The depletion layer in the $p-n$ junction is caused by

$A$ body thrown vertically upwards from the ground reaches a maximum height $h$. The ratio of the kinetic and potential energies of the body at a height $40 \%$ of $h$ from the ground is

Identify the incorrect statements from the following.
$I$. Tin in $+2$ state acts as reducing agent while lead in $+4$ state acts as strong oxidising agent.
$II$. Silicon exists as $[SiF_6]^{2-}$ form,but $[SiCl_6]^{2-}$ does not.
$III$. The hybridisation of carbon in fullerene is $sp^3$.
$IV$. Among $Ge, Sn$ and $Pb$,the lowest melting point is for $Sn$.

If $\cos ^{-1}\left(\frac{5}{13}\right)+\cos ^{-1}\left(\frac{3}{5}\right)=\cos ^{-1} x$,then $x$ is equal to

$A$ body is sliding down a rough inclined plane. The coefficient of friction between the body and the plane is $0.5$. The ratio of the net force required for the body to slide down and the normal reaction on the body is $1:2$. Then the angle of the inclined plane is: (in $^{\circ}$)

$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is