What should be the minimum age to give iit exam?

There's no minimum age to *give* the IIT entrance exam (JEE Advanced), but there is a maximum age limit and eligibility requirements based on educational qualifications. You must have passed your 12th standard (or equivalent) exam to be eligible. Since most students complete their 12th standard at age 17 or 18, this effectively makes the minimum age around 17. However, there's no explicit lower age limit.