$A$ string is vibrating in its fifth overtone between two rigid supports $2.4 ~m$ apart. The distance between successive node and antinode is (in $~m$)

The electron affinity values of elements $A, B, C$ and $D$ are respectively $-135, -60, -200$ and $-348 \ kJ \ mol^{-1}$. The outer electronic configuration of element $B$ is

If $2 \vec{a} + 3 \vec{b} + \vec{c} = \vec{0}$,then $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is equal to

If $z=\log (\tan x+\tan y)$, then $(\sin 2x) \frac{\partial z}{\partial x}+(\sin 2y) \frac{\partial z}{\partial y}$ is equal to

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 ~cm$, the total length of the hollow cylinder is: (in $~cm$)

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be