The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $pi$)

Which has the maximum number of molecules among the following?

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

$6.023 \times 10^{22}$ molecules are present in $10 \ g$ of a substance $x$. The molarity of a solution containing $5 \ g$ of substance $x$ in $2 \ L$ of solution is $\dots \dots \dots \times 10^{-3} \ M$.

If $\omega$ is a complex cube root of unity,then $(x+1)(x+\omega)(x-\omega-1)$ is equal to

$A$ ray of light is incident normally on a glass slab of thickness $5 ~cm$ and refractive index $1.6$. The time taken by a ray to travel from the source to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is (in $~cm$)