A regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be

A flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^{\circ}$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is $\_\_\_\_$ .

Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4 I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is :

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is $\_\_\_\_$ m .

$$ \left(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} . \mathrm{s}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right) $$