From a solid sphere of mass \(M\) and radius \(R\) a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its faces is

The velocity of a small ball of mass ' \(m\) ' and density \(d _{1}\), when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is \(d _{2}\), then the viscous force acting on the ball, will be

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed \('v'\) in a uniform magnetic field \(B\) going into the plane of the paper (See figure). If charge densities \({\sigma _1}\) and \({\sigma _2}\) are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects)

A \(16\, \Omega\) wire is bend to form a square loop. A \(9 \,{V}\) supply having internal resistance of \(1 \,\Omega\) is connected across one of its sides. The potential drop across the diagonals of the square loop is \(.......\,\times 10^{-1} \,{V}\)

When a potential difference \(V\) is applied across a wire of resistance \(R\), it dissipates energy at a rate \(W\). If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the same supply, the energy dissipation rate will become what?

The \(K_{\alpha}\; X-\)ray of molybdenum has wavelength \(0.071\, {nm}\). If the energy of a molybdenum atoms with a \(K\) electron knocked out is \(27.5\, {keV}\), the energy of this atom when an \(L\) electron is knocked out will be \(....\,keV.\) (Round off to the nearest integer) \(\left[{h}=4.14 \times 10^{-15} \,{eVs}, {c}=3 \times 10^{8}\, {ms}^{-1}\right.]\)

The half-life of a radioactive nucleus is \(5\) years, The fraction of the original sample that would decay in \(15\) years is

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 _______.

Given below are two statements :
Statement-I : A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement-II : The curvature of a spherical wave emerging from a slit will increase for increasing slit width.
In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below