Determinant – JEE Advanced Previous Year Questions with Solutions

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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]

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Sol. 3

Q. Which of the following values of  satisfy the equation (A) –4            (B) 9              (C) –9                (D) 4 [JEE(Advanced)-2015, 4M, –2M]

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Sol. (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]

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Sol. (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]

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Sol. 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]

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Sol. 4