Which of the following processes does not involve a catalyst?

The number of electrons in the valence shell of the central atom of a molecule is $8$. The molecule is

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:

The expression $\tan 9^{\circ}-\tan 27^{\circ}-\tan 63^{\circ}+\tan 81^{\circ}$ is equal to

The energy of a photon is $3 \times 10^{-12} \ erg$. What is its wavelength in $nm$?
$(h = 6.62 \times 10^{-27} \ erg \cdot s; c = 3 \times 10^{10} \ cm/s)$

The centre of mass of a system of particles does not depend on: