Laser beams are used to measure long distances because

The number of points in $(-\infty, \infty)$ for which $x^2 - x \sin x - \cos x = 0$ is

$\int \frac{dx}{1-\cos x-\sin x}$ is equal to

$A$ launching vehicle carrying an artificial satellite of mass $m$ is set for launch on the surface of the earth of mass $M$ and radius $R$. If the satellite is intended to move in a circular orbit of radius $7R$,the minimum energy required to be spent by the launching vehicle on the satellite is (Gravitational constant $= G$)

If the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a pair of straight lines,then the square of the distance of their point of intersection from the origin is

Identify the mixture that shows positive deviation from Raoult's law.