If $\omega$ is a complex cube root of unity,then $225 + (3\omega + 8\omega^2)^2 + (3\omega^2 + 8\omega)^2 = $

$A$ gas is filled in a cylinder. Its temperature is increased by $20\%$ on the Kelvin scale and its volume is reduced by $10\%$. How much percentage of the gas will leak out?

$A$ random variable $X$ has the probability distribution given below. Its variance is

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$k$	$2k$	$3k$	$2k$	$k$

$\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ} = $

The figure shows the experimentally measured $B$ vs $H$ variation in a ferromagnetic material. The values of retentivity,coercivity,and saturation magnetic field of the material are respectively:

If the vectors $\overline{AB}=3 \hat{i}+4 \hat{k}$ and $\overline{AC}=5 \hat{i}-2 \hat{j}+4 \hat{k}$ are the sides of the triangle $ABC$,then the length of the median through $A$ is