The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

Calculate the heat of combustion (in $kJ$) of methane from the following data:
$(I)$ $C_{(graphite)} + 2H_{2(g)} \rightarrow CH_{4(g)} \quad \Delta H = -74.8 \ kJ$
$(II)$ $C_{(graphite)} + O_{2(g)} \rightarrow CO_{2(g)} \quad \Delta H = -393.5 \ kJ$
$(III)$ $H_{2(g)} + 1/2 O_{2(g)} \rightarrow H_2O_{(l)} \quad \Delta H = -286.2 \ kJ$

Which one of the following elements,when present as an impurity in silicon,makes it a $p$-type semiconductor?

Assertion $(A)$: White tin is an example of a tetragonal system.
Reasoning $(R)$: For a tetragonal system,$a=b=c$ and $\alpha=\beta=\gamma \neq 90^{\circ}$. The correct answer is

If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1$ where $x \geq \frac{1}{2}$,then $\sqrt{4x^2-1}$ is equal to

When a ceiling fan is switched off,its angular velocity falls to half while it makes $36$ rotations. How many more rotations will it make before coming to rest? (Assume uniform angular retardation)