A particle is thrown with a speed v from a point O at an angle θ with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m from O, as shown in the figure. If acceleration due to gravity is g $\text{ms}^{-2}$, then the correct statement(s) is/are:

A quasi-static cycle of a monoatomic ideal gas contains an isothermal process $(ab)$, followed by an isochoric process $(bc)$ and an adiabatic process $(ca)$ as shown in the figure. The volumes of the gas are $V_1$ and $V_2$ at $a$ and $b$, respectively. If the cycle has heat input $Q_{\mathrm{in}}$ and output $Q_{\mathrm{out}}$, then the efficiency of the cycle is defined as $$\eta = \frac{Q_{\mathrm{in}} - Q_{\mathrm{out}}}{Q_{\mathrm{in}}}.$$ The correct statement(s) is/are:

[Given: $\ln 2 \approx 0.7$]

The electric field associated with an electromagnetic wave travelling in vacuum is given by

$E_0 \sin(3y + 4z + \omega t) \hat{i}$, where $\\omega$ is the angular frequency. All quantities are in SI units. The correct statement(s) about this wave is/are:

[Given: speed of light in vacuum $c = 3 \times 10^8\ \mathrm{m\,s^{-1}}$.]

A tank contains two immiscible liquids of densities $6\rho$ and $2\rho$. The higher density liquid is filled up to a height $L/2$ from the bottom. A thin rod of density $\rho$ and length $L$ is fully immersed and hinged at the bottom so that it can oscillate freely, as shown in the figure. If the rod is slightly disturbed from its equilibrium, the time period of small oscillations is $$\frac{2\pi}{n}\sqrt{\frac{L}{g}},$$ where $g$ is the acceleration due to gravity. The value of $n$ is: