In the uranium radioactive series, the initial nucleus is ${ }_{92}^{238} \mathrm{U}$ and that the final nucleus is ${ }_{82}^{206} \mathrm{~Pb}$. When uranium nucleus decays into lead, the number of $\alpha$-particles and $\beta$-particles emitted are

When photons of energy hv fall on a photosensitive surface of work function $\mathrm{E}_0$, photoelectrons of maximum energy $k$ are emitted. If the frequency of radiation is doubled the maximum kinetic energy will be equal to ( $\mathrm{h}=$ Planck's constant)

The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their respective radii (A to B) is (outside pressure $=1 \mathrm{~atm}$.)

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. If the speed of sound in air is $350 \mathrm{~ms}^{-1}$, then the speed of engine in $\mathrm{ms}^{-1}$ is