JEE Main 2023MathematicsMatricesHardMCQ

JEE Main 2023 — Matrices Question with Solution

JEE Main 2023 (08 Apr Shift 1)

Question

Let P=3212-1232, A=1101 and Q=PAPT. If PTQ2007 P=abcdthen 2a+b-3c-4d is equal to

Choose an option

Show full solutionCorrect option: B
Correct answer
B2005

Step-by-step explanation

Given:

P=3212-1232

∴PPT=3212-123232-121232=1001

⇒PPT=I

Now,

PTPAPT2007P=PTPAPTPAPTPAPT...PAPT⏟2007 timesP

⇒PTPAPT2007P=A2007

Now,

A=1101A2=1201A3=1301  ⋮   ⋮   ⋮  ⋮  ⋮   ⋮   ⋮  ⋮A2007=1200701

So,

⇒PTPAPT2007P=1200701

⇒PTQP=1200701=abcd

So,

a=1, b=2007, c=0, d=1

2a+b+3c-4d=2+2007-4=2005

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About this question

This is a previous-year question from JEE Main 2023, 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.