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Determinants and matrices of order two and three Concepts for JEE

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Quick answer

Master Determinants and matrices of order two and three by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

Build clear conceptual foundations for Determinants and matrices of order two and three before speed practice. This guide covers what JEE expects and how to test yourself with MCQs.

Concept explainer

Determinants and matrices of order two and three is a core JEE Main Mathematics subtopic under Matrices and Determinants. Master the definitions, standard results, and typical MCQ patterns tested in JEE Main and Advanced.

Key points

  • Understand the definition and scope of Determinants and matrices of order two and three in the JEE syllabus
  • Memorise key formulas and standard results linked to Determinants and matrices of order two and three
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

  • Revise Determinants and matrices of order two and three with a one-page formula sheet before attempting mixed tests
  • After each practice set, log mistakes specific to Determinants and matrices of order two and three and reattempt after 48 hours

Common trap

Students often rush Determinants and matrices of order two and three questions without checking units, sign conventions, or boundary conditions — always verify assumptions before calculating.

Syllabus context

Part of Matrices and Determinants in JEE Main Mathematics.

Free sample questions

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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
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
Q4MathsUnit 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
Q5MathsUnit 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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