The wave number of the last line of the Balmer series in hydrogen spectrum will be

(Rydberg's constant $$=10^7 \mathrm{~m}^{-1}$$ )

A bucket containing water is revolved in a vertical circle of radius $$r$$. To prevent the water from falling down, the minimum frequency of revolution required is

($$\mathrm{g}=$$ acceleration due to gravity)

Two monatomic ideal gases A and B of molecular masses '$$m_1$$' and '$$m_2$$' respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by

A particle starts oscillating simple harmonically from its mean position with time period '$$T$$'. At time $$t=\frac{T}{12}$$, the ratio of the potential energy to kinetic energy of the particle is $$\left(\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right)$$