If Allah forgave Adam in 2.37, then why was he exiled from Heaven & sent to earth as a punishment ? Reply me as soon as possible. Its urgent!

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Allaah is the All-Knowing and Most Wise. He created Aadam (Adam ) and his descendants as inheritors of the earth to see their deeds. Allaah ordained that Aadam would eat from the tree and that would be reason for him to be brought down to earth. Allaah did not make him live on the earth from the beginning so that the devil's enmity toward him would become evident and so that he would be wary of him.

Aadam along with his descendants being brought down to earth is one of the greatest favors of Allaah to him and his descendants. Allaah has great wisdom in doing so, wisdom that would not have been achieved if Aadam had remained in Paradise.

Ibn Al-Qayyim pointed out some of this wisdom as per the following:

1. Aadam would return to Paradise in the best  condition. Allaah, The Almighty, wanted to make him and his descendants taste the hardship of the worldly life - its distress, its concerns, its grief, and this would make them know the honor of going to Paradise.

2. It is only by knowing the opposite of something that one appreciates it, and if they were brought up in Paradise, they would not have known its value.

3. Allaah wanted to command, forbid and test them. Paradise is not a place of Takleef (i.e. imposition of religious obligations), so Allaah brought them down to earth and made them experience those things so that they get a reward that could not be attained without commands and prohibitions.

4. Allaah wanted to select from among them (sons of Aadam) prophets, messengers, martyrs and allies of Allaah, those who would love Him and He would love them, so He put them with their enemies and tested them by doing so.

5. The effects of the Names and Attributes of Allaah would become evident to them. His Wisdom necessitated that He bring down Aadam and his descendants to a place where He would show them the effects of His beautiful Names and Attributes: He forgives whom He wills and has mercy upon whom He wills, He humbles whom He wills and honors whom He wills, He avenges whom He wills, He gives to whom He wills and holds from whom He wills, and Allaah provides for whom He wills, and so on. These are the effects of His Names and Attributes.

Allaah Knows best.