The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x - y + 4z = 8

has a solution ($$\alpha$$, $$\beta$$, $$\gamma$$) satisfying $$\alpha$$ + $$\beta$$ 2 + $$\gamma$$ 3 = 12

The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is inconsistent if :

k = 3, m $$ \ne $$ $${4 \over 5}$$

k $$ \ne $$ 3, m $$ \in $$ \mathbb{R}

k = 3, m $$ = $$ $${4 \over 5}$$

k $$ \ e $$ 3, m $$ \ e $$ $${4 \over 5}$$

Matrices And Determinants — JEE Main Previous Year Questions

306 solved PYQs · 2016–2026 · Mathematics

Solved PYQs: 306
Years covered: 2016–2026
Avg / year: ~28
Subject: Mathematics

How many JEE Main questions come from Matrices And Determinants?

Matrices And Determinants has contributed 306 questions to Joint Entrance Examination (Main) papers between 2016 and 2026 — an average of about 28 questions a year. That count is measured from EByAi’s bank of 55,289 JEE Main questions, not estimated from a syllabus. Every one of the 306 questions carries a written, step-by-step solution, and each is tagged to Matrices And Determinants within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Matrices And Determinants questions from real JEE Main papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 306 Matrices And Determinants questions (with full written solutions) are available in practice.

Question 1 · JEE Main 2025
Let the system of equations x + 5y - z = 1 4x + 3y - 3z = 7 24x + y + λz = μ λ, μ ∈ ℝ, have infinitely many solutions. Then the number of the solutions of this system, if x, y, z are integers and satisfy 7 ≤ x + y + z ≤ 77, is :
1. (A) $4$
2. (B) $5$
3. (C) $3$
4. (D) $6$
Show answerAnswer
$Answer: (C) 3$
Question 2 · JEE Main 2021
The following system of linear equations 2x + 3y + 2z = 9 3x + 2y + 2z = 9 x - y + 4z = 8
1. (A) $does not have any solution$
2. (B) $has a solution (α, β, γ) satisfying α + β 2 + γ 3 = 12$
3. (C) $has a unique solution$
4. (D) $has infinitely many solutions$
Show answerAnswer
$Answer: (C) has a unique solution$
Question 3 · JEE Main 2021
The system of linear equations 3x - 2y - kz = 10 2x - 4y - 2z = 6 x+2y - z = 5m is inconsistent if :
1. (A) $k 3, m \mathbb{R}$
2. (B) $k = 3, m \neq = \frac{4}{5}$
3. (C) $k = 3, m = \frac{4}{5}$
4. (D) $k e 3, m e \frac{4}{5}$
Show answerAnswer
$Answer: (B) k = 3, m \neq = \frac{4}{5}$
Question 4 · JEE Main 2021
The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k^2 has no solution if k is equal to :
1. (A) $0$
2. (B) $- 1$
3. (C) $- 2$
4. (D) $1$
Show answerAnswer
$Answer: (C) - 2$
Question 5 · JEE Main 2021
The 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 :
1. (A) $a = 3, b \neq = 13$
2. (B) $a \neq = 3, b \neq = 13$
3. (C) $a e 3, b = 3$
4. (D) $a = 3, b = 13$
Show answerAnswer
$Answer: (A) a = 3, b \neq = 13$

Matrices And Determinants questions by year

Year	Questions	Share of chapter questions
2026	33
2025	34
2024	40
2023	36
2022	34
2021	52
2020	28
2019	29
2018	8
2017	6
2016	6

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FAQs

How many JEE Main questions have been asked from Matrices And Determinants?

EByAi's bank holds 306 real JEE Main questions from Matrices And Determinants, asked between 2016 and 2026 — about 28 per year on average. Every count is measured from actual papers, not estimated.

Is Matrices And Determinants important for JEE Main?

306 questions over 11 papers make Matrices And Determinants a high-weightage chapter in JEE Main Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Matrices And Determinants PYQs online for free?

Yes. EByAi lets you solve JEE Main past-year questions in the browser with written solutions — free daily practice, no card needed.

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