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Saturday, 31 October

JEE Main · Maths · Determinants

Determinant of Product

JEE Main asked Determinant of Product 6 times in 5 of the 108 shifts Lumi analysed, in 2020, 2021, 2022 and 2024. It belongs to Matrix Multiplication, in Determinants (Maths). The longest wait between two years asking it was 2 years. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 5 shifts
Years
4 of 8
First asked
2020
last in 2024
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022 and 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170.08’200.03’210.07’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 1 in 24 shifts · 2022: 2 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20242 of 18
  • 20230 of 12
  • 202221 of 24
  • 20211 of 24
  • 20201 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Determinant and trace of matrix from column equations
  • Determinant of product of matrices

Difficulty

Easy 2Medium 4Hard 0

1 of the 6 questions had a numerical answer.

Every question

All 6 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 27 Jan 2024, Shift 1 · Q22Let A=[201110101]A=\begin{bmatrix}2&0&1\\1&1&0\\1&0&1\end{bmatrix}, B=[B1,B2,B3]B=[B_1, B_2, B_3], where B1,B2,B3B_1, B_2, B_3 are column matrices, and…MediumNumerical value
  2. 1 Feb 2024, Shift 1 · Q3If A=[21−12]A=\begin{bmatrix}\sqrt{2}&1\\-1&\sqrt{2}\end{bmatrix}, B=[1011]B=\begin{bmatrix}1&0\\1&1\end{bmatrix}, C=ABATC=ABA^T and X=ATC2AX=A^TC^2A, then…EasySingle correct
  3. 30 Jun 2022, Shift 1 · Q4Let A=[1−2αα2−1]A = \begin{bmatrix} 1 & -2 & \alpha \\ \alpha & 2 & -1 \end{bmatrix} and…MediumSingle correct
  4. 30 Jun 2022, Shift 1 · Q5Let A and B be two square matrices of order 2. If det⁡(A)=2\det(A) = 2, det⁡(B)=3\det(B) = 3 and…MediumSingle correct
  5. 17 Mar 2021, Shift 1 · Q63If A =(0sin⁡αsin⁡α0)=\begin{pmatrix}0 & \sin\alpha\\ \sin\alpha & 0\end{pmatrix} and det⁡(A2−12I)=0\det\left(A^{2}-\frac{1}{2}I\right)=0, then a possible value of…EasySingle correct
  6. 4 Sep 2020, Shift 2 · Q55Suppose the vectors x1x_1, x2x_2 and x3x_3 are the solutions of the system of linear equations, Ax=bAx=b when the vector b on the right side…MediumSingle correct

Shifts: 4 Sep 2020, Shift 2, 17 Mar 2021, Shift 1, 30 Jun 2022, Shift 1, 27 Jan 2024, Shift 1, 1 Feb 2024, Shift 1.

Same topic

Other ideas in Matrix Multiplication

Matrix Multiplication has 19 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas