JEE Main 2021MathematicsMatricesHardNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (24 Feb Shift 1)

Question

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 MTM is seven, is______.

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Show full solutionCorrect answer: 540
Correct answer
540

Step-by-step explanation

abcdefghiadgbehcfi

a2+b2+c2+d2+e2+f2+g2+h2+i2=7

Case-I : Seven 1's and two 0's

C29=36

Case-II: One 2 and three 1's and five 0's

9!5!3!=504

∴ Total =540

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About this question

This is a previous-year question from JEE Main 2021, covering the Matrices chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.