Hello aspirant,
Yes you will be able to get admission in Thapar Institute without appearing in JEEMain examination. There is mode 2 in which  30 percent of the B.E/ B.Tech seats are reversed on the basis of merit of marks secured in 10+2 or equivalent examinations. The candidate should have atleast 75% if he/she belongs to general category and 70% for the other candidates.
As you have scored 95% , therefore you will easily get admission in the institute.

Hope it helps!

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