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Evaluation of determinants Revision for JEE

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Revise Evaluation of determinants by covering every subtopic once, drilling formulas, then solving 5+ timed MCQs with full solutions.

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Revision checklist

  1. 1.Core idea: Evaluation of determinants
  2. 2.Relates to other subtopics in Matrices and Determinants
  3. 3.Matrix operations and types
  4. 4.Determinant evaluation and properties
  5. 5.Master Evaluation of determinants definitions and standard results
  6. 6.Solve 20 timed MCQs for Evaluation of determinants

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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Follow the checklist on this page, revise formulas daily, and attempt mixed MCQs every 2–3 days.

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