30 verified questions · ~45 minutes · answer key checked against the official NTA final key across multiple sources. Text-only questions (diagram-based excluded until they can be shown properly).
Let A = [[2, 1, 2], [6, 2, 11], [3, 3, 2]] and P = [[1, 2, 0], [5, 0, 2], [7, 1, 5]]. The sum of the prime factors of |P⁻¹AP − 2I| is equal to
Number of ways of arranging 8 identical books into 4 identical shelves where any number of shelves may remain empty is equal to
Answers are revealed after you attempt — that's what makes the diagnosis honest.