The time taken for the magnetic energy to reach \(25\, \%\) of its maximum value, when a solenoid of resistance \(R ,\) inductance \(L\) is connected to a battery, is :

A letter \('A'\) is constructed of a uniform wire with resistance \(1.0\,\Omega \) per \(cm\) , The sides of the letter are \(20\, cm\) and the cross piece in the middle is \(10\, cm\) long. The apex angle is \(60\) . The resistance between the ends of the legs is close to ................ \(\Omega\)

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is \(4\) cm\(^2\). The gas is heated slowly to raise the temperature by \(1.2\,^\circ\)C during which the piston moves by \(25\) mm. The amount of heat supplied to the gas is ________ J. (Atmospheric pressure \(=100\) kPa, \(R=8.3\) J/mol·K) (Neglect mass of the piston)

An electric dipole of mass m, charge q, and length \(l\) is placed in a uniform electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_0 \hat{i}\). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. \(A\). In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. \(B.\) The energy in electromagnetic wave is divided equally between electric and magnetic fields. \(C.\) Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. \(D.\) The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. \(E.\) The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below:

\(300 \,cal\). of heat is given to a heat engine and it rejects \(225 \,cal\). of heat. If source temperature is \(227^{\circ} C\), then the temperature of sink will be____\({ }^{\circ} C\).

An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).

Let \(d \in R\), and  \(A = \left[ {\begin{array}{*{20}{c}} { - 2}&{4 + d}&{\left( {\sin \,\theta } \right) - 2}\\ 1&{\left( {\sin \,\theta } \right) + 2}&d\\ 5&{\left( {2\sin \,\theta } \right) - d}&{\left( { - \sin \,\theta } \right) + 2 + 2d} \end{array}} \right]\), \(\theta  \in \left[ {0,2\pi } \right]\). If the minimum value of det \((A)\) is \(8\), then a value of \(d\) is

Under steady state condition the potential difference across the capacitor in the circuit is _______ V.

In a ferromagnetic material, below the curie temperature, a domain is defined as:

The derivative of \(\tan ^{-1}\left(\frac{\sqrt{1+x^{2}}-1}{x}\right)\) with respect to \(\tan ^{-1}\left(\frac{2 x \sqrt{1-x^{2}}}{1-2 x^{2}}\right)\) at \(x=\frac{1}{2}\) is

Let in a Binomial distribution, consisting of \(5\) independent trials, probabilities of exactly \(1\) and \(2\) successes be \(0.4096\) and \(0.2048\) respectively. Then the probability of getting exactly \(3\) successes is equal to ....... .

The number of seven digit positive integers formed using the digits \(1,2,3\) and \(4\) only and sum of the digits equal to \(12\) is \(...........\).