The cyclotron frequency is given in Hz, so we must assume it is not an angular frequency. The formula for the cyclotron frequency (not an angular frequency) is
$\begin{align*}f = \frac{q B}{2 \pi m}\end{align*}$
This can be derived as follows. The Lorentz force must equal the force required to maintain circular motion
$\begin{align*}\frac{v^2}{r} m = q B v \Rightarrow v = \frac{q B r}{m}\end{align*}$
The frequency is then given by
$\begin{align*}f = \frac{v}{ 2 \pi r} = \frac{q B r}{2 \pi m r} = \frac{q B}{2 \pi m}\end{align*}$
So, we solve for $m$ and plug in the given numbers
$\begin{align*}m = \frac{q B}{2 \pi f} = \frac{2 \cdot 1.60 \cdot 10^{-19} \mbox{ C} \cdot \frac{\pi}{4}}{2 \pi \cdot 1600 \mb...$
Therefore, answer (A) is correct.

Solution to 2001 Problem 62