Monochromatic light is incident on a glass prism of angle $$A$$. If the refractive index of the material of the prism is $$\mu$$, a ray, incident at an angle $$\theta$$. on the face $$AB$$ would get transmitted through the face $$AC$$ of the prism provided :

In the circuit shown, the current in the $$1\Omega$$ resistor is :

When $$5V$$ potential difference is applied across a wire of length $$0.1$$ $$m,$$ the drift speed of electrons is $$2.5\times 10^{-4}m{s}^{-1}.$$ If the electron density in the wire is $$8\times 10^{28}{m}^{-3},$$ the resistivity of the material is close to :

Distance of the center of mass of a solid uniform cone from its vertex is $$z{}_0$$. If the radius of its base is $$R$$ and its height is $$h$$ then $$z{}_0$$ is equal to :

A particle of mass $$m$$ moving in the $$x$$ direction with speed $$2v$$ is hit by another particle of mass $$2m$$ moving in the $$y$$ direction with speed $$v.$$ If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

A red $$LED$$ emits light at $$0.1$$ watt uniformly around it. The amplitude of the electric field of the light at a distance of $$1$$ $$m$$ from the diode is :

The period of oscillation of a simple pendulum is T = 2\pi \sqrt {{L \over g}}. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its displacement $$d.$$ Which one of the following represents these correctly? $$(graphs$$ $$are$$ $$schematic$$ $$and$$ $$not$$ $$drawn$$ $$to$$ $$scale)$$

A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is added to its bob, the time period changes to $$T_{M.}$$ If the Young's modulus of the material of the wire is $$Y$$ then {1 \over Y} is equal to : ($$g=$$ $$gravitational$$ $$acceleration$$)

For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for $$\overrightarrow{E}$$ and $$\overrightarrow{B}$$ field respectively ?

An electromagnetic wave travelling in the x-direction has frequency of 23 $$\times$$ 1014 Hz and electric field amplitude of 27 Vm$$-$$1. From the options given below, which one describes the magnetic field for this wave ?

An inductor $$(L=0.03$$ $$H)$$ and a resistor $$\left(R=0.15k\Omega \right)$$ are connected in series to a battery of $$15V$$ $$EMF$$ in a circuit shown below. The key $$K_1$$ has been kept closed for a long time. Then at $$t=0$$, $$K_1$$ is opened and key $$K_2$$ is closed simultaneously. At $$t=1$$ $$ms,$$ the current in the circuit will be : $$\left(e^5\cong 150\right)$$

An $$LCR$$ circuit is equivalent to a damped pendulum. In an $$LCR$$ circuit the capacitor is charged to $$Q_0$$ and then connected to the $$L$$ and $$R$$ as shown below : If a student plots graphs of the square of maximum charge $$\left(Q_{Max}^2\right)$$ on the capacitor with time$$(t)$$ for two different values $$L_1$$ and $$L_2$$ $$\left(L_1>L_2\right)$$ of $$L$$ then which of the following represents this graph correctly ? $$\left(plotsareschematicandniotdrawntoscale\right)$$

A signal of $$5$$ $$kHz$$ frequency is amplitude modulated on a carrier wave of frequency $$2$$ $$MHz.$$ The frequencies of the resultant signal is/are :

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

Consider a spherical shell of radius $$R$$ at temperature $$T$$. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = {U \over V}\, \propto \,{T^4} and pressure p = {1 \over 3}\left( {{U \over V}} \right) . If the shell now undergoes an adiabatic expansion the relation between $$T$$ and $$R$$ is:

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as $$V^q,$$ where $$V$$ is the volume of the gas. The value of $$q$$ is: \left( {\gamma = {{{C_p}} \over {{C_v}}}} \right)

A solid body of constant heat capacity $$1$$ $$J/{}^{\circ }C$$ is being heated by keeping it in contact with reservoirs in two ways: $$(i)$$ Sequentially keeping in contact with $$2$$ reservoirs such that each reservoir supplies same amount of heat. $$(ii)$$ Sequentially keeping in contact with $$8$$ reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature $$100^{\circ }C$$ to final temperature $$200^{\circ }C$$. Entropy change of the body in the two cases respectively is :

A uniformly charged solid sphere of radius $$R$$ has potential $$V_0$$ (measured with respect to $$\infty$$) on its surface. For this sphere the equipotential surfaces with potentials {{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}} \over 4} and {{{V_0}} \over 4} have radius $$R_1,R_2,R_3$$ and $$R_4$$ respectively. Then

A long cylindrical shell carries positives surfaces change $$\sigma$$ in the upper half and negative surface charge - $$\sigma$$ in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale)