A

Step 1: Identify the forces acting on the monkey. The weight (mg) acts downward and static friction (f) acts upward if the monkey is accelerating upwards.
Step 2: Apply Newton's second law. The net force (F_net) acting on the monkey is given by:
F_{net} = m imes a = T - mg - f,
where T is the tension in the rope.
Step 3: The static friction can be expressed as:
f \leq \mu N,
where N is the normal force acting on the monkey, which is equal to the weight in this case, so N = mg.
Step 4: Thus, static friction can be maximized:
f_{max} = \mu mg.
Step 5: Since the monkey is accelerating upwards with acceleration 'a', the direction of the friction force is upwards to assist the monkey in climbing up.
Therefore, the direction of frictional force is upward, and its maximum value is \mu mg.