Limestone is present in the blast furnace production of iron in order to:
$(I)$ provide a source of $CaO$
$(II)$ remove some impurities
$(III)$ supply $CO_2$

The element with atomic number $12$ belongs to ......... group and ......... period.

The solution of $\frac{dy}{dx} + y = e^x$ is

$A$ particle of mass $4 M$ which is initially at rest explodes into three pieces of masses $M$,$M$ and $2 M$. The equal masses move along $X$ and $Y$-axes with velocities $4 ~ms^{-1}$ and $6 ~ms^{-1}$,respectively. The magnitude of the velocity of the heavier mass is

$P$ is a point on the segment joining the feet of two vertical poles of heights $a$ and $b$. The angles of elevation of the tops of the poles from $P$ are $45^{\circ}$ each. Then,the square of the distance between the tops of the poles is