JEE Main 2021MathematicsMatricesMediumNumerical

JEE Main 2021 — Matrices Question with Solution

JEE Main 2021 (25 Jul Shift 1)

Question

Let M=A=abcd:a,b,c,d∈±3,±2,±1,0. Define f:M→Z, as fA=detA, for all A∈M where Z is set of all integers. Then the number of A∈M such that fA=15 is equal to                 .

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Show full solutionCorrect answer: 16
Correct answer
16

Step-by-step explanation

.A=ad-bc=15

where a,b,c,d∈±3,±2,±1,0

Case I: ad=9 & bc=-6

For ad possible pairs are 3,3,-3,-3. 

For bc possible pairs are 3,-2,-3,2,-2,3,2,-3 

So, total number of matrices in case I=2×4=8

Case II: ad=6 & bc=-9

Similarly, total number of matrices in case II =2×4=8

Hence, total number of matrices are 16.

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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.