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

One mole of $N_2H_4$ loses $10$ moles of electrons to form a new compound $Z$. Assuming that all the nitrogen atoms appear in the new compound,what is the oxidation state of nitrogen in $Z$? (There is no change in the oxidation state of hydrogen.)

Match the items given in Column $I$ with those in Column $II$ and select the correct option given below:

Column $I$	Column $II$
$(a)$ Proliferative Phase	$(i)$ Breakdown of endometrium
$(b)$ Secretory Phase	$(ii)$ Follicular phase
$(c)$ Menstruation	$(iii)$ Luteal Phase

$A$ circle passes through the point $(3, 4)$ and cuts the circle $x^2 + y^2 = a^2$ orthogonally. The locus of its centre is a straight line. If the distance of this straight line from the origin is $25$,then $a^2$ is equal to

$A$ plot of the kinetic energy $\left(\frac{1}{2} m v^2\right)$ of ejected electrons as a function of the frequency $(\nu)$ of incident radiation for four alkali metals $(M_1, M_2, M_3, M_4)$ is shown below.
The alkali metals $M_1, M_2, M_3$ and $M_4$ are,respectively:

Water rises in a capillary tube of radius $r$ to a height $h$. The mass of water in the capillary is $m$. What will be the mass of water that rises in a capillary tube of radius $\frac{r}{3}$?