Let $\vec{p} = 2\hat{i} + 3\hat{j} + a\hat{k}$,$\vec{q} = b\hat{i} + 5\hat{j} - \hat{k}$,and $\vec{r} = \hat{i} + \hat{j} + 3\hat{k}$. If $\vec{p}, \vec{q}, \vec{r}$ are coplanar and $\vec{p} \cdot \vec{q} = 20$,then the ordered pair $(a, b)$ is:

If two identical bar magnets,each of length $l$,pole strength $m$ and magnetic moment $M$ are placed perpendicular to each other with their unlike poles in contact,the magnetic moment of the combination is

If $x^2+\alpha y^2+2 \beta y=a^2$ represents a pair of perpendicular lines,then $\beta$ equals to

The set of all solutions of the inequation $x^2 - 2x + 5 \leq 0$ in $R$ is

Three very large plates of the same area are kept parallel and close to each other. They are considered as ideal black surfaces and have very high thermal conductivity. The first and third plates are maintained at temperatures $2\,T$ and $3\,T$ respectively. The temperature of the middle (i.e.,second) plate under steady-state conditions is

Which one of the following is not a biofertilizer?