The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be

The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ counts per minute at $$t=6 \mathrm{~min}$$. The time (in minutes) at which the activity reduces to half its value is.

The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The wavelength of the $$k_\beta$$-line emitted by the same element will be

A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is