If $A$ and $B$ are any two events,then $P(A \cup B) = $

$A$ rod of length $L$ is held vertically on a smooth horizontal surface. The top end of the rod is given a gentle push. At a certain instant of time,when the rod makes an angle $\theta$ with the horizontal,the velocity of the $COM$ of the rod is $v_0$. The velocity of the end of the rod in contact with the surface at that instant is:

Four charges are placed at the circumference of a dial clock as shown in the figure. If the clock has only an hour hand, then the resultant force on a charge $q_0$ placed at the center points in the direction which shows the time as: (in $.30$)

The number of elements present in the fourth period is

If $x = \frac{1}{2} \left( \sqrt{3} + \frac{1}{\sqrt{3}} \right)$,then the value of $\frac{\sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}}$ is equal to

The adjacent graph shows the extension $(\Delta l)$ of a wire of length $1 \ m$ suspended from the top of a roof at one end with a load $W$ connected to the other end. If the cross-sectional area of the wire is $10^{-6} \ m^2$,calculate the Young's modulus of the material of the wire.