If $|x| < 1$,then the sum of the series $1 + 2x + 3x^2 + 4x^3 + \dots \infty$ will be

$\int_0^2 \frac{2x-2}{2x-x^2} dx$ is equal to

Radioactive disintegration differs from a chemical change in being

An artificial satellite of mass $m$ is moving along an elliptical path around the Earth. The areal velocity of the satellite is proportional to

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to

Work done in time $t$ on a body of mass $m$ which is accelerated from rest to a speed $v$ in time $t_1$ as a function of time $t$ is given by