Learn

Saturday, 31 October

JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2024, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

If the domain of the function sin⁡−1(3x−222x−19)+log⁡e(3x2−8x+5x2−3x−10)\sin^{-1}\left(\frac{3x-22}{2x-19}\right)+\log_e\left(\frac{3x^2-8x+5}{x^2-3x-10}\right) is (α,β](\alpha, \beta], then 3α+10β3\alpha+10\beta is equal to :
  1. (1)9595
  2. (2)9797Official answer
  3. (3)9898
  4. (4)100100

Official answer

Option 2

NTA final key.

Chapter
Relations and Functions
Topic
Functions and Domain
Idea tested
Inverse Trig Function Domain

Same idea in other shifts

Asked 6× in all
  1. 3 Apr 2025, Shift 1 · Q2If the domain of the function f(x)=log⁡e(2x−35+4x)+sin⁡−1(4+3x2−x)f(x) = \log_e\left(\frac{2x-3}{5+4x}\right) + \sin^{-1}\left(\frac{4+3x}{2-x}\right) is [α,β)[\alpha, \beta),…MediumSingle correct
  2. 8 Apr 2025, Shift 2 · Q21Let the domain of the function f(x)=cos⁡−1(4x+53x−7)f(x) = \cos^{-1}\left(\frac{4x+5}{3x-7}\right) be [α,β][\alpha, \beta] and the domain of…MediumNumerical value
  3. 30 Jan 2024, Shift 1 · Q1If the domain of the function f(x)=cos⁡−1(2−∣x∣4)+{log⁡e(3−x)}−1f(x)=\cos^{-1}\left(\frac{2-|x|}{4}\right)+\{\log_e(3-x)\}^{-1} is [−α,β)−{γ}[-\alpha,\beta)-\{\gamma\}, then…MediumSingle correct
  4. 15 Apr 2023, Shift 1 · Q1If the domain of the function f(x)=log⁡e(4x2+11x+6)+sin⁡−1(4x+3)+cos⁡−1(10x+63)f(x)=\log_e\left(4x^2+11x+6\right)+\sin^{-1}(4x+3)+\cos^{-1}\left(\frac{10x+6}{3}\right) is…MediumSingle correct
  5. 27 Jul 2022, Shift 2 · Q1The domain of the function f(x)=sin⁡−1[2x2−3]+log⁡2(log⁡12(x2−5x+5))f(x) = \sin^{-1}[2x^2 - 3] + \log_2\left(\log_{\frac{1}{2}}(x^2 - 5x + 5)\right), where [t] is the greatest…HardSingle 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.