$A$ given mass of gas expands reversibly from the state $A$ to the state $B$ by three paths $1, 2$ and $3$ as shown in the figure. If $w_1, w_2$ and $w_3$ respectively be the work done by the gas along three paths then

If $\cos x + \cos^2 x = 1$,then the value of $\sin^2 x + \sin^4 x$ is

The number of values of $x$ in the interval $[0, 3\pi]$ satisfying the equation $2 \sin^2 x + 5 \sin x - 3 = 0$ is

$CFCl_3$ is responsible for the decomposition of ozone to oxygen. Which of the following reacts with ozone to form oxygen?

The diameter of an oxygen molecule is $2.94 \times 10^{-10} \ m$. The Van der Waals gas constant '$b$' in $m^3/mol$ will be:

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1) = \frac{1}{2}$,$P(B_2) = \frac{1}{3}$,and $P(B_3) = \frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it has come from box $B_2$ is: