A p-n junction is fabricated from a semiconductor with band gap of \(2.8 \mathrm{eV}\). What approximate wavelength it cannot detect? [use \(\mathrm{h}=6 \times 10^{-34} \mathrm{~m}^2 \mathrm{~kg} / \mathrm{s}\) ]

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} \(\begin{array}{llll}A & B & C & D\end{array}\)

If a planet of mass \(6.4 \times 10^{23} \mathrm{~kg}\) can be compressed into a sphere such that the escape velocity from its surface is \(8 \times 10^4 \mathrm{~m} / \mathrm{s}\), then what showld be the radius of the sphere? (Gravitational constant, \(G=6.6 \times 10^{11} \mathrm{Nm}^2 \mathrm{~kg}^2\) )

A constant force of $5 \mathrm{N}$ accelerates a stationary particle of mass $500 \mathrm{gm}$ through a displacement of $5\mathrm{m}.$The average power delivered is

A ball falls freely from a height \(\mathrm{h}\) on a rigid horizontal plane. If the coefficient of restitution is e, then the total distance travelled by the ball before hitting the plane second time is

In the circuit shown in the figure, the current ' \(T\) ' is

Statement (I) : An object subjected to velocities \(\overrightarrow{v_1}\) and \(\overrightarrow{v_2}\) has a resultant velocity with magnitude \(|\vec{v}|=\left|\overrightarrow{v_1}\right|+\left|\overrightarrow{v_2}\right|\).
Statement (II) : The magnitude of displacement is either less or equal to the path length of an object between two points.
Statement (III) : The instantaneous acceleration is the limiting value of the average acceleration as the time interval approaches zero.
Which of the following is correct?

Consider a spherical drop of mercury of radius $R$ with capacitance $C=4\pi \epsilon R.$ If two such droplets combine to form a larger one, what would be its capacitance in terms of $C$ ?

Two circular loops $L_1$ and $L_2$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_1$ is $R_1$ and that of $L_2$ is $R_2$. The distance between the centres of the loops is $\sqrt{3}{R}_1$. The magnetic field at the centre of $L_2$ shall be zero if

A bar magnet having magnetic moment \(M\) is bent as an arc. Its magnetic moment

A man can swim with a speed of \(4 \mathrm{kmh}^{-1}\) in still water. How long does he take to cross a river \(1 \mathrm{~km}\) wide, if the river flows steadily \(3 \mathrm{kmh}^{-1}\) and he makes his strokes normal to the river current?

A metal sheet $4 \mathrm{m}$ on a side and of negligible thickness is attached to a balance and inserted into container fluid. The balance to which metal sheet is attached reads $0.50 \mathrm{N}$ and the contact angle is found to be zero. A small amount of oil is then spread over the metal sheet. The contact angle now becomes $180°$ and the balance now reads $0.49 \mathrm{N}.$ The surface tension of the fluid is

The ratio of the height above the surface of earth to the depth below the surface of earth, for gravitational accelerations to be the same (assuming small heights), is