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JEE Main 2021 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 16 March 2021, Shift 2, Maths Q88

Question 88 of 90 in this shift, Maths question 28 of 30, Section B.

Let

A=\begin{bmatrix}a_1\\a_2\end{bmatrix}

and

B=\begin{bmatrix}b_1\\b_2\end{bmatrix}

be two

2\times1

matrices with real entries such that

A=XB

, where

X=\frac{1}{\sqrt3}\begin{bmatrix}1&-1\\1&k\end{bmatrix}

, and

k\in\mathbf R

. If

a_1^2+a_2^2=\frac23(b_1^2+b_2^2)

and

(k^2+1)\,b_2^2\neq-2b_1b_2

, then the value of k is ________.

Official answer

1

NTA final key.

Chapter: Matrices
Topic: Matrix Multiplication
Idea tested: Row-by-Column Multiplication

Same idea in other shifts

Asked 3× in all

26 Jul 2022, Shift 2 · Q3Let $A=\begin{bmatrix}1\\1\\1\end{bmatrix}$ and $B=\begin{bmatrix}9^2&-10^2&11^2\\12^2&13^2&-14^2\\-15^2&16^2&17^2\end{bmatrix}$ , then the…EasySingle correct
4 Aug 2021, Shift 1 · Q82Let $M=(a_{ij})_{3\times3}$ , where $a_{ij}=\begin{cases}-1, & i=j\\ i^2-j^2, & i<j\\ 2i-j, & i>j\end{cases}$ $(i, j=1,2,3)$ If…EasyNumerical value

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.