JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 2 September 2020, Shift 1, Maths Q55

Question 55 of 75 in this shift, Maths question 5 of 25.

Let

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

x+\lambda y+z=4

has no solution. Then the set

S

(1)is an empty set.
(2)is a singleton.
(3)contains exactly two elements.Official answer
(4)contains more than two elements.

Official answer

Option 3

NTA final key (Sep 2020).

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
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
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 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.