The idea of secondary wavelets for the propagation of a wave was first given by

If the roots of the equation $x^2 - 8x + (a^2 - 6a) = 0$ are real,then:

The formal charges of $C$ and $O$ atoms in $CO_2$ $(\ddot{O}=C=\ddot{O})$ are,respectively

If the amplitude of $z - 2 - 3i$ is $\pi / 4$,then the locus of $z = x + iy$ is

An object is placed at a distance of $50 \, cm$ in front of a convex mirror. $A$ plane mirror is inserted covering half of the convex mirror. If the distance between the object and the plane mirror is $30 \, cm$,it is observed that there is no parallax between the images formed by the two mirrors. The radius of curvature of the convex mirror is ..... $cm$.

If $\int \sec ^2 x \operatorname{cosec}^4 x \, dx = -\frac{1}{3} \cot ^3 x + k \tan x - 2 \cot x + C$,then $k$ is equal to