JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 24 June 2022, Shift 1, Maths Q6

Question 6 of 90 in this shift, Maths question 6 of 30, Section A.

The 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 inconsistent, is

(1)0
(2)1Official answer
(3)2
(4)3

Official answer

Option 2

NTA final key (2022 Session 1).

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

Same idea in other shifts

Asked 6× 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
25 Jul 2021, Shift 1 · Q79The values of a and b, for which the system of equations $2x+3y+6z=8$ $x+2y+az=5$ $3x+5y+9z=b$ has no solution, are :EasySingle correct
8 Jan 2020, Shift 1 · Q53For which of the following ordered pairs $(\mu, \delta)$ , the system of linear equations $x+2y+3z=1$ $3x+4y+5z=\mu$ $4x+4y+4z=\delta$ is…MediumSingle correct
2 Sep 2020, Shift 1 · Q55Let $S$ be the set of all $\lambda\in\mathbf{R}$ for which the system of linear equations $2x-y+2z=2$ $x-2y+\lambda z=-4$ …MediumSingle correct
2 Apr 2017 (offline) · Q65If S is the set of distinct values of 'b' for which the following system of linear equations $x+y+z=1$ $x+ay+z=1$ $ax+by+z=0$ has no…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 42 of the 174 JEE Main shifts held from 2017 to 2026.