JEE Main 2024 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 6 April 2024, Shift 1, Maths Q22

Question 22 of 90 in this shift, Maths question 22 of 30, Section B.

Let

\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

x,y,z \in \mathbb{R}

xyz\neq 0

, then

6\alpha+4\beta+\gamma

is equal to __________

Official answer

NTA final key.

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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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
6 Sep 2020, Shift 2 · Q71The sum of distinct values of $\lambda$ for which the system of equations $(\lambda-1)x+(3\lambda+1)y+2\lambda z=0$ …MediumNumerical value

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.