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Saturday, 31 October

JEE Main 2021 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 31 August 2021, Shift 2, Maths Q79

Question 79 of 90 in this shift, Maths question 19 of 30, Section A.

The domain of the function f(x)=sin⁡−1(3x2+x−1(x−1)2)+cos⁡−1(x−1x+1)f(x) = \sin^{-1}\left(\frac{3x^2+x-1}{(x-1)^2}\right)+\cos^{-1}\left(\frac{x-1}{x+1}\right) is :
  1. (1)[0,14]\left[0, \frac{1}{4}\right]
  2. (2)[0,12]\left[0, \frac{1}{2}\right]
  3. (3)[14,12]∪{0}\left[\frac{1}{4}, \frac{1}{2}\right] \cup \{0\}Official answer
  4. (4)[−2,0]∪[14,12][-2, 0] \cup \left[\frac{1}{4}, \frac{1}{2}\right]

Official answer

Option 3

NTA final key.

Chapter
Inverse Trigonometric Functions
Topic
Inverse Trig Domains
Idea tested
Domain Intersection of Multiple Inverse Trig Functions

Same idea in other shifts

Asked 2× in all
  1. 22 Jul 2021, Shift 2 · Q61If the domain of the function f(x)=cos⁡−1x2−x+1sin⁡−1(2x−12)f(x)=\frac{\cos^{-1}\sqrt{x^2-x+1}}{\sqrt{\sin^{-1}\left(\frac{2x-1}{2}\right)}} is the interval…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.