IIT

Yes, you can do MCA from IITs.
For MCA form IIT after BCA you have to give IIT JAM which is conducted every year by IITs for admission in MCA course. Here I am giving you all important details including Requirements to join IIT through IIT JAM.
Eligibility Criteria:
(i) For IISc Bangalore:
First class marks (As declared by the University) for unreserved / OBC Category Candidates and Second class (As declared by the University) or 50% aggregate marks, without rounding off, for SC / ST and PwD Category Candidates in the qualifying degree.
(ii) For IIT Guwahati:
At least
(a) 55% marks or 6.0 CPI in a scale of 10, without rounding off, in Major / Honors and Pass in all other subjects, including Languages and Subsidiaries or
(b) 60% aggregate marks or 6.5 CPI in a scale of 10, without rounding off, taking into account all subjects, including Languages and Subsidiaries, all years combined, for un-reserved / OBC (NCL) Category Candidates; and
(a) 50% marks or 5.5 CPI in a scale of 10, without rounding off, in Major / Honors and pass in all other subjects, including Languages and Subsidiaries, or
(b) 55% aggregate marks or 6.0 CPI in a scale of 10, without rounding off, taking into account all subjects, including Languages and Subsidiaries, all years combined, for SC/ST and PwD Category Candidates, in the qualifying degree.
(iii) For IIT Indore:
A first class in the qualifying degree At IIT Indore, the First Class is defined as:
(i) A minimum of 60% marks for GEN / OBC (55% for SC / ST) category in aggregate or as specified by the university / institute OR
(ii) A minimum CPI of 6.0 for GEN / OBC (5.5 for SC / ST) category on the scale of 10; with corresponding proportional requirements when the scales are other than on 10 (for example 4.8 for GEN / OBC category (4.4 for SC / ST) on a scale of 8) OR
(iii) A first class as specified by the university / institute.
(iv) For all other IITs:
At least 55% aggregate marks, without rounding off, (taking into account all subjects, including Languages and Subsidiaries, all years combined ) for un-reserved / OBC Category Candidates and at least 50% aggregate marks, without rounding off, (Taking into account all subjects, including Languages and Subsidiaries, all years combined) for SC / ST and PwD Category Candidates in the qualifying degree.
Algebra:
Set theory and its simple applications. Basic concepts of groups, fields and vector spaces.