Learn

Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceOtherMediumApplication

JEE Main 24 February 2021, Shift 2, Maths Q72

Question 72 of 90 in this shift, Maths question 12 of 30, Section A.

For the system of linear equations : x−2y=1x-2y=1, x−y+kz=−2x-y+kz=-2, ky+4z=6ky+4z=6, k∈k\in R, consider the following statements : (A) The system has unique solution if k≠2k\neq2, k≠−2k\neq-2. (B) The system has unique solution if k=−2k=-2. (C) The system has unique solution if k=2k=2. (D) The system has no-solution if k=2k=2. (E) The system has infinite number of solutions if k≠−2k\neq-2. Which of the following statements are correct ?
  1. (1)(A) and (D) onlyOfficial answer
  2. (2)(A) and (E) only
  3. (3)(C) and (D) only
  4. (4)(B) and (E) only

Official answer

Option 1

NTA final key.

Chapter
Determinants
Topic
Cramer's Rule
Idea tested
Condition for Unique Solution

Same idea in other shifts

Asked 4× in all
  1. 31 Jan 2024, Shift 2 · Q4Let AA be a 3×33\times3 real matrix such that A(101)=2(101)A\begin{pmatrix}1\\0\\1\end{pmatrix}=2\begin{pmatrix}1\\0\\1\end{pmatrix},…MediumSingle correct
  2. 24 Jun 2022, Shift 2 · Q3Let the system of linear equations x+y+αz=2x + y + \alpha z = 2 3x+y+z=43x + y + z = 4 x+2z=1x + 2z = 1 have a unique solution (x∗,y∗,z∗)(x^*, y^*, z^*). If…MediumSingle correct
  3. 25 Feb 2021, Shift 2 · Q63The following system of linear equations 2x+3y+2z=92x + 3y + 2z = 9 3x+2y+2z=93x + 2y + 2z = 9 x−y+4z=8x - y + 4z = 8EasySingle 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.