Let me answer this question in stages:
Cutoff for CAT:- Depends upon the following factors:
*Your own total score
*difficulty level of the exam
*Number of students appearing for the exam in that year
*Number of students qualifying the exam
*Number of seats
*institute (different institutes will have different cutoffs) for instance in the year 2017:
Cutoffs of IIM AHMEDABAD, IIM BANGALORE, IIM CALCUTTA, IIM Lucknow, IIM KOZHIKODE and IIM INDORE respectively were:
(General category)
VA-RC-70, 85, 80+,  85, 80,  80
DI-LR-70,80,80+,85,80,80
QA-70,80,80+,85,80,80
Overall-80,90,90+,90,90,90
(NC-OBC, Transgender)
VA-RC-65,75,75+,77,70,70
DI-LR-65,70,75+,77,70,70
QA-65,70,75+,77,70,70
Overall-75,80,85+,82,80,80
(SC - ST)
VA-RC-60,70,65+,55,50,55
DI-LR-60,65,65+,55,50,55
QA-60,65,65+,55,50,55
Overall-70,75,70+,70,65,60
Note these are just the cutoffs, means you need to cross this level of percentile in order to be eligible for calls for further rounds. However sending the calls will be at complete discretion of the institute looking into a number of other parameters.
For more comprehensive list of cutoffs of the new and baby IIMs you can refer to:

https://www.google.co.in/amp/s/bschool.careers360.com/articles/cat-cutoff%3famp#ampshare=https://bschool.careers360.com/articles/cat-cutoff

Talking about the fee structure and average placement respectively of the top B-schools of India:
*IIMA: 21lacs for two years and 23 lac p.a
*IIMB: 21 lacs for two years and 22.6 lac p.a
*IIMC: 19 lacs for two years and 21.9 lac p.a
*IIML: 15 lacs approx for two years
*IIMK: 19lacs for two years and 18 lac p.a
*IIMI: 13 lacs for two years and 15 lacs p.a
*MDI, Gurgaon: 18.86 lacs for two years and 18.85 lacs p.a (subject to be revised)
*IMI, New Delhi: 15 lacs for two years and 14 lacs p.a(subjected to revision).
And about MBA in finance, there is no such specialisation provided by any of the institutes. You can opt for finance related electives in your second year.
Hope this helps.

DSM DTU

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