The equation of the pair of lines joining the origin to the points of intersection of $x^2+y^2=9$ and $x+y=3$ is:

Lichens indicate $SO_2$ pollution because they

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

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

The maximum potential energy due to electrostatic repulsion between two hydrogen nuclei is nearly (radius of the nucleus $= 1.1 \text{ fermi}$). $\left[\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ Nm}^2 \text{C}^{-2}\right]$ (in $MeV$)

If $\bar{M}_w$ is the weight average molecular weight and $\bar{M}_n$ is the number average molecular weight of a polymer,the poly dispersity index $(PDI)$ of the polymer is given by