Three plates of common surface area $A$ are connected as shown. The effective capacitance between points $A$ and $B$ will be

Two metal plates each of area $A$ form a parallel plate capacitor with air in between the plates. The distance between the plates is $d$. $A$ metal plate of thickness $d/2$ and of same area $A$ is inserted between the plates to form two capacitors of capacitances $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitors is $C^{\prime}$ and the capacitance of the capacitor initially is $C$,then $C^{\prime}/C$ is

The centroid of the triangle formed by the pair of straight lines $12x^2 - 20xy + 7y^2 = 0$ and the line $2x - 3y + 4 = 0$ is:

What is $X$ in the following reaction?
${}_{12}Mg^{26} + {}_{1}H^{2} \longrightarrow {}_{12}Mg^{27} + X$

Solid $BeH_2$ and solid $BeCl_2$ differ in

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is