Q. The total number of turns and cross section area in a solenoid is fixed. However, its length $L$ is varied by adjusting the separation between windings. The inductance of solenoid will be proportional to:

1. $1/L^2$
2. $L^2$
3. $1/L$
4. $L$

Q. A ball thrown vertically up (taken as +z axis) from the ground. The correct momentum height (p-h) diagram is:

1. 
   
2. 
   
3. 
   
4. 
   

Q. In the density measurement of a cube, the mass an edge length are measured as $(10.00\pm 0.10)kg$ and $(0.10\pm 0.01)m$, respectively. The error in the measurement of density:

Q. An $HCl$ molecule has rotational, translational and vibrational motions. If the rms velocity of $HCl$ molecules in its gaseous phase is $\overrightarrow{v}$, $m$ is its mass and $k_B$ is Boltzmann constant, then its temperature will be:

Q. The figure shows two process $A$ and $B$ for a gas. If $\Delta Q_A$ and $\Delta Q_B$ are the amount of heat absorbed by the system in two cases. and $\Delta U_A$ and $\Delta U_B$ are changes in internal energies, respectively, then:

Q. A wire of resistance $R$ is bent to form a square $ABCD$ as shown in figure. The effective resistance between $E$ and $C$ is:
($E$ is mid-point of arm $CD$)

Q. A simple pendulum oscillating in air has period $T$. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is $\frac{1}{16}$th of material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:

Q. Determine the charge on the capacitor in the given circuit:

Q. A system of three charges are placed as shown in the figure:
If $D>>d$ the potential energy of the system is best given by

Q. The stream of a river is flowing with a speed of $2km/h$. A swimmer can swim at a speed of $4km/h$. What should be the direction of the swimmer with respect to the flow of the river to cross the river straight?

Q. A body of mass $2kg$ makes an elastic collision with a second body at rest and continues to move in the original direction but with is one fourth of its original speed. What is the mass of the second body?

Q. A solid sphere of mass $M$ and radius $a$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $3a$ from the centre will be:

Q. The pressure wave, $P=0.01\sin [1000t-3x]N{m}^{-2}$, corresponds to the second produced by a vibrating blade on a day when atmospheric temperature is $0^{o}C$. On some other day, when temperature is $T$. the speed of sound produced by the same blade and at the same frequency is found to be $336m{s}^{-1}$. Approximate value of $T$ is

Q. An NPN transistor is used in common emitter configuration as an amplifier with $1kOmega$ load resistance. Signal voltage of $10mV$ is appled across the base-emitter. This produces a $3mA$ change in the collector current and $15\mu A$ change in the base current of the amplifier. The input resistance and voltage gain are:

Q. A moving coil galvanometer has resistance $50\Omega$ and it indicates full deflection at $4mA$ current. A voltmeter is made using this galvanometer and a $5k\Omega$ resistance. The maximum voltage that can be measured using this voltmeter, will be close to:

Q. The electric field of light wave is given as
$\overrightarrow{E}={10}^{-3}\cos (\frac{2\pi x}{5\times {10}^{-7}}-2\pi \times 6\times {10}^{14}t)\hat{x}\frac{N}{C}$. This light falls on a metal plate of work function $2eV$. The stopping potential of the photo-electrons is:
Given $E$ ( in eV) $=\frac{12375}{\lambda \left(in\mathring{A}\right)}$

Q. A capacitor with capacitance $5\mu F$ is charged to $5\mu C$. If the plates are pulled apart to reduce the capacitance to $2\mu F$, how much work is done:

Q. A rigid square loop of side $a$ carrying current $I_2$ is lying on a horizontal surface near a long current $I_1$ carrying wire in the same plane as shown in figure. The net force on the loop due to wire will be:

Q. The figure shows a Ypung's double slit experimental setup. It is observed that when a thin transparent sheet of thickness $t$ and refractive index $\mu$ is put in front of one of the slits, the central maximum gets shifted by a distance equal to $n$ fringe widths. If the wavelength of light used is $\lambda$, $t$ will be

Q. A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $Y=0.3\sin \left(0.157x\right)\cos \left(200\pi t\right)$. The length of the string is: (All quantities are in SI units)

Q. The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane: (i) a ring of radius $R$, (ii) a solid cylinder of radius $\frac{R}{2}$ and (iii) a solid sphere of radius $\frac{R}{4}$. If in each case, the speed of the centre of mass at the bottom of the incline is same, the ratio of the maximum heights they climb is:

Q. A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta$, where $\theta$ is the angle by which it has rotated, is given as $k{\theta }^2$. If its moment of inertia is $I$ then the angular acceleration of the disc is:

Q. A uniform cable of mass $M$ and length $L$ is placed on a horizontal surface such that its $\frac{1}{n}$th parth is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be:

Q. If $M$ is the mass of water that rises in a capillary tube of radius $r$, then mass of water which will rise in a capillary tube of radius $2r$ is:

Q. Taking the wavelength of first Balmer line in hydrogen spectrum ($n=3$ to $n=2$) as $660nm$, the wavelength of the 2nd Balmer line ($n=4$ to $n=2$) will be:

Q. The magnetic field of a plane electromagnetic wave is given by:
$\overrightarrow{B}=B_0\hat{i}\left[\cos (kz-\omega t)\right]+B_1\hat{j}\left[\cos (kz+\omega t)\right]$ where $B_0=3\times {10}^{-5}T;B_1=2\times {10}^{-6}T$. The rms value of the force experienced by a stationary charge $Q={10}^{-4}C$ at $z=0$ is closest to:

Q. A rectangular coil (dimension $5cm\times 2.5cm$) with $100$ turns, carrying a current of $3A$ in the clockwise directionis kept centered at the origin and in the X-Z plane. A magnetic field of $1T$ is applied along X-axis. If the coil is tilted through ${45}^o$ about Z-axis, then the torque on the coil is:

Q. A concave mirror for face viewing has focal length of $0.4m$. The distance at which you hold the mirror from your face in order to see your image upright with a magnificient of $5$ is:

Q. A signal $A\cos \omega t$ is transmitted using $v_0\sin {\omega }_{0}t$ as carrier wave. The correct amplitude modulated (AM) signal is:

Q. For a given gas at $1$ atm pressure, rms speed of the molecule is $200m/s$ at ${127}^{o}C$. At $2$ atm pressure and at ${227}^{o}C$, the rms speed of the molecules will be: