If for some $x \in \mathbb{R}^{+} \cup\{0\}$, the frequency distribution of the marks obtained by 20 students in a test is
| Marks : | 2 | 3 | 5 | 7 |
|---|---|---|---|---|
| Frequency : | $(x+1)^2$ | $2x-5$ | $x^2-3x$ | $x$ |
then the mean of the marks is
One hundred identical coins, each with probability p , of showing up heads are tossed once. If $0<\mathrm{p}<1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of $p$ is
An electric dipole will have minimum potential energy when it subtends an angle
$$\left[\begin{array}{l} \cos 0^{\circ}=1 \\ \sin 0^{\circ}=0 \end{array}\right]\left[\begin{array}{l} \cos 90^{\circ}=0 \\ \cos \pi=-1 \end{array}\right]$$
A particle is performing S.H.M. about its mean position with an amplitude ' $a$ ' and periodic time ' $T$ '. The speed of the particle when its displacement from mean position is $\frac{a}{3}$ will be