Which of the following is the strongest conjugate base?

The amplitude of vibration of a particle is given by $a_m = a_0 / (a\omega^2 - b\omega + c)$,where $a_0$,$a$,$b$,and $c$ are positive constants. The condition for a single resonant frequency is:

An insect crawls up a hemispherical surface very slowly (see figure). The coefficient of friction between the insect and the surface is $\mu = 1/3$. If the line joining the centre of the hemispherical surface to the insect makes an angle $\alpha$ with the vertical,the maximum possible value of $\alpha$ is given by

$\sec ^2(\tan ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3)$ is equal to

The angular resolution of a $10\,cm$ diameter telescope at a wavelength of $5000\,\mathring{A}$ is of the order of

The following compound is used as: