
2. $1:3$
3. $1:4$
4. $1:5$

Q. Unpolarized light of intensity $I$ is incident on a system of two polarizes, A followed by $B$. The intensity of emergent light is $I/2$. If a third polarizer $C$ is placed between $A$ and $B$, the intensity of emergent light is reduced to $I/3$. The angle between the polarizers $A$ and $C$ is $\theta$. Then

1. $\cos \theta ={\left(\frac{2}{3}\right)}^{1/4}$
2. $\cos \theta ={\left(\frac{1}{3}\right)}^{1/4}$
3. $\cos \theta ={\left(\frac{1}{3}\right)}^{1/2}$
4. $\cos \theta ={\left(\frac{2}{3}\right)}^{1/2}$

Q. In the given circuit, the current through zener diode is:

1. $2.5mA$
2. $3.3mA$
3. $6.7mA$
4. $5.5mA$

Q. A particle executes simple harmonic motion and is located at $x=a,b$ and $c$ at times $t_0,2t_0$ and $3t_0$ respectively. The frequency of the oscillation is

1. $\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+b}{2c}\right)$
2. $\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+b}{3c}\right)$
3. $\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{2a+3c}{b}\right)$
4. $\frac{1}{2\pi t_0}{\cos }^{-1}\left(\frac{a+c}{2b}\right)$

Q. Let $\overrightarrow{A}=(\hat{i}+\hat{j})$ and, $\overrightarrow{B}=(2\hat{i}-\hat{j})$. The magnitude of a coplanar vector $\overrightarrow{C}$ such that $\overrightarrow{A}\cdot \overrightarrow{C}=\overrightarrow{B}\cdot \overrightarrow{C}=\overrightarrow{A}\cdot \overrightarrow{B}$, is given by

1. $\sqrt{\frac{10}{9}}$
2. $\sqrt{\frac{9}{12}}$
3. $\sqrt{\frac{20}{9}}$
4. $\sqrt{\frac{5}{9}}$

Q. Two particles of the same mass $m$ are moving in circular orbits because of force, given by $F\left(r\right)=\frac{-16}{r}-r^3$
The first particle is at a distance $r=1$, and the second, at $r=4$. The best estimate for the ratio of kinetic energies of the first and the second particle is closest to

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

Q. The relative uncertainty in the period of a satellite orbiting around the earth is ${10}^{-2}$. If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the earth is :

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

Q. In the following circuit, the switch $S$ is closed at $t=0$. The charge on the capacitor $C_1$ as a function of time will be given by $(C_{eq}=\frac{C_1{C}_2}{C_1+C_2})$.

1. $C_{2}E[1-exp(-t/R{C}_2\left)\right]$
2. $C_{1}E[1-exp(-tR/C_1\left)\right]$
3. $C_{eq}E[1-exp(-t/R{C}_{eq}\left)\right]$
4. $C_{eq}Eexp(-t/R{C}_{eq})$

Q. The percentage errors in quantities $P,Q,R$ and $S$ are $0.5$%, $1$%, $3$% and $1.5$% respectively in the measurement of a physical quantity $A=\frac{P^3{Q}^2}{\sqrt{R}S}$.
The maximum percentage error in the value of $A$ will be

1. $8.5\%$
2. $6.0\%$
3. $7.5\%$
4. $6.5\%$

Q. A ray of light is incident at an angle of ${60}^{\circ }$ on one face of a prism of angle ${30}^{\circ }$. The emergent ray of light makes an angle of ${30}^{\circ }$ with incident ray. The angle made by the emergent ray with second face of prism will be:

1. ${30}^{\circ }$
2. ${90}^{\circ }$
3. $0^{\circ }$
4. ${45}^{\circ }$

Q. A small soap bubble of radius $4cm$ is trapped inside another bubble of radius $6cm$ without any contact. Let $P_2$ be the pressure inside the inner bubble and $P_0$, the pressure outside the outer bubble. Radius of another bubble with pressure difference $P_2-P_0$ between its inside and outside would be

1. $6cm$
2. $12cm$
3. $4.8cm$
4. $2.4cm$

Q. A plane electromagnetic wave of wavelength $\lambda$ has an intensity $I$. It is propagating along the positive $Y-direction$. The allowed expressions for the electric and magnetic fields are given by

1. $\overrightarrow{E}=\sqrt{\frac{I}{{ϵ}_{0}C}}\cos \left[\frac{2\pi }{\lambda }\right(y-ct\left)\right]\hat{i};\overrightarrow{B}=\frac{1}{c}E\hat{k}$
2. $\overrightarrow{E}=\sqrt{\frac{I}{{ϵ}_{0}C}}\cos \left[\frac{2\pi }{\lambda }\right(y-ct\left)\right]\hat{k};\overrightarrow{B}=-\frac{1}{c}E\hat{i}$
3. $\overrightarrow{E}=\sqrt{\frac{2I}{{ϵ}_{0}C}}\cos \left[\frac{2\pi }{\lambda }\right(y-ct\left)\right]\hat{k};\overrightarrow{B}=+\frac{1}{c}E\hat{i}$
4. $\overrightarrow{E}=\sqrt{\frac{2I}{{ϵ}_{0}C}}\cos \left[\frac{2\pi }{\lambda }\right(y+ct\left)\right]\hat{k};\overrightarrow{B}=\frac{1}{c}E\hat{i}$

Q. The de-Broglie wavelength $\left({\lambda }_B\right)$ associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state $\left({\lambda }_G\right)$ by :

1. ${\lambda }_B={\lambda }_G/3$
2. ${\lambda }_B={\lambda }_G/2$
3. ${\lambda }_B=2{\lambda }_G$
4. ${\lambda }_B=3{\lambda }_G$

Q. A carrier wave of peak voltage $14V$ is used for transmitting a message signal. The peak voltage of modulating signal given to achieve a modulation index of $80$% will be:

1. $11.2V$
2. $7V$
3. $28V$
4. $22.4V$

Q. A charge $q$ is spread uniformly over an insulated loop of radius $r$. If it is rotated with an angular velocity $\omega$ with respect to normal axis then the magnetic moment of the loop is

1. $\frac{1}{2}q\omega r^2$
2. $\frac{3}{2}q\omega r^2$
3. $\frac{4}{3}q\omega r^2$
4. $q\omega r^2$