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Important Questions: Determinants and matrices of order two and three for JEE

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Part of Matrices and Determinants in JEE Main Mathematics.

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Q1MathsUnit 3: Matrices and Determinants
If A=[11111+x1111+y]\boldsymbol{A}=\left[\begin{array}{ccc}\mathbf{1} & \mathbf{1} & \mathbf{1} \\ \mathbf{1} & \mathbf{1}+\boldsymbol{x} & \mathbf{1} \\ \mathbf{1} & \mathbf{1} & \mathbf{1}+\boldsymbol{y}\end{array}\right] for x≠\boldsymbol{x} \neq 0,y≠0,\mathbf{0}, \boldsymbol{y} \neq \mathbf{0}, then D\boldsymbol{D} is:
Q2MathsUnit 3: Matrices and Determinants
Consider the following statements: 1. Determinant is a square matrix. 2. Determinant is a number associated with a square matrix. Which of the above statements is/are correct?
Q3MathsUnit 3: Matrices and Determinants
If AA and BB are square matrices of order 3 such that ∣A∣=−1,∣B∣=3,|\boldsymbol{A}|=-\mathbf{1},|\boldsymbol{B}|=\mathbf{3}, then the determinant of 3AB3 A B is equal to
Q4MathsUnit 3: Matrices and Determinants
In a triangle ABC,A B C, with usual notations, if ∣1ab1ca1bc∣=0,\left|\begin{array}{ccc}1 & a & b \\ 1 & c & a \\ 1 & b & c\end{array}\right|=0, then 4sin⁡2A+4 \sin ^{2} A+ 24sin⁡2B+36sin⁡2C24 \sin ^{2} B+36 \sin ^{2} C is equal to
Q5MathsUnit 3: Matrices and Determinants
If DP=∣P158P2359P32510∣,D_{P}=\left|\begin{array}{ccc}\boldsymbol{P} & \mathbf{1 5} & \mathbf{8} \\ \boldsymbol{P}^{2} & \mathbf{3 5} & \mathbf{9} \\ \boldsymbol{P}^{3} & \mathbf{2 5} & \mathbf{1 0}\end{array}\right|, then D1+\boldsymbol{D}_{1}+ D2+D3+D4+D5D_{2}+D_{3}+D_{4}+D_{5} is equal to
Q6MathsUnit 3: Matrices and Determinants
Assertion Δ=sin⁡πcos⁡(x+π/4)tan⁡(x−sin⁡(x−π/4)−cos⁡(π/2)log⁡(xcot⁡(π/4+x)log⁡(y/x)tan⁡\begin{array}{ccc}\mathbf{\Delta}= & & \\ & \sin \pi & \cos (\boldsymbol{x}+\boldsymbol{\pi} / \mathbf{4}) & \tan (\boldsymbol{x}- \\ \sin (\boldsymbol{x}-\boldsymbol{\pi} / \mathbf{4}) & -\cos (\boldsymbol{\pi} / \mathbf{2}) & \log (\boldsymbol{x} \\ \cot (\boldsymbol{\pi} / \mathbf{4}+\boldsymbol{x}) & \log (\boldsymbol{y} / \boldsymbol{x}) & \tan \end{array} 0 Reason A skew symmetric determinant of odd order equals 0

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