According to Bohr atom model, in which of the following transitions will the frequency be maximum ?

Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^6\,m / s\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(m / s\) is \(........\times 10^6\)

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \(8.0\times10^{-3}\, m^2\) . Initially the gas is at \(300\, K\) and occupies a volume of \(2.4\times10^{-3}\, m^3\) and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by \(0.1\, m\). The force constant of the spring is \(8000\, N/m\) and the atmospheric pressure is \(1.0\times10^5\, N/m^2\) . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater . The heat capacity of the heater coil is also negligible)

\(\sqrt{d_{1}}\) and \(\sqrt{d_{2}}\) are the impact parameters corresponding to scattering angles \(60^{\circ}\) and \(90^{\circ}\) respectively, when an \(\alpha\) particle is approaching a gold nucleus. For \(d_{1}=x d_{2}\), the value of \(x\) will be ________

The distance of the Sun from earth is \(1.5 \times 10^{11} \,m\) and its angular diameter is \((2000) \,s\) when observed from the earth. The diameter of the Sun will be ...........

If we need a magnification of \(375\) from a compound microscope of tube length \(150\; \mathrm{mm}\) and an objective of focal length \(5\; \mathrm{mm}\), the focal length of the eye-piece, should be close to.....\(mm\)

The equivalent resistance between points \(A\) and \(B\) in the given network is ............ \(\Omega\)

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis \(A B\) as shown in figure is \(\sqrt{\frac{8}{x}}\). The value of \(x\) is _______.

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \(\mathrm{A}\) and \(B\), their readings are \(V_1, V_2\) and \(V_3\). Choose the correct option.

If \(10^{22}\) gas molecules each of mass \(10^{-26}\, kg\) collide with a surface (perpendicular to it)elastically per second over an area \(1\, m^2\) with a speed \(10^4\,m/s\), the pressure exerted by the gas molecules will be of the order of

A hydraulic press can lift \(100\, kg\) when a mass \('m'\) is placed on the smaller piston. It can lift ......... \(kg\) when the diameter of the larger piston is increased by \(4\) times and that of the smaller piston is decreased by \(4\) times keeping the same mass \('m'\) on the smaller piston.