The number of nodal planes in a $p_x$ orbital is

$\int_0^{\pi / 2} \sin ^8 x \cos ^2 x \, dx$ is equal to

In an acute angled triangle,$\cot B \cot C + \cot A \cot C + \cot A \cot B$ is equal to

The mean and the standard deviation (s.d.) of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new s.d. become half of their original values,then $q$ is equal to

If $\cos 2x = (\sqrt{2} + 1) \left(\cos x - \frac{1}{\sqrt{2}}\right)$ and $\cos x \neq \frac{1}{\sqrt{2}}$,then $x \in$

Which of the following possesses a dome-shaped thalamus?