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Evaluation of determinants Concepts for JEE

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Master Evaluation of determinants by understanding definitions, standard results, and typical JEE question patterns — then practise with syllabus-aligned MCQs on Goodmarks.

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Concept explainer

Evaluation of determinants 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 Evaluation of determinants in the JEE syllabus
  • Memorise key formulas and standard results linked to Evaluation of determinants
  • Practise 20–40 syllabus-aligned MCQs with step-by-step solutions

JEE tips

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

Common trap

Students often rush Evaluation of determinants 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
STATEMENT 1: In a ΔABC,a,b,c\Delta A B C, a, b, c denotes lengths of the sides and ∣abcbcacab∣=0\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{b} & \boldsymbol{c} & \boldsymbol{a} \\ \boldsymbol{c} & \boldsymbol{a} & \boldsymbol{b}\end{array}\right|=\mathbf{0} then the triangle is equilateral triangle. STATEMENT 2: Sum of three non- negative numbers =0⇒=0 \Rightarrow each number is zero.
Q2MathsUnit 3: Matrices and Determinants
tet⁡f(θ)=∣cos⁡θ2111cos⁡θ2−cos⁡θ2−cos⁡θ21−1∣\operatorname{tet} f(\theta)=\left|\begin{array}{ccc}\cos \frac{\theta}{2} & 1 & 1 \\ 1 & \cos \frac{\theta}{2} & -\cos \frac{\theta}{2} \\ -\cos \frac{\theta}{2} & 1 & -1\end{array}\right| f(π)+f(−π)f(\pi)+f(-\pi) is equal to
Q3MathsUnit 3: Matrices and Determinants
Let⁡A=∣abcpqrxyz∣\operatorname{Let} A=\left|\begin{array}{lll}\boldsymbol{a} & \boldsymbol{b} & \boldsymbol{c} \\ \boldsymbol{p} & \boldsymbol{q} & \boldsymbol{r} \\ \boldsymbol{x} & \boldsymbol{y} & \boldsymbol{z}\end{array}\right| and suppose that det. (A)=2(A)=2 then the det.(B) equals, where B=∣4x2a−p4y2b−q4z2c−t∣\boldsymbol{B}=\left|\begin{array}{ccc}\mathbf{4} \boldsymbol{x} & \mathbf{2} \boldsymbol{a} & -\boldsymbol{p} \\ \mathbf{4} \boldsymbol{y} & \mathbf{2} \boldsymbol{b} & -\boldsymbol{q} \\ \boldsymbol{4} \boldsymbol{z} & \boldsymbol{2} \boldsymbol{c} & -\boldsymbol{t}\end{array}\right|
Q4MathsUnit 3: Matrices and Determinants
f∣x+1352x+2523x+4∣=0,f\left|\begin{array}{ccc}\boldsymbol{x}+\mathbf{1} & \mathbf{3} & \mathbf{5} \\ \mathbf{2} & \boldsymbol{x}+\mathbf{2} & \mathbf{5} \\ \mathbf{2} & \mathbf{3} & \boldsymbol{x}+\mathbf{4}\end{array}\right|=\mathbf{0}, then x=?\boldsymbol{x}=?
Q5MathsUnit 3: Matrices and Determinants
If each row of a determinant of third order of value Δ\Delta is multipled by 3,3, then the value of new determinant is

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