The wavelength of the photon emitted by a hydrogen atom when an electron makes a  transition from \(n =2\) to \(n =1\) state is ...... \(nm.\)

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

An electromagnetic wave travelling in \(x\)-direction is described by field equation \(E_y = 300\sin\omega\left(t - \dfrac{x}{c}\right)\). If the electron is restricted to move in \(y\)-direction only with speed of \(1.5 \times 10^6\) m/s then ratio of maximum electric and magnetic forces acting on the electron is _______.

A gas mixture consists of \(3\) moles of oxygen and \(5\) moles of argon at temperature \(T\). Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of \(RT\) ) of the mixture is

During an adiabatic compression, \(830\, J\) of work is done on \(2\, moles\) of a diatomic ideal gas to reduce its volume by \(50\%\). The change in its temperahture is nearly..... \(K\) \((R\, = 8.3\, J\,K^{-1}\, mol^{-1} )\)

Charge is distributed within a sphere of radius \(R\) with a volume charge density \(\rho (r) = \frac{A}{{{r^2}}}{e^{ - 2r/a}}\) where \(A\) and \(a\) are constants. If \(Q\) is the total charge of this charge distribution, the radius \(R\) is.

Two slabs with square cross section of different materials \((1,2)\) with equal sides \((l)\) and thickness \(\mathrm{d}_1\) and \(\mathrm{d}_2\) such that \(\mathrm{d}_2=2 \mathrm{~d}_1\) and \(l \gt \mathrm{d}_2\). Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta_2=2 \theta_1\). If the shear moduli of material 1 is \(4 \times 10^9 \mathrm{~N} / \mathrm{m}^2\), then shear moduli of material 2 is \(\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2\), where value of \(x\) is ________.

The typical output characteristics curve for a transistor working in the common-emitter configuration is shown in the figure. The estimated current gain from the figure is

If \(\lim _{x \rightarrow 0} \frac{e^{a x}-\cos (b x)-\frac{c x e^{-c x}}{2}}{1-\cos (2 x)}=17\), then \(5 a ^2+ b ^2\) is equal to

Let \(D _{ k }=\left|\begin{array}{ccc}1 & 2 k & 2 k -1 \\ n & n ^2+ n +2 & n ^2 \\ n & n ^2+ n & n ^2+ n +2\end{array}\right|\). If \(\sum \limits_{ k =1}^n\) \(D _{ k }=96\), then \(n\) is equal to

Two blocks (\(P\) and \(Q\)) with respectively masses \(2\) kg and \(1.5\) kg are joined by a massless thread. These blocks are mounted on a frictionless pulley which is fixed on the edge of a cube (\(S\)), as shown in the figure below. Block \(P\) is positioned on the top surface which has no friction and block \(Q\) is in contact with side-surface, having coefficient friction \(\mu\). The cube (\(S\)) moves towards the right with acceleration of \(\dfrac{g}{2}\), where \(g\) is gravitational acceleration. During this movement the block \(P\) and \(Q\) remain stationary. The value of \(\mu\) is _______. (take \(g = 10\) m/s\(^2\))

Three harmonic waves having equal frequency \(\mathrm{v}\) and same intensity \(\mathrm{I}_{0}\), have phase angles \(0 , \frac{\pi}{4}\) and \(-\frac{\pi}{4}\) respectively. When they are superimposed the intensity of the resultant wave is close to

The alternating current is given by \({i}=\left\{\sqrt{42} \sin \left(\frac{2 \pi}{{T}} {t}\right)+10\right\} {A}\) The \(r.m.s.\) value of this current is \({A}\)