The oxoanion which contains all equivalent $M-O$ bonds is:
$(I)$ $CrO_4^{2-}$
$(II)$ $MnO_4^{-}$
$(III)$ $Cr_2O_7^{2-}$

The minimum value of $(x-\alpha)(x-\beta)$ is

The maximum tension a rope can withstand is $60 ~kg-wt$. The ratio of maximum acceleration with which two boys of masses $20 ~kg$ and $30 ~kg$ can climb up the rope at the same time is

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same (total) energy stored in it as the first combination has. The value of $C_2$,in terms of $C_1$,is then