Two capacitors $C_1$ and $C_2$ are charged to $120 \ V$ and $200 \ V$ respectively. It is found that by connecting them together,the potential on each can be made zero. Then:

The coefficient of apparent expansion of a liquid when determined using two different vessels $A$ and $B$ are $\gamma_1$ and $\gamma_2$ respectively. If the coefficient of linear expansion of the vessel $A$ is $\alpha$,then find the coefficient of linear expansion of vessel $B$.

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of $4$ and $9$ is

If the points with position vectors $60 \hat{i}+3 \hat{j}$, $40 \hat{i}-8 \hat{j}$, and $a \hat{i}-52 \hat{j}$ are collinear, then $a$ is equal to

The order of reactivity of phenol $(I)$,nitrobenzene $(II)$ and benzene $(III)$ towards nitration is

If the direction cosines of two lines are such that $l+m+n=0$ and $l^2+m^2-n^2=0$,then the angle between them is: