$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

Observe the following statements regarding the purification of bauxite:
$I$. During Hall's process,silica is removed as $Si$ (vapour).
$II$. Bauxite ore contaminated with $Fe_2O_3$ is purified in Baeyer's process.
$III$. During Serpeck's process,$AlN$ is formed.
The correct answer is:

The angle of elevation of a stationary cloud from a point $2500 \ m$ above a lake is $15^{\circ}$ and from the same point the angle of depression of its reflection in the lake is $45^{\circ}$. The height (in metres) of the cloud above the lake,given that $\cot 15^{\circ}=2+\sqrt{3}$,is

$A$ particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement $x$ is proportional to:

The solution of the differential equation $\frac{dy}{dx} - 2y \tan 2x = e^x \sec 2x$ is

The type of bond connecting two nucleotides is