A circular coil having \(N\,turns\) and radius \(r\) carries a current. It is held in the \(XZ\) plane in a magnetic field \(B\hat i\) . The torque on the coil due to the magnetic field is

This question has Statement \(- 1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement \(1\) : The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume.
Statement \(2\) : A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume.

A single slit of width \(0.1\, mm\) is illuminated by a parallel beam of light of wavelength \(6000\,\mathop A\limits^o \) and diffraction bands are observed on a screen \(0.5\, m\) from the slit. The distance of the third dark band from the central bright band is........\(mm\)

\(N\,moles\) 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 ?

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is \(10\,s^{-1}\).  At, \(t = 0\) the displacement is \(5\, m\). What is the maximum acceleration ? The initial phase is \(\frac{\pi }{4}\)

A fluid is flowing through a horizontal pipe of varying cross-section, with speed \(v\;ms^{-1}\) at a point where the pressure is \(P\) Pascal. At another point where pressure is \(\frac{ P }{2}\) Pascal its speed is \(V\;ms^{-1}\). If the density of the fluid is \(\rho\, kg\, m ^{-3}\) and the flow is streamline, then \(V\) is equal to

An infinitely long wire has uniform linear charge density \(\lambda=2 \mathrm{nC} / \mathrm{m}\). The net flux through a Gaussian cube of side length \(\sqrt{3} \mathrm{~cm}\), if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be \(\mathrm{xNm}^2 \mathrm{C}^{-1}\), where x is :
[Neglect any edge effects and use \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\) SI units]

What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of \(5\) times its mass? (Assume the collision to be head-on elastic collision)

Two inclined planes are placed as shown in figure. A block is projected from the Point \(A\) of inclined plane \(A B\) along its surface with a velocity just sufficient to carry it to the top Point \(B\) at a height \(10 m\). After reaching the Point \(B\) the block slides down on inclined plane \(BC\). Time it takes to reach to the point \(C\) from point \(A\) is \(t (\sqrt{2}+1) s\). The value of \(t\) is........(use \(g =10 m / s ^{2}\) )

\(1\,\mu\)C charge moving with velocity \(\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)\) m/s in the region of magnetic field \(\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)\) T. The magnitude of force acting on it is \(\sqrt{\alpha} \times 10^{-6}\) N. The value of \(\alpha\) is _______.

For hydrogen atom, \(\lambda_1\) and \(\lambda_2\) are the wavelengths corresponding to the transitions \(1\) and \(2\) respectively as shown in figure. The ratio of \(\lambda_1\) and \(\lambda_2\) is \(\frac{x}{32}\). The value of \(x\) is \(..........\)

Two resistance of \(100\ \Omega\) and \(200\  \Omega\) are connected in series with a battery of \(4 \mathrm{~V}\) and negligible internal resistance. \(A\) voltmeter is used to measure voltage across \(100 \Omega\) resistance, which gives reading as \(1 \mathrm{~V}\). The resistance of voltmeter must be _______ \(\Omega\).

In the given potentiometer circuit arrangement, the balancing length \({AC}\) is measured to be \(250\) \({cm}\). When the galvanometer connection is shifted from point \((1)\) to point \((2)\) in the given diagram, the balancing length becomes \(400\, {cm}\). The ratio of the emf of two cells, \(\frac{\varepsilon_{1}}{\varepsilon_{2}}\) is -