Imagine that a reactor converts all given mass into energy and that it operates at a power level of \(10^9\, watt\). The mass of the fuel consumed per hour in the reactor will be : (velocity of light, \(c\) is \(3\times10^8\, m/s\))

A charge of \(4.0 \mu \mathrm{C}\) is moving with a velocity of \(4.0 \times 10^6 \mathrm{~ms}^{-1}\) along the positive \(\mathrm{y}\)-axis under a magnetic field \(\vec{B}\) of strength \((2 \hat{k})\  T\). The force acting on the charge is \(x \hat{i} N\). The value of \(x\) is _______.

12 wires each having resistance \(2 \Omega\) are joined to form a cube. A battery of \(6 \mathrm{~V}\) emf is joined across point \(\mathrm{a}\) and \(\mathrm{c}\). The voltage difference between \(e\) and \(f\) is ______V.

A monochromatic light is incident on a metallic plate having work function \(\phi\). An electron, emitted normally to the plate from a point \(A\) with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of electron. The electron passes through a curve and hits back the plate at a point \(B\). The distance between A and B is :
(Given : The magnitude of charge of an electron is e and mass is \(\mathrm{m}, \mathrm{h}\) is Planck's constant and c is velocity of light. Take the magnetic field exists throughout the path of electron)

Two coherent sources of sound, \(S_{1}\) and \(S_{2}\) produce sound waves of the same wavelength, \(\lambda=1\, m ,\) in phase. \(S_{1}\) and \(S_{2}\) are placed \(1.5\, m\) apart (see fig.) A listener, located at \(L,\) directly in front of \(S_{2}\) finds that the intensity is at a minimum when he is \(2\,m\) away from \(S _{2}\). The listener moves away from \(S _{1},\) keeping his distance from \(S_{2}\) fixed. The adjacent maximum of intensity is observed when the listener is at a distance \(d\) from \(S\)\(_{1}\). Then, \(d\) is\(......m\)

A bar magnet having a magnetic moment of \(2.0 \times\) \(10^{5} \; JT ^{-1}\), is placed along the direction of uniform magnetic field of magnitude \(B =14 \times 10^{-5}\; T\). The work done in rotating the magnet slowly through \(60^{\circ}\) from the direction of field is .............. \(J\) 

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

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is

Let \(\alpha\) be the angle between the lines whose direction cosines satisfy the equations \(l+m-n=0\) and \(l^{2}+m^{2}-n^{2}=0 .\) Then the value of \(\sin ^{4} \alpha+\cos ^{4} \alpha\) is

In a hydrogen like ion, the energy difference between the \(2^{\text {nd }}\) excitation energy state and ground is 108.8 eV. The atomic number of the ion is

A block of mass \(40 \,kg\) slides over a surface, when a mass of \(4 \,kg\) is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is \(0.02\). The acceleration of block is ............ \(ms ^{-2}\) (Given \(g =10 \,ms ^{-2}\).)

An \(\alpha\) particle and a proton are accelerated from rest by a potential difference of \(200\, V\). After this, their de Broglie wavelengths are \(\lambda_{\alpha}\) and \(\lambda_{p}\) respectively. The ratio \(\frac{\lambda_{p}}{\lambda_{a}}\) is

The radius of gyration of a uniform rod of length \(l,\) about an axis passing through a point \(\frac{l}{4}\) away from the centre of the rod, and perpendicular to it, is