Answer
The correct answer is: (b) The climber will accelerate down the surface.
Work Step by Step
If the climber starts to slip, then the component of weight directed down the slope is greater than the maximum possible force of static friction directed up the slope. This means that as the climber is sliding, the component of weight directed down the slope must also be greater than the force of kinetic friction directed up the slope (since the force of kinetic friction is less than the maximum possible force of static friction).
$\sum F = ma$
$mg~sin(theta) - mg~cos(\theta)~\mu_k = ma$
Since the force directed down the slope is greater than the force directed up the slope, the climber will accelerate down the surface. The correct answer is (b).