When an observer moves towards a stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted note is ' $\mathrm{F}_1$ '. When observer moves away from stationary source with velocity ' $\mathrm{V}_1$ ' the apparent frequency is ' $\mathrm{F}_2$ '. If ' v ' is velocity of sound in air and $\frac{\mathrm{F}_1}{\mathrm{~F}_2}=2$, then $\frac{\mathrm{V}}{\mathrm{V}_1}$ is equal to

$$ \begin{aligned} &\text { For the following reaction, the particle ' } \mathrm{x} \text { ' is }{ }_6 \mathrm{C}^{11}\longrightarrow{ }_5 \mathrm{~B}^{11}+\beta+\mathrm{X} \end{aligned} $$

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is ' $t$ ' second. The frequency of vibration of air column is (Neglect end correction)

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' $O$ ' of the semicircle by three sections together is ( $\mu_0=$ permiability of free space)