Determinant - JEE Advanced Previous Year Questions with Solutions

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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. [esquestion] 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 #tag# [JEE 2010,3] #sol# 3 [/esquestion] [esquestion] Which of the following values of  satisfy the equation (A) –4            (B) 9              (C) –9                (D) 4 #tag# [JEE(Advanced)-2015, 4M, –2M] #sol# (B,C) [/esquestion] [esquestion] 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 $a=-3$ #tag# [JEE(Advanced)-2016] #sol# (B,C,D) [/esquestion] [esquestion] 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 #tag# [JEE(Advanced)-2016] #sol# 2 [/esquestion] [esquestion] 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 #tag# [JEE(Advanced)-2018] #sol# 4 [/esquestion]

After solving Determinants - JEE Advanced PYQs (Maths), practise the concepts in real timed papers using the JEE Advanced exam paper.