Two liquids A and B form an ideal solution. At 320 K , the vapour pressure of the solution, containing 3 mol of $A$ and 1 mol of $B$ is 500 mm Hg . At the same temperature, if 1 mol of A is further added to this solution, vapour pressure of the solution increases by 20 mm Hg . Vapour pressure (in mm Hg ) of B in pure state is $\_\_\_\_$ . (Nearest integer)

The number of ways, in which 16 oranges can be distributed to four children such that each child gets at least one orange, is

Let $\sum\limits_{k=1}^n a_k=\alpha n^2+\beta n$. If $a_{10}=59$ and $a_6=7 a_1$, then $\alpha+\beta$ is equal to :

If $z=\frac{\sqrt{3}}{2}+\frac{i}{2}, i=\sqrt{-1}$, then $\left(z^{201}-i\right)^8$ is equal to