Are there chances of getting into PI after scoring less in CAT?

Yep, Bahra University gives tuition fee waivers based on entrance exam scores. The commonly listed slabs look like this:

• JEE Main (rank): below 16,999 gets 40%, 17,000 to 29,999 gets 30%, 30,000 to 50,000 gets 20%, and above 50,000 gets 10%.
• NEET (score): 500 and above gets 40%, 400 to 499 gets 30%

No, according to the estimated data, you would need a CAT cutoff of atleast 94 percentile to be qualified for final admission offer. Note that this percentile is not official and is only an estimate, since the institute does not release the cutoff publicly. 

No, CAT is not the only Management entrance exam accepted by SASTRA University for its MBA programme. Candidates can also accept TANCET/ XAT/ AIMAT / CMAT/ AIMCAT scores for selection, followed by a Group Discussion and Personal Interview round.

Yes, you can join IIM Kashipur without CAT, depending on the desired programme. You can get admission to any of the offered courses except MBA. Check the list below to know which exam is accepted for which programme. 

• Executive MBA (EMBA): GMAT, IIM Kashipur EMAT (Executive Management Aptitude T

Candidates must maintain a dedicated formula sheet for properties of polygons, circle theorems, and mensuration formulas. Instead of memorising blindly, candidates must solve 15-20 problems for each sub-topic to understand how and when to apply each formula.