The probability distribution of a random variable X is given by

Then the variance of X is

If $\left(\cos ^{-1} x\right)^2-\left(\sin ^{-1} x\right)^2>0$, then

If $\bar{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \bar{b}=\hat{i}-2 \hat{j}-2 \hat{k}, \bar{c}=-\hat{i}+4 \hat{j}+3 \hat{k}$ and if $\overline{\mathrm{d}}$ is vector perpendicular to both $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}, \overline{\mathrm{a}} \cdot \overline{\mathrm{d}}=18$, then $|\overline{\mathrm{a}} \times \overline{\mathrm{d}}|^2=$

The rate of change of volume of spherical balloon at any instant is directly proportional to its surface area. If initially its radius is 3 cm , after 2 minutes its radius becomes 9 cm , then radius of balloon after 4 minutes is