If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then the rate of change of its volume with respect to $x$ 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 $(1, 3)$	$IV$. $x = 9$

In a permanent magnet at room temperature,

One line of the pair of lines $x^2+xy-2y^2=0$ is perpendicular to one line of the pair of lines $3y^2-5xy-2x^2=0$. If the combined equation of the two lines other than those two perpendicular lines is $ax^2+2hxy+by^2=0$,then $a+2h+b=$

Shown in the figure is a circular loop of radius $r$ and resistance $R$. $A$ variable magnetic field of induction $B = B_0e^{-t}$ is established inside the coil. If the key $(K)$ is closed,the electrical power developed right after closing the switch is equal to

Which of the following statements are correct for alkali metal compounds?
$(i)$ Superoxides are paramagnetic in nature.
$(ii)$ The basic strengths of hydroxides increase down the group.
$(iii)$ The conductivity of chlorides in their aqueous solutions decreases down the group.
$(iv)$ The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.