The dimensions of \(\left(\frac{ B ^{2}}{\mu_{0}}\right)\) will be. (if \(\mu_{0}\) : permeability of free space and \(B\) : magnetic field)

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

The equation of state for a gas is given by \(PV = nRT + \alpha V\), where \(n\) is the number of moles and \(\alpha \) is a positive constant. The initial temperature and pressure of one mole of the gas contained in a cylinder are \(T_o\) and \(P_o\) respectively. The work done by the gas when its temperature doubles isobarically will be

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, \(\lambda _1/\lambda _2\), of the photons emitted in this process is

A square loop of side \(2a\) and carrying current I is kept in \(xz\) plane with its centre at origin. A long wire carrying the same current I is placed parallel to \(z-\)axis and passing through point \((0, b , 0),( b >> a ) .\) The magnitude of torque on the loop about \(z-\)ax is will be

A straight rod of length \(L\) extends from \(x = a\) to \(x = L + a\). The gravitational force it exerts on a point mass \(‘m’\) at \(x = 0\), if the mass per unit length of the rod is \(A + Bx^2\), is given by

A person observes two moving trains, '\(A\)' reaching the station and '\(B\)' leaving the station with equal speed of \(30\,m / s\). If both trains emit sounds with frequency \(300\,Hz\), (Speed of sound : \(330\,m / s\) ) approximate difference of frequencies heard by the person will be \(..........Hz\)

A Carnot engine take \(5000 \,k\,cal\) of heat from a reservoir at \(727\,^{\circ}C\) and gives heat to a \(\operatorname{sink}\) at \(127\,^{\circ}C\). The work done by the engine is \(.......... \times 10^{6}\,J\)

The velocity of a particle is given as \(\vec{v} = -x\hat{i} + 2y\hat{j} - z\hat{k}\) m/s. The magnitude of acceleration at point \((1, 2, 4)\) is _______ m/s\(^2\).

A gas mixture consists of \(8\) moles of argon and \(6\) moles of oxygen at temperature \(T\). Neglecting all vibrational modes, the total internal energy of the system is _______.

A bat moving at \(10\,ms^{-1}\) towards a wall sends a sound signal of \(8000\,Hz\) towards it. On reflection it hears a sound of frequency \(f\). The value of \(f\) in \(Hz\) is close to (speed of sound \(= 320\,ms^{-1}\) )