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$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$,then $P(X=0)$ is equal to:

Suppose $X$ follows a binomial distribution with parameters $n$ and $p$,where $0 < p < 1$. If $\frac{P(X=r)}{P(X=n-r)}$ is independent of $n$ for every $r$,then $p$ is equal to

The method of asexual reproduction in algae is -

Two liquids $A$ and $B$ have $P_A^o$ and $P_B^o$ in the ratio of $1 : 3$ and the ratio of number of moles of $A$ and $B$ in the liquid phase are $1 : 3$. The mole fraction of $A$ in the vapour phase in equilibrium with the solution is equal to:

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