A particular hydrogen like ion emits radiation of frequency \(2.92 \times 10^{15}\, {Hz}\) when it makes transition from \({n}=3\) to \({n}=1 .\) The frequency in \({Hz}\) of radiation emitted in transition from \({n}=2\) to \({n}=1\) will be : (in \(\,\times 10^{15}\))

A vector has magnitude same as that of \(\overrightarrow{\mathrm{A}}-=3 \hat{\mathrm{j}}+4 \hat{\mathrm{j}}\) and is parallel to \(\overrightarrow{\mathrm{B}}=4 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}\). The \(\mathrm{x}\) and \(y\) components of this vector in first quadrant are \(\mathrm{x}\) and \(3\) respectively where  \(x\)= _______.

A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(x -\) axis. Identify all figures that correctly represent the motion qualitatively. (\(a =\) acceleration, \(v =\) velocity, \(x =\) displacement, \(t =\) time)

The root mean square velocity of molecules of gas is

A block of mass \(1 \mathrm{~kg}\) is pushed up a surface inclined to horizontal at an angle of \(60^{\circ}\) by a force of \(10 \mathrm{~N}\) parallel to the inclined surface as shown in figure. When the block is pushed up by \(10 \mathrm{~m}\) along inclined surface, the work done against frictional force is _______. \(\left[\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right]\)

In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)

A body of mass \(200\,g\) is tied to a spring of spring constant \(12.5\,N / m\), while the other end of spring is fixed at point \(O\). If the body moves about \(O\) in a circular path on a smooth horizontal surface with constant angular speed \(5\,rad / s\), then the ratio of extension in the spring to its natural length will be :

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

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)

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is \(\frac{\pi}{2}\) at point \(P\) and \(\pi\) at point \(Q\). Then the difference between the resultant intensities at \(P\) and \(Q\) will be.......\(I\)

At the interface between two materials having refractive indices \(n_1\) and \(n_2\), the critical angle for reflection of an em wave is \(\theta_{1 C}\). The \(n_2\) material is replaced by another material having refractive index \(n_3\) such that the critical angle at the interface between \(n_1\) and \(n_3\) materials is \(\theta_{2 \mathrm{C}}\). If \(\mathrm{n}_3\gt\mathrm{n}_2\gt\mathrm{n}_1 ; \frac{\mathrm{n}_2}{\mathrm{n}_3}=\frac{2}{5}\) and \(\sin \theta_{2 \mathrm{C}}-\sin \theta_{1 \mathrm{C}}=\frac{1}{2}\), then \(\theta_{1 \mathrm{C}}\) is :

For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric \(\left( U _{ e }\right)\) and magnetic \(\left( U _{ m }\right)\) fields is

In a hydrogen like atom electron make transition from an energy level with quantum number \(n\) to another with quantum number \((n- 1)\). If \(n > >  1\), the frequency ofradiation emitted is proportional to