If the series limit of the Lyman series for a Hydrogen atom is equal to the series limit of the Balmer series for a hydrogen-like atom,then the atomic number of this hydrogen-like atom will be:

The difference between the fundamental frequencies of an open pipe and a closed pipe of the same length is $100 \ Hz$. The difference between the frequencies of the second harmonic of the open pipe and the third harmonic of the closed pipe is: (in $Hz$)

The velocities of two particles $A$ and $B$ are $0.05 \ ms^{-1}$ and $0.02 \ ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de-Broglie's wavelength is

When $10 \ g$ of methane is completely burnt in oxygen,the heat evolved is $560 \ kJ$. What is the heat of combustion (in $kJ \ mol^{-1}$) of methane?

The angle between the lines whose direction cosines are given by the equations $l^2+m^2-n^2=0$ and $l+m+n=0$ is

In the arrangement shown in the figure,the masses of blocks $B$ and $A$ are $2m$ and $m$ respectively. The surface between $B$ and the floor is smooth. Block $B$ is connected to block $C$ by means of a string-pulley system. If the whole system is released,find the minimum value of the mass of block $C$ so that block $A$ remains stationary with respect to $B$. The coefficient of friction between $A$ and $B$ is $\mu$.