The cause of water pollution is due to

Two identical square rods of metal are welded end to end as shown in figure $(a)$. $20 \text{ calories}$ of heat flows through them in $4 \text{ minutes}$. If the rods are welded as shown in figure $(b)$,the same amount of heat will flow through the rods in ...... $\text{min}$.

The electrons which take part in order to exhibit variable oxidation states by transition metals are

If $u=e^{x^2-y^2}$, then

Match the appropriate pairs from List-$I$ and List-$II$ :

List-$I$	List-$II$
$1$. Nitrogen molecules	$(A)$ Continuous spectrum
$2$. Incandescent solids	$(B)$ Absorption spectrum
$3$. Fraunhoffer lines	$(C)$ Band spectrum
$4$. Electric arc between iron rods	$(D)$ Emission spectrum

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 + 4x + 1 = 0$,then $(\alpha + \beta)^{-1} + (\beta + \gamma)^{-1} + (\gamma + \alpha)^{-1} = $