JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q10

Question 10 of 90 in this shift, Maths question 10 of 30, Section A.

Let

A = [a_{ij}]

be a square matrix of order 3 such that

a_{ij} = 2^{j-i}

, for all

i, j = 1, 2, 3

. Then, the matrix

A^2 + A^3 + \ldots + A^{10}

is equal to :

(1) $\left(\frac{3^{10} - 3}{2}\right)A$ Official answer
(2) $\left(\frac{3^{10} - 1}{2}\right)A$
(3) $\left(\frac{3^{10} + 1}{2}\right)A$
(4) $\left(\frac{3^{10} + 3}{2}\right)A$

Official answer

Option 1

NTA final key (2022 Session 1).

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

Same idea in other shifts

Asked 6× 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 42 of the 174 JEE Main shifts held from 2017 to 2026.