The rate of disintegration of a fixed quantity of a radioactive element can be increased by

If the impurity in a metal has a greater affinity for oxygen and is more easily oxidised than the metal,then the purification of metal may be carried out by

$\int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right) d x$ is equal to

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is . . . . . . .

Magnetic lines of force due to a bar magnet do not intersect because

Let $a = \min \{x^2 + 2x + 3, x \in R\}$ and $b = \lim_{x \to 0} \frac{\sin x \cos x}{e^x - e^{-x}}$. Then the value of $\sum_{r=0}^n a^r b^{n-r}$ is