JEE Main 2020 · MathsNumerical answerNumerical valueMediumCalculation

JEE Main 6 September 2020, Shift 2, Maths Q71

Question 71 of 75 in this shift, Maths question 21 of 25.

The sum of distinct values of

\lambda

for which the system of equations

(\lambda-1)x+(3\lambda+1)y+2\lambda z=0

(\lambda-1)x+(4\lambda-2)y+(\lambda+3)z=0

2x+(3\lambda+1)y+3(\lambda-1)z=0

, has non-zero solutions, is ________.

Official answer

3.00

NTA final key (Sep 2020).

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Parameter Evaluation in Homogeneous Systems

Same idea in other shifts

Asked 9× in all

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6 Apr 2024, Shift 1 · Q22Let $\alpha\beta\gamma=45$ ; $\alpha, \beta, \gamma \in \mathbb{R}$ . If $x(\alpha,1,2)+y(1,\beta,2)+z(2,3,\gamma)=(0,0,0)$ for some…MediumNumerical value
8 Apr 2023, Shift 2 · Q3Let S be the set of all values of $\theta \in [-\pi, \pi]$ for which the system of linear equations $x + y + \sqrt{3}z = 0$ …MediumSingle correct
3 Aug 2021, Shift 2 · Q65For the system of linear equations $(k-3)x + y + z = 0$ $x + (k-3)y + z = 0$ $x + y + (k-3)z = 0$ the number of distinct values of $k$ ,…MediumSingle correct
26 Aug 2021, Shift 1 · Q64Let $\theta \in \left(0, \frac{\pi}{2}\right)$ . If the system of linear equations.…MediumSingle correct
18 Mar 2021, Shift 1 · Q64Let $\alpha,\beta,\gamma$ be the real roots of the equation, $x^3+ax^2+bx+c=0$ , ( $a,b,c\in\mathbf{R}$ and $a,b\ne0$ ). If the system of…HardSingle correct
18 Mar 2021, Shift 2 · Q75Let the system of linear equations $4x+\lambda y+2z=0$ $2x-y+z=0$ $\mu x+2y+3z=0$ , $\lambda, \mu\in\mathbb{R}$ . has a non-trivial…EasySingle 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.