If the direction ratios of two lines are given by $3lm - 4ln + mn = 0$ and $l + 2m + 3n = 0$, then the angle between the lines is:

For a binomial variate $X$ with $n=6$, if $P(X=2)=9 P(X=4)$, then its variance 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

If the line $2x + 5y = 12$ intersects the ellipse $4x^2 + 5y^2 = 20$ in two distinct points $A$ and $B$,then the mid-point of $AB$ is

In an electroplating experiment,$m \ g$ of silver is deposited when $4 \ A$ of current flows for $2 \ min$. The amount (in $g$) of silver deposited by $6 \ A$ of current flowing for $40 \ s$ will be:

$A$ random variable $X$ has the following probability distribution:

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.15$	$0.23$	$K$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

For the event $E = \{X \mid X \text{ is a prime number}\}$ and the event $F = \{X \mid X < 4\}$, the probability $P(E \cup F) = $