Explanation:

As B is the brother of A, so B must be a man.
Now, B and E (a married man, as given in the question) are males.
A and D are unmarried students, hence E must be married to C. Thus, C is a female.
B is neither an IAS Officer nor an Engineer.
C is not an IAS Officer.
Therefore, E must be an IAS Officer.
Now, out of B and C, one is an IPS Officer and other is an Engineer.
And, as B is not an Engineer, he must be an IPS Officer.
Hence, C is an Engineer.