JEE Main 2023 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 April 2023, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

Let 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

-x + (\tan\theta)y + \sqrt{7}z = 0

x + y + (\tan\theta)z = 0

has non-trivial solution. Then

\frac{120}{\pi}\sum_{\theta \in S}\theta

is equal to

(1)10
(2)20Official answer
(3)30
(4)40

Official answer

Option 2

NTA final key.

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

Same idea in other shifts

Asked 5× in all

5 Apr 2026, Shift 1 · Q4Consider the system of linear equations in $x, y, z$ : $x + 2y + tz = 0$ , $6x + y + 5tz = 0$ , $3x + t^2y + f(t)\,z = 0$ , where…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
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
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 42 of the 174 JEE Main shifts held from 2017 to 2026.