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Saturday, 31 October

JEE Main 2022 · MathsMultiple choiceSingle correctMediumApplication

JEE Main 29 June 2022, Shift 1, Maths Q15

Question 15 of 90 in this shift, Maths question 15 of 30, Section A.

The domain of the function cos⁡−1(2sin⁡−1(14x2−1)π)\cos^{-1}\left(\frac{2\sin^{-1}\left(\frac{1}{4x^2 - 1}\right)}{\pi}\right) is :
  1. (1)R−{−12,12}\mathbf{R} - \left\{-\frac{1}{2}, \frac{1}{2}\right\}
  2. (2)(−∞,−1]∪[1,∞)∪{0}(-\infty, -1] \cup [1, \infty) \cup \{0\}
  3. (3)(−∞,−12)∪(12,∞)∪{0}\left(-\infty, \frac{-1}{2}\right) \cup \left(\frac{1}{2}, \infty\right) \cup \{0\}
  4. (4)(−∞,−12]∪[12,∞)∪{0}\left(-\infty, \frac{-1}{\sqrt{2}}\right] \cup \left[\frac{1}{\sqrt{2}}, \infty\right) \cup \{0\}Official answer

Official answer

Option 4

NTA final key (2022 Session 1).

Chapter
Inverse Trigonometric Functions
Topic
Inverse Trig Domains
Idea tested
Domain of Rational Composite Inverse Trig

Same idea in other shifts

Asked 3× in all
  1. 28 Jul 2022, Shift 1 · Q2Considering only the principal values of the inverse trigonometric functions, the domain of the function…EasySingle correct
  2. 29 Jul 2022, Shift 2 · Q19The domain of the function f(x)=sin⁡−1(x2−3x+2x2+2x+7)f(x)=\sin^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right) is :MediumSingle 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.