The length of the subtangent at $(2,2)$ to the curve $x^5=2y^4$ is

$A$ rope is used to lower a block of mass $M$ vertically by a distance $x$ with a constant downward acceleration of $\frac{g}{2}$. The work done by the rope on the block is:

Two monoatomic ideal gases $1$ and $2$ of molecular masses $M_1$ and $M_2$ respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas $1$ to that in gas $2$ 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 cubic unit cell of a metal (molar mass $= 63.55 \ g \ mol^{-1}$) has an edge length of $362 \ pm$. Its density is $8.92 \ g \ cm^{-3}$. The type of unit cell is

The cubic equation whose roots are the squares of the roots of $x^3-2x^2+10x-8=0$ is