Start Prep From 0 & Get IIT Bombay with Most Powerful JEE Dropper Course
Enroll Now!

Determinant - JEE Advanced Previous Year Questions with Solutions

Determinant – JEE Advanced Previous Year Questions covers important exam-level problems on matrices, determinants, consistency of linear equations, and determinant properties, helping students strengthen conceptual understanding and problem-solving skills for JEE Advanced.

eSaral Updated on:
Determinant - JEE Advanced Previous Year Questions with Solutions

Table of Contents

› JEE › JEE Main ›Determinant - JEE Advanced Previous Year Questions with Solutions

esaral jee batches

🚀 Checkout eSaral Courses

What Is the Determinant Topic in JEE Advanced? 

Determinants form a critical part of the JEE Advanced Mathematics syllabus, appearing under the broader chapter of Matrices and Determinants. According to the official JEE Advanced syllabus released by IIT (the organising institute rotates annually among the IITs), this chapter contributes questions worth 8–12 marks in some years.

JEE Advanced Previous Year Questions 

 Download eSaral app for free study material and video tutorials.

Q. The number of all possible values of $\theta,$ where $0<\theta<\pi,$ for which the system of equations $(\mathrm{y}+\mathrm{z}) \cos 3 \theta=(\mathrm{xyz}) \sin 3 \theta \mathrm{x} \sin 3 \theta=\frac{2 \cos 3 \theta}{\mathrm{y}}+\frac{2 \sin 3 \theta}{\mathrm{z}}(\mathrm{xyz}) \sin 3 \theta=(\mathrm{y}+2 \mathrm{z}) \cos 3 \theta+\mathrm{ysin} 3 \theta$ have a solution $\left(\mathrm{x}_{0}, \mathrm{y}_{0}, \mathrm{z}_{0}\right)$ with $\mathrm{y}_{0} \mathrm{z}_{0} \neq 0,$ is [JEE 2010,3]
Ans. 3
Q. Which of the following values of  satisfy the equation (A) –4            (B) 9              (C) –9                (D) 4 [JEE(Advanced)-2015, 4M, –2M]
Ans. (B,C)
Q. Let a, $\lambda, \mathrm{m} \in \square .$ Consider the system of linear equations $a x+2 y=\lambda$ $3 x-2 y=\mu$ Which of the following statement(s) is(are) correct? (A) If $a=-3,$ then the system has infinitely many solutions for all values of $\lambda$ and $\mu$ (B) If $a \neq-3,$ then the system has a unique solution for all values of $\lambda$ and $\mu$ (C) If $\lambda+\mu=0,$ then the system has infinitely many solutions for $a=-3$ (D) If $\lambda+\mu \neq 0,$ then the system has no solution for $a=-3$ [JEE(Advanced)-2016]
Ans. (B,C,D)
Q. The total number of distinct $\mathrm{x} \in \mathrm{R}$ for which $\left|\begin{array}{ccc}{\mathrm{x}} & {\mathrm{x}^{2}} & {1+\mathrm{x}^{3}} \\ {2 \mathrm{x}} & {4 \mathrm{x}^{2}} & {1+8 \mathrm{x}^{3}} \\ {3 \mathrm{x}} & {9 \mathrm{x}^{2}} & {1+27 \mathrm{x}^{3}}\end{array}\right|=10$ is [JEE(Advanced)-2016]
Ans. 2
Q. Let $\mathrm{P}$ be a matrix of order $3 \times 3$ such that all the entries in $\mathrm{P}$ are from the set $\{-1,0,1\} .$ Then, the maximum possible value of the determinant of $\mathrm{P}$ is [JEE(Advanced)-2018]
Ans. 4

Frequently Asked Questions

Find answers to common questions.

How many determinant questions are asked in JEE Advanced each year?

JEE Advanced typically asks 1–2 questions from Determinants and Matrices combined each year. These questions carry 3–4 marks each and appear in both the integer-type and multiple-correct formats. Some years, determinant concepts are embedded inside coordinate geometry or calculus problems as well.


What is the difficulty level of determinant questions in JEE Advanced?

Determinant questions in JEE Advanced are moderate to high difficulty. The calculation itself is rarely the challenge — the difficulty lies in identifying which property or row/column operation to apply first. Students who have practised at least 30–40 problems of this type can usually solve JEE Advanced determinant questions within 5–7 minutes.

Is Cramer's Rule directly tested in JEE Advanced?

Cramer's Rule is tested indirectly. JEE Advanced does not ask you to state the rule but instead gives a system of equations and asks you to determine conditions for consistency, uniqueness, or infinitely many solutions — all of which require applying the logic behind Cramer's Rule correctly.

What is the maximum value of a 3×3 determinant with entries from {–1, 0, 1}?

The maximum value is 4. This was directly tested in JEE Advanced 2018. The answer can be verified by constructing a specific 3×3 matrix with entries from {–1, 0, 1} — for example, using all 1s and –1s in a pattern that maximises the expansion terms while minimising cancellations.

How is the topic of determinants related to matrices in JEE Advanced?

Determinants and matrices are deeply connected in JEE Advanced. Every matrix question involving invertibility, consistency of equations, or eigenvalues uses determinant concepts. In practice, JEE Advanced treats them as one unified topic. A student strong in matrix algebra but weak in determinant properties will struggle with system-of-equations questions.

Leave a comment

Comments

Mssp
May 9, 2024, 6:35 a.m.
Good question
Aditya
April 23, 2023, 6:35 a.m.
Very good
CICADA 1050
July 1, 2020, 5:43 p.m.
Hello cicada 1050 here . we are looking for intelligent human beings . We have hidden a message in this conversation . Use it to reach us GOOD LUCK !
by
April 21, 2020, 4:32 p.m.
hi
None

eSaral Gurukul

NEET

JEE Main

JEE Advanced

Our Telegram Channel

All Study Material