Identify the conformer of $2-$methylpentane.

If $\frac{dy}{dx} = \frac{y + x \tan(\frac{y}{x})}{x}$,then $\sin(\frac{y}{x})$ is equal to

The vapour pressure in $mm$ of $Hg$,of an aqueous solution obtained by adding $18 \ g$ of glucose $(C_6H_{12}O_6)$ to $180 \ g$ of water at $100^{\circ} C$ is

In the compound $M-O-H$,the $M-O$ bond will be broken if

If the function $f$ defined by $f(x) = K(x - x^2)$ for $0 < x < 1$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(X < \frac{1}{2})$ is

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