Is it permissible to go to an exam without performing ghusl from janabah when hot water is unavailable and there is a fear of missing the exam, knowing that the missed prayers were made up later?

Whoever erred by missing a prayer upon waking up and going to an exam before performing purification and prayer, must repent to Allah. Cold water is not an excuse for abandoning prayer; rather, it was obligatory to heat the water for ghusl (definition) and prayer. If one only found cold water and was unable to heat it, then one should perform tayammum (definition) and pray. Exams are not an excuse for abandoning prayer, for prayer is the first thing a servant will be held accountable for on the Day of Resurrection, as the Messenger of Allah, peace and blessings be upon him, said: "Indeed, the first thing a servant will be held accountable for from his deeds on the Day of Resurrection is his prayer. If it is sound, he will have succeeded and prospered; but if it is corrupt, he will have failed and lost." Prayer must be given the highest priority, and one must not prioritize worldly life over the Hereafter.