If the potential difference between \(B\) and \(D\) is zero, the value of \(x\) is \(\frac{1}{n} \Omega\). The value of \(n\) is .......

A particle of mass \(100\,g\) is projected at time \(t =0\) with a speed \(20\,ms ^{-1}\) at an angle \(45^{\circ}\) to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time \(t=2\,s\) is found to be \(\sqrt{ K }\,kg\,m ^2 / s\). The value of \(K\) is \(............\) \(\left(\right.\) Take \(\left.g =10\,ms ^{-2}\right)\)

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is \(10 \mathrm{~m} / \mathrm{s}\)
(B) The average velocity during 3 to 5 s is \(0 \mathrm{~m} / \mathrm{s}\)
(C) The instantaneous velocity at \(\mathrm{t}=2 \mathrm{~s}\) is \(5 \mathrm{~m} / \mathrm{s}\)
(D) The average velocity during 5 to 7 s and instantaneous velocity at \(\mathrm{t}=6.5 \mathrm{~s}\) are equal
(E) The average velocity from \(t=0\) to \(t=9 \mathrm{~s}\) is zero
Choose the correct answer from the options given below:

In a resonance tube experiment when the tube is filled with water up to height of \(17.0\, cm\) from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of \(24.5\, cm\). If the velocity of sound in air is \(330\, m / s ,\) the tuning fork frequency is\(......Hz\)

A light whose electric field vectors are completely removed by using a good Polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

\(N\,moles\) of a diatomic gas in a cylinder are at a temperature \(T\). Heat is supplied to the cylinder such that the temperature remains constant but \(n\,moles\) of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas ?

A stream of a positively charged particles having \(\frac{ q }{ m }=2 \times 10^{11} \frac{ C }{ kg }\) and velocity \(\overrightarrow{ v }_0=3 \times 10^7 \hat{ i ~ m} / s\) is deflected by an electric field \(1.8 \hat{ j } kV / m\). The electric field exists in a region of \(10 cm\) along \(x\) direction. Due to the electric field, the deflection of the charge particles in the \(y\) direction is \(...........mm\)

A ray of light is incident at an angle of \(60^o\) on one face of a prism of angle \(30^o\) . The emergent ray of light makes an angle of \(30^o\)  with incident ray. The angle made by the emergent ray with second face of prism will be....\(^o\)

When the \(rms\) voltages \(V_L, V_C\) and \(V_R\) are measured respectively across the inductor \(L\), the capacitor \(C\) and the resistor \(R\) in a series \(LCR\) circuit connected to an \(AC\) source, it is found that the ratio \(V_L : V_C : V_R = 1 : 2 : 3\). If the \(rms\) voltage of the \(AC\) sources is \(100\, V\), the \(V_R\) is close to........\(V\)

Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is \(x: y .\) The value of \(x\) is ...... .

The correct relation between \(\gamma=\frac{ C _p}{ c _v}\) and temperature \(T\) is :

In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be \(\dots \;\)%