The time period of a satellite, revolving above earth's surface at a height equal to \(R\) will be (Given \(g =\pi^2 m / s ^2, R =\) radius of earth)

If a copper wire is stretched to increase its length by \(20 \% \). The percentage increase in resistance of the wire is \(..........\%\)

If the earth suddenly shrinks to \(\frac{1}{64}\) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \(\frac{24}{ x } h\). The value of \(x\) is \(.......\)

A proton, a neutron, an electron and an \(\alpha\,-\)particle have same energy. If \(\lambda_{ p }, \lambda_{ n }, \lambda_{ e }\) and \(\lambda_{\alpha}\) are the de Broglie's wavelengths of proton, neutron, electron and \(\alpha\) particle respectively, then choose the correct relation from the following

A sub-atomic particle of mass \(10^{-30} \mathrm{~kg}\) is moving with a velocity \(2.21 \times 10^6 \mathrm{~m} / \mathrm{s}\). Under the matter wave consideration, the particle will behave closely like _______. \(\left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)\)

A set of \(20\) tuning forks is arranged in a series of increasing frequencies. If each fork gives \(4\) beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is \(\dots \; Hz\).

A lead bullet penetrates into a solid object and melts. Assuming that \(40 \%\) of its kinetic energy is used to heat it, the initial speed of bullet is ............ \(ms ^{-1}\) (Given, initial temperature of the bullet \(=127^{\circ} C\), Melting point of the bullet \(=327^{\circ} C\), Latent heat of fusion of lead \(=2.5 \times 10^{4} \,J Kg ^{-1}\), Specific heat capacity of lead \(=125 \,J / kg K\) )

Assuming in forward bias condition there is a voltage drop of 0.7 V across a silicon diode, the current through diode \(D _1\) in the circuit is ___________mA . (Assume all diodes in the given circuit are identical)

A train moves towards a stationary observer with speed \(34\, m/s\). The train sounds a whistle and its frequency registered by the observer is \(f_1\). If the speed of the train is reduced to \(17\, m/s\), the frequency registered is \(f_2\). If speed of sound is \(340\, m/s\), then the ratio \(f_1/f_2\) is

The electric field of a plane electromagnetic wave propagating along the \(x\) direction in vacuum is \(\overrightarrow{ E }= E _{0} \hat{ j } \cos (\omega t - kx )\). The magnetic field \(\overrightarrow{ B },\) at the moment \(t =0\) is :