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Saturday, 31 October

JEE Main 2023 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 12 April 2023, Shift 1, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A. NTA dropped this question from the final key; it is left out of every count on this site.

Let D be the domain of the function f(x)=sin⁡−1(log⁡3x(6+2log⁡3x−5x))f(x)=\sin^{-1}\left(\log_{3x}\left(\frac{6+2\log_3 x}{-5x}\right)\right). If the range of the function g:D→Rg: D \to \mathbb{R} defined by g(x)=x−[x]g(x)=x-[x], ([x][x] is the greatest integer function), is (α,β)(\alpha, \beta), then α2+5β\alpha^2+\frac{5}{\beta} is equal to
  1. (1)4545
  2. (2)4646
  3. (3)135135
  4. (4)136136

Official answer

Dropped by NTA (marks given to all)

NTA final key: NTA final key: DROP (question dropped).

Chapter
Relations and Functions
Topic
Functions and Domain
Idea tested
Domain of Composite Functions

Same idea in other shifts

Asked 1× in all
  1. 26 Feb 2021, Shift 2 · Q69Let f(x)=sin⁡−1xf(x)=\sin^{-1}x and g(x)=x2−x−22x2−x−6g(x)=\frac{x^2-x-2}{2x^2-x-6}. If g(2)=lim⁡x→2g(x)g(2)=\lim_{x \to 2} g(x), then the domain of the function f∘gf \circ g 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.