Why is it that even after getting a 412 rank you didn't take...

The question likely refers to a scenario where a candidate, despite having a relatively good rank (e.g., 412 in JEE Advanced), chose not to take admission in a particular IIT. There could be various reasons behind such a decision, including the following:

1. Branch Preferences:
   Even with a rank of 412, candidates might not get into their preferred branch at a prestigious IIT. Many candidates with similar ranks may have to settle for branches that are less competitive but are still valuable. For instance, a candidate who prefers Computer Science may not get it with a rank of 412, even though they could get admission into a different engineering branch.
2. IIT Ranking and Seat Availability:
   Some candidates may prefer to wait for a subsequent attempt, hoping to improve their rank. The choice of not accepting an offer from an IIT could be based on a desire to secure a better branch or a more prestigious IIT. Students might also be aiming for admission to a different IIT where their rank guarantees a better stream.
3. Personal Reasons:
   In some cases, candidates may decide not to take admission due to personal or financial reasons, or they may opt for other career opportunities that better align with their interests and goals.