The group velocity is defined as
$\begin{align*}v_g = \frac{d \omega}{dk}\end{align*}$
The phase velocity is defined as
$\begin{align*}v_p = \frac{w}{k}\end{align*}$
In the range $k_1 < k < k_2$ , we can see that both $\omega$ and $k$ are positive, so the phase velocity is positive. On the other hand, the slope of the function $\omega (k)$ is negative, therefore, the group velocity is negative. Therefore, answer (A) is correct.

Solution to 1992 Problem 79