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Saturday, 31 October

JEE Main 2020 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 8 January 2020, Shift 2, Maths Q51

Question 51 of 75 in this shift, Maths question 1 of 25, Section A.

Let f:(1,3)→Rf : (1, 3) \to \mathbf{R} be a function defined by f(x)=x[x]1+x2f(x) = \frac{x[x]}{1 + x^2}, where [x][x] denotes the greatest integer ≤x\leq x. Then the range of ff is :
  1. (1)(35,45)\left(\frac{3}{5}, \frac{4}{5}\right)
  2. (2)(25,45]\left(\frac{2}{5}, \frac{4}{5}\right]
  3. (3)(25,12)∪(35,45]\left(\frac{2}{5}, \frac{1}{2}\right) \cup \left(\frac{3}{5}, \frac{4}{5}\right]Official answer
  4. (4)(25,35]∪(34,45)\left(\frac{2}{5}, \frac{3}{5}\right] \cup \left(\frac{3}{4}, \frac{4}{5}\right)

Official answer

Option 3

NTA final key (Jan 2020).

Chapter
Relations and Functions
Topic
Functions and Domain
Idea tested
Range Involving Mixed GIF and Fractional Part

Same topic in other shifts

All Functions and Domain questions
  1. 2 Apr 2026, Shift 1 · Q21If the domain of the function f(x)=log⁡(0.6)(∣2x−5x2−4∣)f(x)=\sqrt{\log_{(0.6)}\left(\left|\frac{2x-5}{x^2-4}\right|\right)} is…HardNumerical value
  2. 4 Apr 2026, Shift 2 · Q1For 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…HardOther
  3. 2 Apr 2025, Shift 2 · Q1If the domain of the function f(x)=110+3x−x2+1x+∣x∣f(x) = \frac{1}{\sqrt{10+3x-x^2}} + \frac{1}{\sqrt{x+|x|}} is (a,b)(a, b), then (1+a)2+b2(1+a)^2 + b^2 is equal to :EasySingle correct
  4. 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
  5. 3 Apr 2025, Shift 2 · Q2If the domain of the function f(x)=log⁡7(1−log⁡4(x2−9x+18))f(x) = \log_7 (1 - \log_4 (x^2 - 9x + 18)) is (α,β)∪(γ,δ)(\alpha, \beta) \cup (\gamma, \delta), then…MediumSingle correct
  6. 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

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.