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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceTwo statementsMediumConceptual

JEE Main 11 April 2023, Shift 2, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

For a∈Ca \in \mathbb{C}, let A={z∈C:Re(a+z‾)>Im(a‾+z)}A = \{z \in \mathbb{C} : \mathrm{Re}(a + \overline{z}) > \mathrm{Im}(\overline{a} + z)\} and B={z∈C:Re(a+z‾)<Im(a‾+z)}B = \{z \in \mathbb{C} : \mathrm{Re}(a + \overline{z}) < \mathrm{Im}(\overline{a} + z)\}. Then among the two statements: (S1) : If Re(a),Im(a)>0\mathrm{Re}(a), \mathrm{Im}(a) > 0, then the set AA contains all the real numbers (S2) : If Re(a),Im(a)<0\mathrm{Re}(a), \mathrm{Im}(a) < 0, then the set BB contains all the real numbers,
  1. (1)both are true
  2. (2)both are falseOfficial answer
  3. (3)only (S1) is true
  4. (4)only (S2) is true

Official answer

Option 2

NTA final key.

Chapter
Complex Numbers and Quadratic Equations
Topic
No close match in our taxonomy
Idea tested
No close match in our taxonomy

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.