The sum of the last eight coefficients in the expansion of $(1 + x)^{15}$ is:

Two liquids $A$ and $B$ have vapour pressures in the ratio $P_A^0 : P_B^0 = 1 : 3$ at a certain temperature. If the ratio of mole fractions of $A$ to $B$ in the vapour phase is $4 : 3$,then the mole fraction of $B$ in the solution at the same temperature is

$A$ uniform meter scale is balanced at the $30 \ cm$ mark on a knife edge,when weights of $60 \ N$ and $10 \ N$ are suspended at the $10 \ cm$ and $80 \ cm$ marks,respectively. The mass of the meter scale is: (in $kg$)

In contrast to annelids,the Platyhelminthes show:

Find the binomial probability distribution whose mean is $3$ and variance is $2$.

$\left|\begin{array}{ccc} \log e & \log e^2 & \log e^3 \\ \log e^2 & \log e^3 & \log e^4 \\ \log e^3 & \log e^4 & \log e^5 \end{array}\right|$ is equal to :