$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at distances of $2 \ m$ and $3 \ m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y + 5 = 0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x = 1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x + 8y = 27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x = 9$

The equation of the radical axis of the pair of circles $7x^2+7y^2-7x+14y+18=0$ and $4x^2+4y^2-7x+8y+20=0$ is

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 ~cm$, the total length of the hollow cylinder is: (in $~cm$)

Which of the following is an example of a ketohexose?

$A$ flywheel is in the form of a solid circular disc of mass $72 \, kg$ and radius $0.5 \, m$. If it rotates at $70 \, r.p.m.$,then the rotational kinetic energy is approximately ....... $J$.