Two fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is

$A$ ray of light travels from an optically denser to a rarer medium. The critical angle for the two media is $C$. The maximum possible deviation of the ray will be

$ \int \frac{\sin 2x}{\sin^2 x + 2\cos^2 x} dx = $

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

The resistance of an ammeter is $13 \Omega$ and its scale is graduated for a current up to $100 \text{ A}$. After an additional shunt has been connected to this ammeter,it becomes possible to measure currents up to $750 \text{ A}$ by this meter. The value of the shunt resistance is

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