The translational degrees of freedom \((f)\) and rotational degrees of freedom \((f)\) of \(\mathrm{CH}_4\) molecule are _______.

A stone is dropped from the top of a building. When it crosses a point \(5\, m\) below the top, another stone starts to fall from a point \(25\, m\) below the top. Both stones reach the bottom of building simultaneously. The height of the building is ..... \(m\).

An unpolarized light of intensity \(I_o\) passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is \(0°\) and intensity of light emerged from analyser is \(\dfrac{3}{8}I_o\), the angle of rotation of the light by the solution with respect to analyser is _______ degrees.

The magnetic field at the centre of a circular coil of radius \(I\), due to current I flowing through it, is \(B\). The magnetic field at a point along the axis at a distance \(\frac{r}{2}\) from the centre is

The measured value of the length of a simple pendulum is \(20 \mathrm{~cm}\) with \(2 \mathrm{~mm}\) accuracy. The time for \(50\) oscillations was measured to be \(40\) seconds with \(1\) second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is \(\mathrm{N} \%\). The value of \(\mathrm{N}\) is _______.

If the time period of a two meter long simple pendulum is \(2\, s\), the acceleration due to gravity at the place where pendulum is executing \(S.H.M.\) is

In a series \(L R\) circuit with \(X_L=R\). power factor is \(P_1\). If a capacitor of capacitance \(C\) with \(X _{ C }= X _{ L }\) is added to the circuit the power factor becomes \(P _2\). The ratio of \(P_1\) to \(P_2\) will be :

When Uranium is bombarded with neutrons, it undergoes fission. The fission reaction can be written as  \({}_{92}{U^{235}} + {}_0{n^1} \to {}_{56}B{a^{141}} + {}_{36}K{r^{92}} + 3x + Q{\rm{( energy)}}\) where three particles named \(x\) are produced and energy \(Q\) is released. What is the name of the particle \(x\) ?

The angular momentum for the electron in Bohr's orbit is \(L\). If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

A body of mass \(M\) at rest explodes into three pieces, in the ratio of masses \(1: 1: 2\). Two smaller pieces fly off perpendicular to each other with velocities of \(30 \,ms ^{-1}\) and \(40 \,ms ^{-1}\) respectively. The velocity of the third piece will be ............... \(\,ms ^{-1}\)

A gas has \(n\) degrees of freedom. The ratio of specific heat of gas at constant volume to the specific heat of gas at constant pressure will be.