The activity of radioactive sample is measured as $\mathrm{N}_0$ counts per minute at time $\mathrm{t}=0$, and $\frac{\mathrm{N}_0}{\mathrm{e}}$ counts per minute at time $\mathrm{t}=3$ minute, The activity reduces to half its value in time (in minute)

Two identical straight wires are stretched so as to produce 6 beats per second when vibrating simultaneously with tensions ' $\mathrm{T}_1$ ' and ' $\mathrm{T}_2$ ' respectively. On changing the tension slightly in one of them, the beat frequency remains unchanged. This will happen when (Given $\rightarrow \mathrm{T}_1>\mathrm{T}_2$ )

How much should the pressure be increased in order to reduce the volume of a given mass of gas by $5 \%$ at the constant temperature?

In Young's double slit experiment the wavelength of light used is $6000 \mathop {\rm{A}}\limits^{\rm{o}}$, the screen is 40 cm from the slits and the fringe width is 0.012 cm , the distance between two slits is