If an electron is moving in the \(n ^{\text {th }}\) orbit of the hydrogen atom, then its velocity \(\left( v _{ n }\right)\) for the \(n ^{\text {th }}\) orbit is given as

All electromagnetic wave is transporting energy in the negative \(z\) direction. At a certain point and certain time the direction of electric field of the wave is along positive y direction. What will be the direction of the magnetic field of the wave at that point and instant?

A simple pendulum of length \(L\) is placed between the plates of a parallel plate capacitor having electric field \(E,\) as shown in figure. Its bob has mass \(m\) and charge \(q.\) the time period of the pendulum is given by

Two identical metallic spheres \(A\) and \(B\) when placed at certain distance in air repel each other with a force of \(F\). Another identical uncharged sphere \(C\) is first placed in contact with \(A\) and then in contact with \(B\) and finally placed at midpoint between spheres \(A\) and \(B\). The force experienced by sphere \(C\) will be.

Keeping the significant figures in view, the sum of the physical quantities \(52.01 m, 153.2 m\) and 0.123 m is :

Equivalent resistance of the following network is _______ \(\Omega\).

The stopping potential \(V_0\) (in \(volt\)) as a function of frequency \((v)\) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be : ................. \(eV\) (Given : Planck's constant \((h) = 6.63 \times 10^{-34}\, Js\), electron charge \(e = 1.6 \times 10^{-19}\, C\))

\(L\), \(C\) and \(R\) represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \(ML^2 T^{-4} A^{-2}\) corresponds to __________.

A square loop of sides \(a=1 \mathrm{~m}\) is held normally in front of a point charge \(\mathrm{q}=1 \mathrm{C}\). The flux of the electric field through the shaded region is \(\frac{5}{\mathrm{p}} \times \frac{1}{\varepsilon_0} \frac{\mathrm{Nm}^2}{\mathrm{C}}\), where the value of p is _____.

The speed of light in media \('A'\) and \('B'\) are \(2.0 \times\) \(10^{10} \,cm / s\) and \(1.5 \times 10^{10} \,cm / s\) respectively. A ray of light enters from the medium \(B\) to \(A\) at an incident angle ' \(\theta\) '. If the ray suffers total internal reflection, then

A particle executes \(S.H.M.\) with amplitude \('a'\) and time period \(V\). The displacement of the particle when its speed is half of maximum speed is \(\frac{\sqrt{ x } a }{2} .\) The value of \(x\) is \(\ldots \ldots \ldots\)

Two strings (A, B) having linear densities \(\mu_{ A }=2 \times 10^{-4} kg / m\) and \(\mu_{ B }=4 \times 10^{-4} kg / m\) and lengths \(L _{ A }=2.5 m\) and \(L _{ B }=1.5 m\) respectively are joined. Free ends of A and B are tied to two rigid supports C and D , respectively creating a tension of 500 N in the wire. Two identical pulses, sent from \(C\) and \(D\) ends, take time \(t_1\) and \(t_2\), respectively, to reach the joint. The ratio \(t_1 / t_2\) is :