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A current $I_{0}$ flows through a metallic circular loop of radius r as shown in the figure. Resistance of the segment ABC is half that of ADC. Magnitude of magnetic field at the centre O of the loop is: [Image Placeholder]

A unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius R, having uniform positive charge density $\rho$, as shown in the figure. The initial and final positions of the charge are marked by A and B at distance 2R and 3R respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\frac{\rho R^{2}}{n\epsilon_{0}}$. The value of n is: ($\epsilon_{0}$ is the permittivity of vacuum) [Image Placeholder]

An ideal gas is made of polyatomic molecules. Each of the molecules has three translational, three rotational and f number of vibrational modes. If the ratio of heat capacities $C_{P}/C_{V}$ of the gas is $8/7,$ then the value of f is:

The following table presents the part of the electromagnetic spectrum and their corresponding major applications.

P. Microwave - I. For purifying the water
Q. UV rays - II. For warming the food
R. Gamma rays - III. For AM and FM communication systems
S. Radio wave - IV. For treating the Cancer cells

The correct option is:

Consider a particle moving along a straight line, whose position as a function of time is given by $s(t)=\alpha t^{2}-\beta t+\gamma$, where $\alpha=1~ms^{-2}$ $\beta=6~ms^{-1}$ and $\gamma=5m.$ The average speed of the particle, in $ms^{-1}$ from $t=0$ to $t=6$ s is:

In an adiabatic expansion, the temperature of one mole of an ideal monatomic gas $(\gamma=5/3)$ decreases from 60 K to 50 K. The work done by the gas in the process is: (Take the universal gas constant as $R=8.3~J~mol^{-1}K^{-1})$

A conducting loop of finite resistance lies on the $x-y$ plane. There is a constant magnetic field in the z direction. The area of the loop varies with time t, as $A=A_{0}(1+\sin t)$ in appropriate units. The figure that correctly indicates the qualitative behaviour of the power P dissipated in the loop as a function of time is: [Image Placeholder]

Three identical capacitors, P, Q and S, each of the capacitance C, are connected to a battery of voltage $V,$ as shown in the figure. If the energy stored in the capacitor P and total energy stored in the system are $U_{P}$ and $U_{T}$ respectively, then the ratio $\frac{U_{P}}{U_{T}}$ is: [Image Placeholder]

Two identical inductors are connected in two different configurations P and Q, where a time varying current $l(t)$ is flowing, as shown in the figure. The induced emf between points a and b for configuration P is $E_{P}$ and that for configuration Q is $E_{Q}$ The ratio $E_{P}/E_{Q}$ is: [Neglect the effect of mutual inductance.] [Image Placeholder]

An ac voltage $V=220~sin(2\times10^{3}t)$ Volt is applied to a series LCR circuit. Then the current amplitude in this circuit is: (Given: $L=10~mH.$ $C=25\mu F,$ $R=100~\Omega)$

Two planets $P_{1}$ and $P_{2}$ with equal mass have radii $R_{1}$ and $R_{2}$, respectively, where $R_{2}=\frac{R_{1}}{2}$. The escape speeds of $P_{1}$ and $P_{2}$ are $v_{1}$ and $v_{2},$ respectively. Then $\frac{v_{2}}{v_{1}}$ is:

In the measurement of viscosity of liquids using terminal velocity experiment, spherical balls of same radius but having different densities are used. The variation of the terminal velocity (v) with the ratio of density of spherical ball ($\sigma$) to density of the liquid ($\rho$), is best represented by:

An ideal Zener diode with breakdown voltage of -3 V is reverse biased with a negative input voltage $V_{i}=-5$ V. The magnitude of voltage difference between point B and A is: [Image Placeholder]

A beam of light falls on a metal surface such that photo-electrons are generated. If power of the light source starts to decrease linearly with time t, then variation of the photocurrent I and magnitude of the stopping potential V with time is best represented by: [Image Placeholder]

Consider two circuits, (A) and (B), each having two resistors. One of them has a positive temperature coefficient of resistance, +$\alpha$, while the other one has a negative temperature of coefficient, -$\alpha$, as shown in the figure. The current through these circuits are denoted by $I_{A}$ and $I_{B}$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:

The temperature of a metallic sphere of radius R is increased by a small amount $\Delta T.$ If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is:

Consider a long solenoid of length $l$ and radius $r$. If $n$ is the number of turns per unit length and $\mu_{0}$ is the permeability of free space, the inductance of the solenoid is:

A thin horizontal disc is rotating about a vertical axis passing through its fixed centre O. Its angular momentum is $L_{A}$ and $L_{B}$ computed about points A and B, respectively, with $OB=2\times OA.$ The value of $\frac{L_{A}}{L_{B}}$ is:

Water flows in a streamline motion through a horizontal pipe of circular cross-section as shown in the figure. The pressure difference of water between P and Q is $15~Nm^{-2}.$ The area of cross-section at P and Q are 40 $cm^{2}$ and $20~cm^{2}$, respectively. The rate of flow of water through the pipe, in $cm^{3}s^{-1}$, is: [Take density of water $=1000~kg~m^{-3}]$ [Image Placeholder]

A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron $p_{e}$ to that of photon $p_{Ph}$, $\frac{p_{e}}{p_{Ph}}$ is [Take speed of light $=3\times10^{8}ms^{-1}$ charge of electron $=-1.6\times10^{-19}C$ and mass of electron $=9\times10^{-31}$ kg]