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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 September 2020, Shift 2, Maths Q55

Question 55 of 75 in this shift, Maths question 5 of 25.

Suppose 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 is equal to b1b_1, b2b_2 and b3b_3 respectively. If x1=[111]x_1 = \begin{bmatrix}1\\1\\1\end{bmatrix}, x2=[021]x_2 = \begin{bmatrix}0\\2\\1\end{bmatrix}, x3=[001]x_3 = \begin{bmatrix}0\\0\\1\end{bmatrix}, b1=[100]b_1 = \begin{bmatrix}1\\0\\0\end{bmatrix}, b2=[020]b_2 = \begin{bmatrix}0\\2\\0\end{bmatrix} and b3=[002]b_3 = \begin{bmatrix}0\\0\\2\end{bmatrix}, then the determinant of A is equal to :
  1. (1)12\frac{1}{2}
  2. (2)22Official answer
  3. (3)32\frac{3}{2}
  4. (4)44

Official answer

Option 2

NTA final key (Sep 2020).

Chapter
Determinants
Topic
Matrix Multiplication
Idea tested
Determinant of Product

Same idea in other shifts

Asked 6× in all
  1. 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
  2. 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
  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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.