JEE Main 2021 · 24 Feb · Shift 1 · Mathematics Q84

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MathematicsInteger+4 / -1Question 84 of 90

Let M be any 3 × 3 matrix with entries from the set {0, 1, 2}. The maximum number of such matrices, for which the sum of diagonal elements of M $^T$ M is seven, is _______.

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Answer and worked solution

Official answer: 540

Trace of MᵀM is the sum of squares of all nine entries (each 0, 1 or 4). Seven: seven 1s ( $\binom97=36$ ) or one 2 and three 1s ( $9\binom83=504$ ). Total 540.

Answer: 540

Topics:Matrix algebra Combinations

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JEE Main 2021 · 24 Feb · Shift 1, Mathematics question 84