The gas that cannot be collected over water is

If $E, M, J$ and $G$ respectively denote energy,mass,angular momentum,and universal gravitational constant,the quantity which has the same dimensions as the dimensions of $\frac{E J^2}{M^5 G^2}$ is:

$A$ radioactive nucleus $A$ with a half-life $T$ decays into a nucleus $B$. At $t = 0$,there is no nucleus $B$. At some time $t$,the ratio of the number of $B$ to that of $A$ is $0.3$. Then,$t$ is given by:

Two particles $P$ and $Q$ start from the origin and execute simple harmonic motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$,respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

An integrating factor of the differential equation $(1-x^2) \frac{dy}{dx} + xy = \frac{x^4}{(1+x^5)} (\sqrt{1-x^2})^3$ is

If $e$ and $e^{\prime}$ are the eccentricities of the ellipse $5x^2 + 9y^2 = 45$ and the hyperbola $5x^2 - 4y^2 = 45$ respectively,then $ee^{\prime}$ is equal to