If ${\left( \frac{2}{3} \right)^{x + 2}} = {\left( \frac{3}{2} \right)^{2 - 2x}}$,then $x =$

The differential of ${e^{{x^3}}}$ with respect to $\log x$ is

$\int_0^{\pi/6} \cos^4 3\theta \cdot \sin^2 6\theta \, d\theta$ is equal to

$A$ random variable $X$ takes the values $0, 1$ and $2$. If $P(X=1)=P(X=2)$ and $P(X=0)=0.4$,then the mean of the random variable $X$ is

Dry air is passed through a solution containing $10 \ g$ of solute and $90 \ g$ of water,and then it is passed through pure water. The loss in weight of the solution is $2.5 \ g$ and the loss in weight of the pure solvent is $0.05 \ g$. Calculate the molecular weight of the solute.