Verdigris is

If the polar of a point on the circle $x^2+y^2=p^2$ with respect to the circle $x^2+y^2=q^2$ touches the circle $x^2+y^2=r^2$,then $p, q, r$ are in

What are $\underline{A}, \underline{B}, \underline{C}$ in the following reactions?
$(I)$ $(CH_3 CO_2)_2 Ca \xrightarrow{\Delta} \underline{A}$
$(II)$ $CH_3 CO_2 H \xrightarrow[Red\ P]{HI} \underline{B}$
$(III)$ $2 CH_3 CO_2 H \xrightarrow{P_4 O_{10}} \underline{C}$
$\underline{A} \quad \underline{B} \quad \underline{C}$

$A$ mass $M$ attached to a horizontal spring executes $S.H.M.$ of amplitude $A_{1}$. When the mass $M$ passes through its mean position,a smaller mass $m$ is placed over it and both of them move together with amplitude $A_{2}$. The ratio of $\left(\frac{A_{1}}{A_{2}}\right)$ is

$A$ ball is dropped from a height of $5 \ m$. The time after which the ball stops rebounding,if the coefficient of restitution between the ball and the ground is $e = 1/2$,is ................. $s$.

$\frac{1+\tanh \frac{x}{2}}{1-\tanh \frac{x}{2}}$ is equal to