Ajmer

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.

Hi,
RIE, Ajmer application form for NCERT Common Entrance Examination (NCERT CEE) can be filled online.
The minimum eligibility criteria for integrated BA-B.Ed and B.Sc-B.Ed courses is 10+2 with 50% (45% for SC/ST/PWD) from a recognized board. B.Ed programme requires graduation in Arts/ Science or Engineering with 50% (45% for SC/ST/PWD) from a recognized university. Candidates who have passed 10+2 or equivalent examination in 2015, 2016 or appearing /appeared in 2018 are also eligible to apply for BA-B.Ed and B.Sc-B.Ed courses. Admission to all the courses is based on the score in CEE conducted by NCERT followed by preparation of merit list and counselling. Candidates are selected on the basis of CEE score and aggregate marks in the last qualifying exam. 60% weightage will be given to CEE score and remaining 40% for marks in the qualifying examination. Thanks.