B.Tech

No, you will not have to give an entrance exam. This is only based on your marks in Diploma or B.Sc.
There is information below about your Eligibility Criteria:
The candidate should have passed Diploma in Engineering from an AICTE approved institution with a minimum of 45% marks (40% for SC/ST/Non Creamy Layer OBC) or the candidate should have Degree in Science (B.Sc) with mathematics as a subject with minimum of 45% marks (40% for SC/ST/Non Creamy Layer OBC). The marks obtained to award the division in Diploma/Degree will be considered for deciding the eligibility and respective merit. Admission to the candidates will be given as per the following order of preference: -
(a) Candidates having passed Diploma from Board of Technical Education, Rajasthan,
Jodhpur.
(b) Bona-fide residents of Rajasthan (on submission of Certificate from competent authorities) having either passed diploma from institutions located in Rajasthan and considered equivalent by Board of Technical Education Rajasthan, Jodhpur or from Board of Technical Education in other States.
(c) Candidates not covered in point (2) as above, having passed Diploma from State Boards of Technical Education outside Rajasthan.
(d)Candidates having passed B.Sc(with Mathematics) from Universities in Rajasthan.
(e)Candidates having passed B.Sc. (with Mathematics) from any recognized University as defined
by UGC.
As prescribed by the Government of Rajasthan (except in case of Private unaided Institutions and 50% seats in the self-finance course of the aided institutions) the reservation of seats will be made subject to the prevalent statutory provisions of the State of Rajasthan viz. 16% for SC candidates, 12% for ST candidates and 21% for candidates belonging to non-creamy layer OBC category.
Provision will also be made for horizontal reservation of 3% for candidates (of Bonafied of Rajasthan) belonging to physically handicap, 25% for women category and 3% for dependants of Defence Killed/Ex-servicemen / Gallantry award winners.

Top IITs in North India are at Delhi, Kanpur (Uttar Pradesh), Roorkee (Uttarakhand), Ropar (Punjab), Mandi (Himachal Pradesh). They offer Bachelor of Technology (B.Tech) degree in various disciplines, including Aerospace, Chemical, Civil, Computer Science, Electrical, and Mechanical engineering. NITs in North India include those in Delhi, Kurukshetra, Hamirpur, Srinagar, Uttarakhand and Motilal Nehru National Institute of Technology Allahabad, Malaviya National Institute of Technology Jaipur, Dr. BR Ambedkar National Institute of Technology Jalandhar. These are the best colleges depending upon your economical condition you can choose from them.