$A$ 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:

Let $f(x) = \int \frac{\sqrt{x}}{(1+x)^2} \, dx, x \geq 0$. Then $f(3) - f(1)$ is equal to

The force between the plates of a parallel plate capacitor of capacitance $C$ and distance of separation of the plates $d$ with a potential difference $V$ between the plates,is

$ATP$ase enzyme needed for muscle contraction is located in

$A$ straight line passes through the point $A(3, 4)$ such that the portion of the line intercepted between the axes is bisected at $A$. Find the equation of the line.

$A$ vector $\vec{a}$ has components $2p$ and $1$ with respect to a two-dimensional rectangular Cartesian system. This system is rotated through a certain angle $\theta$ about the origin in the counter-clockwise direction. If $\vec{a}$ has components $p+1$ and $1$ with respect to the new system,then: