Q. For a uniformly charged ring of radius $R$, the electric field on its axis has the largest magnitude at a distance $h$ from its centre. Then value of $h$ is :

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

Q. Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index $\mu$. A student finds that, irrespective of what the incident angle $i$ (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of $\mu$ is :

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

Q. Surface of certain metal is first illuminated with light of wavelength ${\lambda }_1=350nm$ and then, by light of wavelength ${\lambda }_2=54nm$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of $2$. The work function of the metal (in $eV$) is close to:
(Energy of photon $=\frac{1240}{\lambda \left(innm\right)}eV)$

1. $1.8$
2. $1.4$
3. $5.6$
4. $2.5$

Q. A gas can be taken from $A$ to $B$ via two different processes $ACB$ and $ADB$. When path $ACB$ is used $60J$ of heat flows into the system and $30J$ of work is done by the system. If path $ADB$ is used work done by the system is $10J$. The heat Flow into the system in path $ADB$ is :

1. $20J$
2. $80J$
3. $100J$
4. $40J$

Q. A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of $10A$. The magnetic field at the point $O$ will be close to :

1. $1.5\times {10}^{-5}T$
2. $1.0\times {10}^{-5}T$
3. $2.0\times {10}^{-7}T$
4. $1.0\times {10}^{-7}T$

Q. Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is $16$. The intensity of the waves are in the ratio:

1. $25:9$
2. $4:1$
3. $6:9$
4. $5:3$

Q. Three charges $+Q,q,+Q$ are placed respectively, at distance, $0,d/2$ and $d$ from the origin, on the x-axis. If the net force experienced by $+Q$, placed at $x=0$, $Ls$ zero, then value of $q$ is :

1. $-Q/4$
2. $+Q/4$
3. $+Q/2$
4. $-Q/2$

Q. When the switch $S$, in the circuit shown, is closed, then the value of current $i$ will be :

1. $3A$
2. $5A$
3. $4A$
4. $2A$

Q. A conducting circular loop made of a thin wire, has area $3.5\times {10}^{-3}{m}^2$ and resistance $10\Omega$. It is placed perpendicular to a time dependent magnetic field $B\left(t\right)=\left(0.4T\right)\sin \left(50\pi t\right)$. The field is uniform in space. Then the net charge flowing through the loop during $t=0s$ and $t=10ms$ is close to:

1. $0.14mC$
2. $0.21mC$
3. $6mC$
4. $7mC$

Q. A particle is moving with a velocity $\overline{v}=K(y\hat{i}+x\hat{j})$, where $K$ is a constant. The general equation for its path is:

1. $xy=constant$
2. $y^2=x^2+constant$
3. $y=x^2+constant$
4. $y^2=x+constant$

Q. A bar magnet is demagnetized by inserting it inside a solenoid of length $0.2m,100turas$, and carrying a current of $5.2A$. The coercivity of the bar magnet is:

1. $1200A/m$
2. $2600A/m$
3. $5200A/jm$
4. $285A/m$

Q. A convex lens is put $10cm$ from a light source and it makes a sharp image on a screen, kept $10cm$ from the lens. Now a glass block (refractive index 1.5) of $1.5cm$ thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance $d$. Then $d$ is :

1. $1.1cm$ away from the lens
2. $0.55cm$ towards the lens
3. $0.55cm$ away from the lens
4. $0$

Q. A parallel plate capacitor is made of two square plates of side '$a$', separated by a distance $d(d<<a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$, as shown in the figure.
The capacitance of this capacitor is :

1. $\frac{1}{2}\frac{k{\in }_0{a}^2}{d}$
2. $\frac{k{\in }_0{a}^2}{2d(K+1)}$
3. $\frac{k{\in }_0{a}^2}{d(K-1)}lnK$
4. $\frac{k{\in }_0{a}^2}{d}lnK$

Q. A copper wire is stretched to make it $0.5\%$ longer. The percentage change in its electrical resistance if its volume remains unchanged is:

1. $0.5\%$
2. $2.5\%$
3. $2.0\%$
4. $1.0\%$

Q. Three blocks $A,B$ and $C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given a brutal speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically $\frac{5}{6}th$ of the initial kinetic energy is lost in the whole process. What is the value of $\frac{M}{m}$?

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

Q. Two masses m and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system (see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $0$. If the rod is rota ted by ${\theta }_0$ and released, the tension in it when it passes through its mean position will be:

1. $\frac{k{\theta }_0^2}{2l}$
2. $\frac{2k{\theta }_0^2}{l}$
3. $\frac{3k{\theta }_0^2}{l}$
4. $\frac{k{\theta }_0^2}{l}$

Q. The temperature difference of ${120}^{o}C$ is maintained between two ends of a uniform rod $AB$ of length $2L$. Another bent rod $PQ$, of same cross-section as $AB$ and length $\frac{3L}{2}$, is connected across $AB$ (see figure). In steady state, the temperature difference between $P$ and $Q$ will be close to:

1. ${60}^{o}C$
2. ${35}^{o}C$
3. ${75}^{o}C$
4. ${45}^{o}C$

Q. An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as showm=n in figure. If $AB=BC$, and the angle made by $AB=B$, and the angle made by $AB$ with downward vertical is $\theta$, then:

1. $\tan \theta =\frac{1}{3}$
2. $\tan \theta =\frac{2}{\sqrt{3}}$
3. $\tan \theta =\frac{1}{2}$
4. $\tan \theta =\frac{1}{2\sqrt{3}}$

Q. A mixture of $2$ moles of helium gas (atomic mass $=4u$), and $1$ mole of argon gas (atomic mass $=40u$) is kept at $300K$ in a container. The ratio of their rms speeds $\left[\frac{V_{rms}\left(helium\right)}{V_{rms}\left(argon\right)}\right]$, is close to:

1. $0.45$
2. $2.24$
3. $0.32$
4. $3.16$

Q. A block of mass $m$, lying on a smooth horizontal surface, is attached to a spring (of negligible mass) of spring constant $k$. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force $F$, the maximum speed of the block is :

1. $\frac{F}{\pi \sqrt{mk}}$
2. $\frac{F}{\sqrt{mk}}$
3. $\frac{2F}{\sqrt{mk}}$
4. $\frac{\pi F}{\sqrt{mk}}$

Q. A resistance is shown in the figure. Its value and tolerance are given respectively by:

1. $270K\Omega ,5\%$
2. $270K\Omega ,10\%$
3. $27K\Omega ,10\%$
4. $27K\Omega ,20\%$

Q. If the angular momentum of a planet of mass $m$ moving around the Sun in a circular orbit $L$ about the center of the Sun its areal velocity is:

1. $\frac{4L}{m}$
2. $\frac{L}{m}$
3. $\frac{L}{2m}$
4. $\frac{2L}{m}$

Q. An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is $d(>>a)$. If the loop applies a force $F$ on the wire then :

1. $F\propto {\left(\frac{a}{d}\right)}^2$
2. $F=0$
3. $F\propto \left(\frac{a^2}{d^3}\right)$
4. $F\propto \left(\frac{a}{d}\right)$

Q. A block of mass $10kg$ is kept on a rough inclined plane as shown in the figure. A force of $3N$ is applied on the block. The coefficient of static friction between the plane and the block is $0.6$. What should be the minimum value of force $P$, such that the block does not move downward? (take $g=10m{s}^{-2}$)

1. $32N$
2. $25N$
3. $18N$
4. $44N$

Q. A rod, of length $L$ at room temperature and uniform area of cross section $A$, is made of a metal having a coefficient of linear expansion ${}^{o}C$. It is observed that an external compressive force $F$, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by $\Delta TK$. Young's modulus, $Y$, for this metal is :

1. $\frac{F}{A\alpha (\Delta T-273)}$
2. $\frac{F}{A\alpha \Delta T}$
3. $\frac{F}{2A\alpha \Delta T}$
4. $\frac{2F}{A\alpha \Delta T}$

Q. Drift speed of electrons, when $1.5A$ of current flows in a copper wire of cross section $5mm2$, is $v$. If the electron density in copper is $9\times {10}^{28}/m^3$ the value of $v$ in $mm/s$ is close to (Take charge of electron to be $=1.6\times {10}^{-19}C$)

1. $0.2$
2. $3$
3. $2$
4. $0.02$

Q. A heavy ball of mass $M$ is suspended from the ceiling of a car by a light string of mass $m(m<<M)$. When the car is at rest, the speed of transverse waves in the string is $60m{s}^{-1}$. When the car has an acceleration a, the wave-speed increases to $60.5m{s}^{-1}$. The value of a, in terms of gravitational acceleration $g$, is closest to :

1. $\frac{g}{5}$
2. $\frac{g}{20}$
3. $\frac{g}{30}$
4. $\frac{g}{10}$

Q. A plane electromagnetic wave of frequency $50MHz$ travels in free space along the positive x-direction. At a particular point in space and time, $\overrightarrow{E}=6.3\hat{j}V/m$. The corresponding magnetic field $\overrightarrow{B}$, at that point will be:

1. $18.9\times {10}^{-8}\hat{k}T$
2. $6.3\times {10}^{-8}\hat{k}T$
3. $2.1\times {10}^{-8}\hat{k}T$
4. $18.9\times {10}^8\hat{k}T$

Q. A sample of radioactive material $A$, that has an activity of $10mCi(1Ci=3.7\times {10}^{10}decays/s)$, has twice the number of nuclei as another sample of a different radioactive maternal B which has an activity of $20mCi$. The correct choices for half-life of $A$ and $B$ would then be respectively :

1. 20 days and 5 days
2. 10 days and 20 days
3. 5 days and 10 days
4. 10 days and 40 days

Q. The mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is ${10}^{19}{m}^{-3}$ and their mobility is $1.6m^2/(V.s)$ then the resistivity of the semiconductor (since it is an n-type semiconductor contribution of holes is ignored) is close to:

1. $0.4\Omega m$
2. $4\Omega m$
3. $0.2\Omega m$
4. $2\Omega m$