When the observer moves towards a stationary source with velocity '$V_1$', the apparent frequency of the emitted note is '$F_1$'. When the observer moves away from the source with velocity '$V_1$', the apparent frequency is '$F_2$'. If 'V' is the speed of sound in air and $F_1/F_2 = 2$, then $V/V_1 =$

The equation of wave motion is $Y = 6\sin\left(12\pi t - 0.02\pi x + \dfrac{\pi}{3}\right)$ where x is in metre and time in second. The velocity of the wave is

The electric field in the region is $\vec{E} = a\hat{i} + b\hat{j}$ where 'a' and 'b' are constants. The net electric flux passing through a square area of side 'l' parallel to Y-Z plane is

Two point charges $q_1 = 6\ \mu\text{C}$ and $q_2 = 4\ \mu\text{C}$ are kept at points A and B in air where distance $AB = 10$ cm. What is the increase in potential energy of the system when $q_2$ is moved towards $q_1$, by 2 cm ? $\left(\dfrac{1}{4\pi\epsilon_0} = 9 \times 10^9\ \text{SI units}\right)$