Variable number of tandem repeats $(VNTRs)$ in the $DNA$ molecule are highly useful in:

The solution of $\frac{dy}{dx} + \frac{1}{3}y = 1$ is

$A$ simple pendulum performs simple harmonic motion about $x=0$ with an amplitude '$a$' and time period '$T$'. The speed of the pendulum at $x=\frac{a}{2}$ is

Using the Trapezoidal rule,find the approximate value of $\int_1^4 y \, dx$ based on the following table:

$x$	$1$	$2$	$3$	$4$
$y$	$0.7111$	$0.7222$	$0.7333$	$0.7444$

(in $.1833$)

$A$ $2 ~kg$ ball moving at $24 ~ms^{-1}$ undergoes an inelastic head-on collision with a $4 ~kg$ ball moving in the opposite direction at $48 ~ms^{-1}$. If the coefficient of restitution is $2/3$,what are their velocities in $ms^{-1}$ after the impact?

Gas is being pumped into a spherical balloon at the rate of $30 \ ft^3 / min$. The rate at which the radius increases when it reaches the value $15 \ ft$,is: