The impedance of a circuit,when a resistance $R$ and an inductor of inductance $L$ are connected in series in an $AC$ circuit of frequency $f$ is

$\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}$ is equal to

The internal energy of a monoatomic gas is $3 \ nRT$. $1$ mole of helium is kept in a cylinder having internal cross section area of $17 \ cm^2$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling $126 \ J$ heat. If the temperature rises by $4 \ ^\circ C$, then the piston will move $. . . . . . \ cm$.
(atmospheric pressure $= 10^5 \ Pa$)

Assuming complete ionisation,the $pH$ of $0.1 \ M \ HCl$ is $1$. The molarity of $H_2SO_4$ with the same $pH$ is (in $M$)

Which of the following pairs of organs includes only the endocrine glands?

$\lim _{x \rightarrow \infty}\left(\frac{x+6}{x+1}\right)^{x+4}$ is equal to