$\lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5}$ is equal to

What are the products formed when chlorine is passed through an aqueous hypo solution?

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 $~K$)

The height at which the weight of a body becomes $\frac{1}{9}^{th}$ of its weight on the surface of the Earth (radius of Earth $R$) is:

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

The amplitude and the time period in a $S.H.M.$ are $0.5 \, cm$ and $0.4 \, s$ respectively. If the initial phase is $\pi / 2 \, rad$,then the equation of $S.H.M.$ will be