From a point on the level ground,the angle of elevation of the top of a pole is $30^{\circ}$. On moving $20 \ m$ nearer to the pole,the angle of elevation becomes $45^{\circ}$. The height of the pole (in metres) is:

There are two wires of the same material and same length. If the diameter of the second wire is $2$ times the diameter of the first wire,then the ratio of the extension produced in the wires by applying the same load will be:

Which one has the maximum oxidation number of phosphorus?

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$,then the equation of the circle is

For the gaseous reactions $(I)$ and $(II)$,the equilibrium constants are $X$ and $Y$ respectively.
$I$. $\frac{1}{2} N_{2(g)} + O_{2(g)} \rightleftharpoons NO_{2(g)}$
$II$. $2 NO_{2(g)} \rightleftharpoons N_2 O_{4(g)}$
Using the above reactions,the equilibrium constant $Z$ for the reaction $(III)$ given below is:
$III$. $N_2 O_{4(g)} \rightleftharpoons N_{2(g)} + 2 O_{2(g)}$

If the charge on a body is increased by $2 \ C$,the energy stored in it increases by $21 \%$. The original charge on the body in coulomb is