Since the problem is quite vague because the number of choice per question is not written here. I’ll just put for 4 choices and 5 choices each.
To compute for the 5 choices each:
Mean = np = 20 (1/5) = 4
Standard deviation = sqrt(npq) = sqrt (4*(4/5) = 1.79
To compute for the 4 choices each:
Mean = np = 20 (1/4) = 5
Standard deviation = sqrt(npq) = sqrt (5*(4/5) = 2