The glenoid cavity articulates:

$A$ person observes the top of a tower from a point $A$ on the ground. The angle of elevation of the tower from this point is $60^{\circ}$. He moves $60 \ m$ in the direction perpendicular to the line joining $A$ and the base of the tower. The angle of elevation of the tower from this new point is $45^{\circ}$. Then,the height of the tower (in metres) is

Let $f$ be a differentiable function such that $f(1)=2$ and $f^{\prime}(x)=f(x)$,for all $x \in \mathbb{R}$. If $h(x)=f(f(x))$,then $h^{\prime}(1)$ is equal to

Two satellites $A$ and $B$,having a ratio of masses $3 : 1$,are in circular orbits of radii $r$ and $4r$ respectively. Calculate the ratio of the total mechanical energy of $A$ and $B$.

$A$ variable plane passes through a fixed point $(1, 2, 3)$. The foot of the perpendicular from the origin to the plane lies on:

Spraying of $D.D.T.$ on crops produces pollution of