The probability distribution of a random variable $X$ is given below:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

Then the variance of $X$ is

$A$ body of mass $5 \ kg$ starts from the origin with an initial velocity $u = 30 \hat{i} + 40 \hat{j} \ ms^{-1}$. When a constant force $F = -(\hat{i} + 5 \hat{j}) \ N$ acts on the body,the time in which the $y$-component of the velocity becomes zero is (in $s$)

Two point charges $-q$ and $+q$ are located at points $(0, 0, -a)$ and $(0, 0, a)$ respectively. The electric potential at a point $(0, 0, z)$,where $z > a$ is

For the reaction sequence given below, the correct statement$(s)$ is$(are)$
image
$(A) \ P$ is optically active.
$(B) \ S$ gives Bayer's test.
$(C) \ Q$ gives effervescence with aq. $NaHCO _3$.
$(D) \ R$ is an alkyne.

If two distinct chords drawn from the point $(p, q)$ to the circle $x^{2} + y^{2} = px + qy$ (where $pq \neq 0$) are bisected by the $x$-axis,then:

$A$ vertical pole subtends an angle $\tan ^{-1}\left(\frac{1}{2}\right)$ at a point $P$ on the ground. If the angles subtended by the upper half and the lower half of the pole at $P$ are respectively $\alpha$ and $\beta$,then $(\tan \alpha, \tan \beta)$ is equal to