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Saturday, 31 October

JEE Main 2026 · MathsMultiple choiceOtherHardMulti-step

JEE Main 4 April 2026, Shift 2, Maths Q1

Question 1 of 75 in this shift, Maths question 1 of 25, Section A.

For the function f:[1,∞)→[1,∞)f:[1,\infty)\to[1,\infty) defined by f(x)=(x−1)4+1f(x)=(x-1)^4+1, among the two statements: (I) The set S={x∈[1,∞):f(x)=f−1(x)}S=\{x\in[1,\infty):f(x)=f^{-1}(x)\} contains exactly two elements, and (II) The set S={x∈[1,∞):f(x)=f−1(x+1)}S=\{x\in[1,\infty):f(x)=f^{-1}(x+1)\} is an empty set,
  1. (1)only (I) is TRUEOfficial answer
  2. (2)only (II) is TRUE
  3. (3)both (I) and (II) are TRUE
  4. (4)neither (I) nor (II) is TRUE

Official answer

Option 1

NTA final key.

Chapter
Relations and Functions
Topic
Functions and Domain
Idea tested
Domain and Range of Inverse Functions

Same idea in other shifts

Asked 3× in all
  1. 17 Mar 2021, Shift 1 · Q69The inverse of y=5log⁡xy=5^{\log x} is :EasySingle correct
  2. 18 Mar 2021, Shift 2 · Q76Let f:R−{3}→R−{1}f:\mathbb{R}-\{3\}\to\mathbb{R}-\{1\} be defined by f(x)=x−2x−3f(x)=\frac{x-2}{x-3}. Let g:R→Rg:\mathbb{R}\to\mathbb{R} be given as g(x)=2x−3g(x)=2x-3.…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.