On a rainy day,a small oil film on water shows brilliant colours. This is due to

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

In which of the following is lead sulfate $(PbSO_4)$ soluble?

Which of the following plants are used as green manure in crop fields and in sandy soils?

The ratio of the lengths of two wires $A$ and $B$ of the same material is $1 : 2$ and the ratio of their diameters is $2 : 1$. If they are stretched by the same force,then the ratio of the increase in their lengths will be:

Six moles of an ideal gas perform a cycle shown in the figure. If the temperatures are $T_A = 600 \ K, T_B = 800 \ K, T_C = 2200 \ K$,and $T_D = 1200 \ K$,the work done per cycle is ..... $kJ$.