You can give these exams including NEET even at the age of 50, check the list

Which exams do not have an upper age limit?

You can give NEET UG exam at any age. There is no maximum age limit to appear in it

IIT GATE
There is no maximum age limit to appear in NEET UG and IIT GATE exam as well

CAT exam
There is no maximum age limit in the Common Admission Test to do MBA from IIM

JAM exam
Candidates of any age can appear in the JAM exam to do a master’s course from IIT

NEET PG
There is no age limit in the NEET PG exam conducted for admission in medical PG course

MAT exam
Apart from this, there are many other national level exams including MAT, which do not have a maximum age limit