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Dear aspirant,
As you have mentioned that you have secured 87.6% in 10th board and 89.33% in 12th board so let me tell you that it's very difficult to get iim Bangalore in this cat percentile because in 90 percentile considering you from gem category.
Although various factors are considered while deciding the cut offs like number of candidates appearing in the examination number of vacant seats in college previous years cut offs.
For more information you can check out the link given below-
https://bschool.careers360.com/articles/cat-cutoff/amp
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