JEE Main 2019MathematicsMatricesHardMCQ

JEE Main 2019 — Matrices Question with Solution

JEE Main 2019 (12 Jan Shift 1)

Question

Let P=100310931 and Q=qij be two 3×3  matrices such that Q-P5=I3. Then q21+q31q32 is equal to :

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Show full solutionCorrect option: A
Correct answer
A10

Step-by-step explanation

Given,

P=100310931

⇒P2=100310931100310931=1006102761

⇒P4=P2×P2=10061027611006102761=100121090121

⇒P5=P4×P=100121090121100310931=1001510135151

Let,

Q=q11q12q13q21q22q23q31q31q33

Now, given Q-P5=I3

⇒q21-15=0, q31-135=0,  q32-15=0

⇒q21=15, q31=135, q32=15

∴q21+q31q32=15+13515=10.

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About this question

This is a previous-year question from JEE Main 2019, 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.