Hello aspirant, admission into either of the two Colleges mentioned in the tabs depends upon their own criteria.

Jawaharlal Nehru University, New Delhi
To get admission into this university you will have to clear your JEE Mains.
On the basis of JEE Main Ranking, you will get admission through "Central Seat Allocation Board" (CSAB) and "Joint Seat Allocation Authority" (JoSAA).

The University has recently extended it's branch to engineering with "School of Engineering".
Therefore, it has proposed to provide the following dual degrees:

• BTech in Computer Science and Engineering and MS/MTech in Social Sciences/Humanities/Science/Technology

• BTech in Electronics and Communication Engineering and MS/MTech in Social Sciences/Humanities/Science/Technology

• BTech in Civil and Environmental Engineering and MS/MTech in Social Sciences/Humanities/Science/Technology

• BTech in Chemical Engineering and MS/MTech in Social Sciences/Humanities/Science/Technology 

• BTech in Mechanical Engineering and MS/MTech in Social Sciences/Humanities/Science/Technology 

Whereas in the year 2018, it offered only the first two dual degree programs.

Jaipur National University, Rajasthan
It is a privately owned state University. Also it has NAAC 'B' accreditation.

According to it's brochure, you can get admission into the University through entrance tests like JNU NET/ AIEEE/ RPET/ GATE/ CLAT/ RMAT/ MAT / CAT etc. Along with  qualifying examination for professional and technical courses+ Personal Interview and merit.

The courses that it provides are:
B.Tech
Biotechnology
Computer Science & Engg.
Food Technology
Electronics & Comm. Engg.
Electrical Engg.
Chemical Engg.
Mechanical Engg.
Civil Engg.
Electronics & Computer Engg.

B.Tech+MBA (Dual Degree)

Now, you can make a choice which university you want to go for, and which exams to appear for.

All the best!
I hope this helps.

Hii Gangadhar!! JNU has recently extended its wing to engineering branch. To take admission in JNU's engineering branch you need to appear in mains exam. No separate counselling takes place. You need to enroll in JOSAA to get a seat. Hope this helped. Good luck!!