JEE Main 2021 · MathsMultiple choiceSingle correctEasyCalculation

JEE Main 31 August 2021, Shift 1, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

If the following system of linear equations

2x+y+z=5

x-y+z=3

x+y+\mathrm{a}z=\mathrm{b}

has no solution, then :

(1) $\mathrm{a}=\frac{1}{3}, \mathrm{b}\neq\frac{7}{3}$ Official answer
(2) $\mathrm{a}\neq\frac{1}{3}, \mathrm{b}=\frac{7}{3}$
(3) $\mathrm{a}=-\frac{1}{3}, \mathrm{b}\neq\frac{7}{3}$
(4) $\mathrm{a}\neq-\frac{1}{3}, \mathrm{b}=\frac{7}{3}$

Official answer

Option 1

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Condition for No Solution

Same idea in other shifts

Asked 17× in all

2 Apr 2026, Shift 1 · Q3Let $\alpha, \beta \in \mathbf{R}$ be such that the system of linear equations $x+2y+z=5$ $2x+y+\alpha z=5$ $8x+4y+\beta z=18$ has no…MediumSingle correct
10 Apr 2023, Shift 2 · Q22Let S be the set of values of $\lambda$ , for which the system of equations $6\lambda x - 3y + 3z = 4\lambda^2$ ,…HardNumerical value
25 Jul 2022, Shift 2 · Q2The number of real values of $\lambda$ , such that the system of linear equations $2x-3y+5z=9$ $x+3y-z=-18$ …MediumSingle correct
24 Jun 2022, Shift 1 · Q6The number of values of $\alpha$ for which the system of equations : $x+y+z=\alpha$ $\alpha x+2\alpha y+3z=-1$ $x+3\alpha y+5z=4$ is…MediumSingle correct
26 Jun 2022, Shift 1 · Q4The ordered pair (a, b), for which the system of linear equations $3x - 2y + z = b$ $5x - 8y + 9z = 3$ $2x + y + az = -1$ has no solution,…MediumSingle correct
27 Jun 2022, Shift 1 · Q2Let the system of linear equations $x+2y+z=2$ , $\alpha x+3y-z=\alpha$ , $-\alpha x+y+2z=-\alpha$ be inconsistent. Then $\alpha$ is equal to :MediumSingle correct
28 Jun 2022, Shift 1 · Q3If the system of linear equations $2x+3y-z=-2$ $x+y+z=4$ $x-y+|\lambda|z=4\lambda-4$ where $\lambda\in\mathbb{R}$ , has no solution, thenMediumSingle correct
24 Feb 2021, Shift 1 · Q63The system of linear equations $3x - 2y - kz = 10$ $2x - 4y - 2z = 6$ $x + 2y - z = 5\mathrm{m}$ is inconsistent if :MediumSingle correct

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.