JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 25 February 2021, Shift 2, Maths Q63

Question 63 of 90 in this shift, Maths question 3 of 30, Section A.

The following system of linear equations

2x + 3y + 2z = 9

3x + 2y + 2z = 9

x - y + 4z = 8

(1)does not have any solution
(2)has a unique solutionOfficial answer
(3)has infinitely many solutions
(4)has a solution $(\alpha, \beta, \gamma)$ satisfying $\alpha + \beta^2 + \gamma^3 = 12$

Official answer

Option 2

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Condition for Unique Solution

Same idea in other shifts

Asked 4× in all

31 Jan 2024, Shift 2 · Q4Let $A$ be a $3\times3$ real matrix such that $A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix}$ ,…MediumSingle correct
24 Jun 2022, Shift 2 · Q3Let the system of linear equations $x + y + \alpha z = 2$ $3x + y + z = 4$ $x + 2z = 1$ have a unique solution $(x^*, y^*, z^*)$ . If…MediumSingle correct
24 Feb 2021, Shift 2 · Q72For the system of linear equations : $x-2y=1$ , $x-y+kz=-2$ , $ky+4z=6$ , $k\in$ R, consider the following statements : (A) The system has…MediumOther

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.