If $y=A \cos n x+B \sin n x$, then $y_2+n^2 y$ is equal to

An electrically charged particle enters a uniform magnetic field in a direction perpendicular to the field with a velocity $v$. Then,it travels

If $\frac{x-4}{x^2-5x+6}$ can be expanded in the ascending powers of $x$,then the coefficient of $x^3$ is

$A$ circular disc of radius $R$ is removed from a bigger circular disc of radius $2R$ such that the circumferences of the discs touch. The centre of mass of the new disc is at a distance $\alpha R$ from the centre of the bigger disc. The value of $\alpha$ is

In an ideal gas at temperature $T$,the average force that a molecule applies on the walls of a closed container depends on $T$ as $T^q$. $A$ good estimate for $q$ is:

The change in the value of $g$ at a height $h$ above the surface of the earth is the same as at a depth $d$ below the surface of the earth. When both $d$ and $h$ are much smaller than the radius of the earth,then which one of the following is correct?