Engineering Entrance Exam

Yes, you can join Rajalakshmi engineering College with JEE percentile as they accept JEE scorecard, and after they take their own interviews and entrance exam. 
The percentile you will required for admission will be around 99 percentile for CS branch. If you want to adopt and if you want to go for ECE or other branch, then 98 or 99 percentile is required.

For All India seats (52%), admissions are based on the rank obtained in the JEE (Main) exam through Institutional counselling.It also depends on your state of domicile but the cutoff of ITNU is so high in each branches either it's CS or Mechanical engineering. 

No, you don't have any chance of getting into ITNU (Institute of Technology, Nirma University) Ahmedabad with a JEE Main rank of 35,000, in any branches.

If you got 78% in JEE mains, the estimated rank in DASA will be more than 8000 according to trends and they are based on JEE Mains actual scores.

You might not get an admission in NIT for CS programme because there is so much difference in DASA rank according to your JEE main percentile. NIT Warangal, Surathkal requires DASA ranks in between 150-400, NIT Calicut requires between 800-1000 and all lower tier NITs requires nearly between 2000-2500. So, it is nearly impossible to get CS in NITs with your JEE 78 percentile.

No, you generally don't have to take the JEE for admission to design colleges. JEE is mainly for engineering and architecture programs, design colleges typically use their own entrance exams or they may consider scores from national-level design entrance exams. Common design entrance exams include NIFT (National Institute of Fashion Technology), NID (National Institute of Design), UCEED (Undergraduate Common Entrance Examination for Design), and CEED (Common Entrance Exam for Design). You can start your preparation for these exams early.

For JEE Main 2025 Session 2, the qualifying percentile cutoffs (needed to be eligible for JEE Advanced) are approximately:

• General (UR): 93.10 percentile
• EWS: 80.38 percentile
• OBC? NCL: 79.43 percentile
• SC: 61.15 percentile
• ST: 47.90 percentile

These are the minimum marks required to be eligible for JEE ADVANCED. Actual admission (JoSAA) cutoffs for NITs, IITs, etc., depend on branch and category—they're typically much higher (e.g., top CSE at NITs needs ~95+ percentile).