Heat energy is incident on the surface at the rate of $1000 ~J/min$. If the coefficient of absorption is $0.8$ and the coefficient of reflection is $0.1$,then the heat energy transmitted by the surface in $5$ minutes is: (in $~J$)

Which one of the following statements is not correct?

If $\cos A = \frac{3}{4}$,then $32 \sin \left(\frac{A}{2}\right) \sin \left(\frac{5A}{2}\right) = $

$A$ solution which is $10^{-3} \ M$ each in $Mn^{2+}$,$Fe^{2+}$,$Zn^{2+}$ and $Hg^{2+}$ is treated with $10^{-16} \ M$ sulphide ion. If the $K_{sp}$ of $MnS$,$FeS$,$ZnS$ and $HgS$ are $10^{-15}$,$10^{-23}$,$10^{-20}$ and $10^{-54}$ respectively,which one will precipitate first?

If the coefficient of $x$ in the expansion of $\left(x^2+\frac{k}{x}\right)^5$ is $270$,then $k$ is equal to

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is