500 mL of 1.2 M KI solution is mixed with 500 mL of $0.2 \mathrm{M} \mathrm{KMnO}_4$ solution in basic medium. The liberated iodine was titrated with standard $0.1 \mathrm{M} \mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ solution in the presence of starch indicator till the blue color disappeared. The volume (in L ) of $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ consumed is $\_\_\_\_$ . (Nearest integer)

The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 8,1 \leq y \leq x^2, x \geq 0\right\}$ is

A bag contains 10 balls out of which $k$ are red and $(10-k)$ are black, where $0 \leq k \leq 10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 red and 9 black balls is: