In an adiabatic process, the density of a diatomic gas becomes \(32\) times its initial value. The final pressure of the gas is found to be \(n\) times the initial pressure. The value of \(n\) is

A light rope is wound around a hollow cylinder of mass \(5\,kg\) and radius \(70\,cm\). The rope is pulled with a force of \(52.5\,N\). The angular acceleration of the cylinder will be.....\( {rad \,s}{ }^{-2}\).

In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)

When \(100\,g\) of a liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of a liquid \(B\) at temperature \(75\,^oC\), the temperature of the mixture becomes \(90\,^oC\). The temperature of the mixture, if \(100\,g\) of liquid \(A\) at \(100\,^oC\) is added to \(50\,g\) of liquid \(B\) at \(50\,^oC\), will be ........\(^oC\)

The general displacement of a simple harmonic oscillator is \(x = A \sin \omega t\). Let \(T\) be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t=\frac{T}{\beta}\). The value of \(\beta\) is \(.........\)

A \(1\,m\) long metal rod \(XY\) completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \(0.15\,T\). If the resistance of the circuit is \(5\,\Omega\), the force needed to move the rod in direction, as indicated, with a constant speed of \(4\,m / s\) will be \(................\,10^{-3}\,N\)

Match List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

Determine the charge on the capacitor in the following circuit ................ \(\mu  C\)

The machine as shown has \(2\) rods of length \(1\, m\) connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor  in a slot As the roller goes back and forth, a \(2\, kg\) weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a

Two light beams of intensities \(4\,I\) and \(9\,I\) interfere on a screen. The phase difference between these beams on the screen at point \(A\) is \(zero\) and at point \(B\) is \(\pi\). The difference of resultant intensities, at the point \(A\) and \(B\), will be \(....I\).

The acceptor level of a p-type semiconductor is \(6 \mathrm{eV}\). The maximum wavelength of light which can create a hole would be _______. (Given hc \(=1242 \mathrm{eV} \mathrm{nm}\).)