If the following function is probability density function of r.v. X
$f(x) = kx^2(1-x)$, for $0 < x < 1 = 0$, otherwise, then the value of $k$ is

Two cards are drawn at random from a standard pack of $52$ cards. Then the probability that the draw consists of exactly one face card and exactly one ace card is...

The period of oscillation of a simple pendulum is given by $T = 2\pi \sqrt{\dfrac{l}{g}}$ where $l$ is about $80$ cm and is known to have $0.1$ cm accuracy. The period is about $1.5$ s. The time of $50$ oscillations is measured by a stop watch of least count $0.1$ s. The percentage error in $g$ is nearly

A car passes three points A, B and C at $3$ m/s, $6$ m/s and $9$ m/s respectively in a straight line with uniform acceleration. If distance $AB = 60$ m then find the distance BC.