The equation $12x^2 + 7xy + ay^2 + 13x - y + 3 = 0$ represents a pair of perpendicular lines. Then the value of $a$ is

Kangaroo rat is found in .........

If the mean and variance of a binomial variate $X$ are $8$ and $4$ respectively, then $P(X < 3)$ equals to

Considering only the principal values of inverse functions,the set $A = \{x \geq 0 : \tan^{-1}(2x) + \tan^{-1}(3x) = \frac{\pi}{4}\}$

$A$ ball falls from a height $h$ and rebounds after striking the floor. The coefficient of restitution is $e$. The total distance covered before it comes to rest is

The lines represented by the equation $x^2-y^2-x+3y-2=0$ are :