Qualified  = (1) certified, officially recognized;  having the necessary qualifications.

• There is a training programme for the newly qualified doctors.
• He’s a highly qualified engineer.
• We’ve to verify his academic qualifications before giving him such a responsible job.
• I am not qualified to give you advice on technical aspects of your project.
• Previous experience is an essential qualification for this job.
• She has all the right qualifications to be a good teacher.

(2) limited, not complete or absolute ; modified in some way.

• The auditor gave a qualified report on the balance sheet of the company.(i.e he gave a report with some comments)
• We can accept the proposal only with some qualifications on the terms of payment of rent. (i.e can be accepted only with some changes/conditions)
• A qualified approval. ( approval with some limiting factors)

Unqualified  = not having suitable knowledge or qualifications.

• He is quite unqualified to talk on this subject.
• The Bank would not permit an unqualified accountant to audit its books.

(2)  total; without limitation or reservation.

• The auditor gave an unqualified report on the balance sheet. (  i.e  a report without comments)
• The proposal has the unqualified support of the entire team. (i.e full support)

Related usages:

Qualify = to have or achieve the necessary skills etc.

• This course will qualify you to work in a bank.
• She doesn’t qualify for LFC/LTC  benefits before putting in the prescribed period of service.

Disqualify = to stop someone from being in a competition/ or doing something.

• He has been disqualified from the championship.
• His bad behaviour resulted in the disqualification.