Determine the probability of no head appearing if two coins are tossed simultaneously. 

In this problem, we must first determine the sample space when two coins are tossed simultaneously.

The sample space when two coins are tossed simultaneously $=\left\{\right(\mathrm{H}, \mathrm{H}),(\mathrm{H}, \mathrm{T}),(\mathrm{T}, \mathrm{H}),(\mathrm{T}, \mathrm{T}\left)\right\}$

Thus, total number of outcomes = 4

Now, for having no head we need $=\left\{\right(\mathrm{T}, \mathrm{T}\left)\right\}$

Thus, number of favourable outcome = 1

$\therefore \mathrm{P}(\mathrm{getting} \mathrm{no} \mathrm{head})=\frac{\mathrm{number} \mathrm{of} \mathrm{favourable} \mathrm{outcome}}{\mathrm{total} \mathrm{number} \mathrm{of} \mathrm{outcomes}}=\frac{1}{4}$

Hence, the correct answer is $\frac{1}{4}$.