JEE Main 2021 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 17 March 2021, Shift 2, Maths Q64

Question 64 of 90 in this shift, Maths question 4 of 30, Section A.

x, y, z

are in arithmetic progression with common difference d,

x\neq 3d

, and the determinant of the matrix

\begin{bmatrix}3 & 4\sqrt{2} & x\\ 4 & 5\sqrt{2} & y\\ 5 & k & z\end{bmatrix}

is zero, then the value of

k^2

is :

(1) $6$
(2) $12$
(3) $36$
(4) $72$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Determinants
Topic: Cramer's Rule
Idea tested: Arithmetic Progression Coefficients Trick

Same topic in other shifts

All Cramer's Rule questions

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6 Apr 2026, Shift 2 · Q4The sum of all possible values of $\theta\in[0,2\pi]$ , for which the system of equations : $x\cos 3\theta-8y-12z=0$ …MediumSingle correct
8 Apr 2026, Shift 2 · Q3If the system of linear equations : $x + y + z = 6$ , $x + 2y + 5z = 10$ , $2x + 3y + \lambda z = \mu$ has infinitely many solutions, then…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.