JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 6 April 2023, Shift 2, Maths Q4

Question 4 of 90 in this shift, Maths question 4 of 30, Section A.

Let

P

be a square matrix such that

P^2=I-P

. For

\alpha,\beta,\gamma,\delta\in\mathbb{N}

, if

P^\alpha+P^\beta=\gamma I-29P

and

P^\alpha-P^\beta=\delta I-13P

, then

\alpha+\beta+\gamma-\delta

is equal to

(1) $40$
(2) $24$ Official answer
(3) $22$
(4) $18$

Official answer

Option 2

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Powers of Square Matrices

Same idea in other shifts

Asked 21× in all

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.