Magnitude of change in kinetic energy of electron can be expressed as $\frac{h}{4\pi}\left|\frac{nv_n}{r_n} - \frac{v_1}{r_1}\right|$.

Magnitude of change in de Broglie wavelength of the electron can be expressed as $\frac{e^2}{4\epsilon_0}\left|\frac{1}{K_n} - \frac{1}{K_1}\right|$.

Frequency of the radiation emitted can be expressed as $\frac{e^2}{8\pi\epsilon_0 h}\left(\frac{1}{r_1} - \frac{1}{r_n}\right)$.

Magnitude of change in total energy of the electron can be expressed as $\frac{h}{2\pi}\left|\frac{v_1}{r_1} - \frac{nv_n}{r_n}\right|$.

If $\theta = 45^\circ$, then $v = \frac{5\sqrt{g}}{2}\ \text{ms}^{-1}$.

If $\theta = 45^\circ$, the particle reaches its maximum height before it reaches P.

If $\theta = 30^\circ$, the particle reaches its maximum height after reaching P.

If $\theta = \tan^{-1}\left(\frac{1}{5}\right)$, then $v = 125\sqrt{g}\ \text{ms}^{-1}$.

If $\dfrac{V_2}{V_1} = 8$, the heat released in the process bc is smaller than the heat absorbed in the process ab.

For a given value of $V_2/V_1$, $\eta$ does not depend on the temperature of the isothermal process.

If $V_2/V_1 = 8$, then the temperature of the gas at a is $4$ times the temperature of the gas at c.

If $V_2/V_1 = 8$, then the pressure of the gas at a is $4$ times the pressure of the gas at b.

The wave is travelling in $-\frac{1}{5} (3 \hat{j} + 4 \hat{k})$ direction.

The magnitude of the wave vector is $0.5\ \mathrm{m}^{-1}$.

The value of $\omega$ is $1.5 \times 10^9 \ \mathrm{rad}\ \mathrm{s}^{-1}$.

The magnetic field associated with this wave is given by $\frac{E_0}{c} \sin(3y + 4z + \omega t)(4 \hat{j} - 3 \hat{k})$.