For two data sets each of size 5 , the variance are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined data set is

The number of ways in which 8 different pearls can be arranged to form a necklace is

If $$p, q$$ are true statements and $$r$$ is false statement, then which of the following is correct.

The curves $$\frac{x^2}{a^2}+\frac{y^2}{4}=1$$ and $$y^3=16 x$$ intersect each other orthogonally, then $$a^2=$$