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

Two thin wires, Wire-1 of diameter 0.650 mm and Wire-2 of unknown diameter d are given. To obtain the value of d, the diameters of the two wires are measured with a screw gauge. The screw gauge has a pitch of 0.5 mm and there are 100 divisions on the circular scale (CS). The smallest division on the linear scale (LS) is 0.5 mm. The table shows the readings of LS and CS for the measurements. The value of d (in µm) is :