Mumbai

Hi Saikant,
The rules for changing the college vary according to university rules from time to time. So, we would suggest you to inquire from the concerned colleges and its authorities.
Generally, the procedure for college to college transfer is: apply to the Registrar in the prescribed manner for permission for such transfer prior to making the desired transfer with valid reasons for the transfer proposed. An application for a transfer shall be accompanied by
(I) Written consent of the Principal of the College in which the student is studying;
(ii) The written promise of admission from the Principal of the College which he proposes to join, together with an assurance by him that the student, if the transfer is permitted, will be able to continue in his college the course of study already commenced by the student in each subject under each part of the examination; and
(iii) A certificate of satisfactory progress and good conduct from the principal of the college he is leaving. Authority to sanction is the Vice-Chancellor. A student, who has been permitted by the Vice-Chancellor to be transferred from one College to another, shall apply for combination of the attendance earned by him in the College in which he was studying before such transfer and the attendance that he would be able to earn in the college to which he has been admitted.
(iv) Every such application shall be accompanied by a chalan receipt for the prescribed fee and shall be sent to the Registrar of the University through the Principal. If university is also changing then the course of study prescribed by the University and the degree or certificate to be awarded after the successful completion of the course shall be the same of both the universities.
(v) However, you should have a valid reason for transfer before going ahead.

You will need to give various entrance exams first like CAT, CET, MAT, XAT, IBSAT, IIFT, ATMA, GMAT, etc. Applications for the same would be starting from this year for batch of 2018 probably some entrance exams application dates are also announced. Please visit the respective examination bodies and check for their enrolment procedure. Also find out as you which institute you are looking to get into and see which entrance exam scores they accept for further selection, CAT score is accepted by many of the institutions but many institutes accept multiple scores like either CAT, CET, CMAT, MAT, GMAT, etc. but if you are looking forward to get into IIM's then you would need to focus on CAT and GMAT.