The pressure of an ideal gas varies with volume as $P = \alpha V$,where $\alpha$ is a constant. One mole of the gas is allowed to undergo expansion such that its volume becomes $m$ times its initial volume. The work done by the gas in the process is

If $X$ is a binomial variate with the range $\{0, 1, 2, 3, 4, 5, 6\}$ and $P(X=2) = 4 P(X=4)$, then the parameter $p$ of $X$ is

One of the major components of the cell wall of most fungi is

In the reaction $LiH + AlH_3 \rightarrow LiAlH_4$,$AlH_3$ and $LiH$ act as

$\overrightarrow{A}$ and $\overrightarrow{B}$ are two vectors of equal magnitudes and $\theta$ is the angle between them. The angle between $\overrightarrow{A}$ or $\overrightarrow{B}$ with their resultant is