Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

The volume of an ideal gas increases 8 times and temperature becomes $(1 / 4)^{\text {th }}$ of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta \mathrm{Q}=0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases) :

The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 \alpha$ particles is $\_\_\_\_$ kHz .

[mass of He nucleus = $4.002 \mathrm{amu}, 1 \mathrm{amu}=1.66 \times 10^{-27} \mathrm{~kg}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ and $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ]

Six point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius $R$ as shown in figure. The net electric field at the center of the circle is $\_\_\_\_$ .

( $\epsilon_0$ is permittivity of free space)