Is it permissible for a student to take examinations after informing the college administration of his inability to pay the fees, knowing that he was able to pay them?

What you told the college administration, that your circumstances do not permit you to pay the remaining fees, contrary to the truth, is a forbidden lie. You must hasten to repent from it and hasten to pay the tuition fees. There is no harm for you in taking the exams and pursuing any work that may result from them in the future.