In a vacuum chamber, a particle of charge $1\ \mu C$ and mass $1\ \mathrm{mg}$ is projected with a velocity $(\hat{i} + 2\hat{j})\ \mathrm{ms}^{-1}$ from the $XZ$ plane at time $t = 0$ in an electric field of $1\hat{i}\ \mathrm{Vm}^{-1}$. At $t = 0.2\ s$, the electric field is switched off and a magnetic field of $6\hat{j}\ \mathrm{T}$ is switched on. The acceleration due to gravity is $-10\hat{j}\ \mathrm{ms}^{-2}$. Correct option(s) is/are :

Two charges $Q_1 = q$ and $Q_2 = mq$ are placed at the points $P_1(a, b)$ and $P_2(ma, mb)$, respectively, in the $XY$ plane, where $a, b \neq 0$ and $m \neq 0, 1$. If $V_1$ is the potential at a point in the $XY$ plane due to charge $Q_1$ and $V_2$ is the potential at that point due to charge $Q_2$. Correct statement(s) for the points at which $|V_1| = |V_2|$ is/are :

Consider an electric dipole comprising two charges $+q$ and $-q$ each with mass $m$, separated by a fixed distance $d$ and initially at rest with its dipole moment pointing along $\hat{\imath}$. A uniform electric field $E \hat{\jmath}$ is turned on at time $t = 0$ and it is turned off at $t = t_f$, when the dipole moment makes an angle $\theta_f$ with $\hat{\imath}$. Neglecting any sources of energy loss, correct option(s) is/are :

Ten moles of an ideal monoatomic gas, initially in state $\boldsymbol{a}$ at atmospheric pressure and temperature $T_a=27^{\circ} \mathrm{C}$, is enclosed in a metal cylinder of volume $V_0$ fitted with a frictionless piston. The gas is suddenly compressed to state $\boldsymbol{b}$ with volume $V_0 / 3$. Now, keeping the piston stationary, the cylinder is submerged in a water bath of temperature $11^{\circ} \mathrm{C}$ until the gas reaches the temperature of the water bath, which is denoted as state $\boldsymbol{c}$. Finally, while still in the water bath, the piston is brought slowly to its initial position, which is denoted as state $\boldsymbol{f}$. If $R$ is universal gas constant, then the correct option(s) is/are :

[Given: $9^{1 / 3}=2.08$ ]