Platinum crystallizes in a face-centered cubic $(FCC)$ crystal with a unit cell length $a$. The distance between nearest neighbors is

Water flows in a streamlined manner through a capillary tube of radius $a$,the pressure difference being $P$ and the rate of flow $Q$. If the radius is reduced to $a/2$ and the pressure is increased to $2P$,the rate of flow becomes:

From the top of a hill $h$ metres high,the angles of depression of the top and the bottom of a pillar are $\alpha$ and $\beta$ respectively. The height (in metres) of the pillar is

The variance of $50$ observations is $7$. If each observation is multiplied by $6$ and then $5$ is subtracted from it,then the variance of the new data is

What is the study of living organisms called?

If $l$ and $m$ are the degree and the order respectively of the differential equation of the family of all circles in the $XY$ plane with radius $5$ units,then $2l + 3m =$