An air column is of length 17 cm . The ratio of frequencies of $5^{\text {th }}$ overtone if the air column is closed at one end to that open at both ends is (velocity of sound in air $=340 \mathrm{~ms}^{-1}$ )

In Paschen series, wavelength of first line is ' $\lambda_1$ ' and for Brackett series, wavelength of first line is ' $\lambda_2$ ' then ratio $\frac{\lambda_1}{\lambda_2}$ is

A sphere of mass ' $m$ ', moving with velocity ' $3 u$ ' collides head-on with another identical sphere at rest. If ' $e$ ' is coefficient of restitution then what will be the ratio of velocity of the second sphere to that of first sphere after collision?

A magnetic field $4 \times 10^{-2} \mathrm{~T}$ acts at right angles to a coil of area $100 \mathrm{~cm}^2$ with 50 turns. The average e.m.f. induced in the coil is 0.1 V , when it is removed from the field in time ' $t$ '. The value of ' $t$ ' is