A ray of light refracts from medium 1 into a thin layer of medium 2, crosses the layer and is incident at the critical angle on the interface between the medium 2 and 3 as shown in the figure. If the angle of incidence of ray is \(\theta\), the value of \(\theta\) is

If the work done in blowing a soap bubble of radius \(\mathrm{K}\) is W, then the work done in blowing the soap bubble of radius \(2 R\) is

When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the internal energy of the gas \((\gamma=5 / 3)\) is

The temperature of \(100 \mathrm{~g}\) of water is to be raised from \(24^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C}\) by adding steam at \(100^{\circ} \mathrm{C}\) to it. The mass of the steam required in this process is (latent heat of steam is \(540 \mathrm{cal} \mathrm{g}^{-1}\) )

A body starting at $t=0$ from origin and oscillates simple harmonically with a period of $4 \mathrm{s}$. After what time will its kinetic energy be $75\%$ of its total energy

Two cylinders \(A\) and \(B\) fitted with pistons contain equal number of moles of an ideal monoatomic gas at \(400 \mathrm{~K}\). The piston of \(A\) is free to move while that of \(B\) is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in \(A\) is \(42 \mathrm{~K}\), the rise in temperature of the gas in \(B\) is

A solid sphere and a disc of same mass ' \(M\) 'and radius ' \(R\) ' are kept such that their curved surfaces are in contact and their centers lie along the same horizontal line. The moment of inertia of the two body system about an axis passing through their point of contact and perpendicular to the plane of the disc is

In a photoelectric experiment, the slope of the graph drawn between stopping potential along y -axis and frequency of incident radiation along x -axis is (Planck's constant \(=6.6 \times 10^{-34} \mathrm{Js}\) )

A small object is placed in the air, at a distance \(45 \mathrm{~cm}\) from a convex refracting surface of radius of curvature \(15 \mathrm{~cm}\). If the surface separates air from glass of refractive index 1.5 , then the position of image is

A body of mass ' \(m\) ' moving with a velocity of ' \(v\) ' collides head on with another body of mass ' 2 m ' at rest. If the coefficient of restitution between the two bodies is ' e ', then the ratio of the velocities of the two bodies after collision is

If a ray of light passes through an equilateral prism such that the angle of incidence and the angle of emergence are both equal to \(70 \%\) of the angle of the prism, then the angle of minimum deviation is

A parallel plate capacitor has a capacity \(80 \times 10^{-6} \mathrm{~F}\), when air is present between the plates. The volume between the plates is then completely filled with a dielectric slab of dielectric constant 20. The capacitor is now connected to a battery of \(30 \mathrm{~V}\) by wires. The dielectric slab is then removed. Then, the charge that passes now through the wire is

Match the following table. \begin{array}{|c|c|c|c|} \hline & List-I & & List-II \ \hline A. & \begin{array}{l}\text { Michelson-Morley } \ \text { experiment }\end{array} & I. & \begin{array}{l}\text { The existence of } \ \text { anti-matter }\end{array} \ \hline B. & \begin{array}{l}\text { Stern-Gerlach } \ \text { experiment }\end{array} & II. & \begin{array}{l}\text { The existence of } \ \text { de-Broglie matter waves }\end{array} \ \hline C. & \begin{array}{l}\text { Davisson-Germer } \ \text { experiment }\end{array} & III. & Electrons have spins \ \hline D. & \begin{array}{l}\text { Anderson discovery } \ \text { of positron }\end{array} & \mathrm{IV}. & \begin{array}{l}\text { The non-existence of } \ \text { ether }\end{array} \ \hline \end{array} \(\begin{array}{llll}A & B & C & D\end{array}\)