If two $+ 5 D$ lenses are mounted at some distance apart,the equivalent power will always be negative if the distance is

The length of a pendulum is measured as $1.01 \ m$ and the time for $30$ oscillations is measured as $1 \ \text{minute} \ 3 \ s$. The error in length is $0.01 \ m$ and the error in time is $3 \ s$. The percentage error in the measurement of acceleration due to gravity is:

An observer is standing $500 ~m$ away from a vertical hill. Starting between the observer and the hill,a police van sounding a siren of frequency $1000 ~Hz$ moves towards the hill with a uniform speed. If the frequency of the sound heard directly from the siren is $970 ~Hz$,the frequency of the sound heard after reflection from the hill (in $Hz$) is about,(velocity of sound $= 330 ~m/s$):

The power dissipated in the circuit shown in the figure is $30 \, W$. The value of $R$ is ............. $\Omega$.

$A$ ball of mass $m$ and radius $r$ is gently released in a viscous liquid. The mass of the liquid displaced by it is $m'$ such that $m > m'$. The terminal velocity is proportional to

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