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Saturday, 31 October

JEE Main · Maths · Trigonometric Functions

Range of Quadratic Rational Functions

JEE Main asked Range of Quadratic Rational Functions 2 times in 2 of the 108 shifts Lumi analysed, all in 2024. It belongs to Functions and Domain, in Trigonometric Functions (Maths). In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
1 of 8
First asked
2024
the only year
Pattern
New since 2024
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2024. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.050.10’170’200’210’220’230.09’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 0 in 24 shifts · 2023: 0 in 12 shifts · 2024: 2 in 18 shifts · 2025: 0 in 8 shifts · 2026: 0 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20260 of 9
  • 20250 of 8
  • 20242 of 18
  • 20230 of 12
  • 20220 of 24
  • 20210 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: application.

  • Range of trig function then gp sum
  • Classify function as one-one or onto

Difficulty

Easy 0Medium 2Hard 0

1 of the 2 questions had a numerical answer.

Every question

All 2 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 8 Apr 2024, Shift 1 · Q21If the range of f(θ)=sin⁡4θ+3cos⁡2θsin⁡4θ+cos⁡2θf(\theta)=\frac{\sin^4\theta+3\cos^2\theta}{\sin^4\theta+\cos^2\theta}, θ∈R\theta\in\mathbb{R} is [α,β][\alpha,\beta], then…MediumNumerical value
  2. 6 Apr 2024, Shift 1 · Q2The function f(x)=x2+2x−15x2−4x+9f(x)=\frac{x^2+2x-15}{x^2-4x+9}, x∈Rx \in \mathbb{R} isMediumSingle correct

Shifts: 6 Apr 2024, Shift 1, 8 Apr 2024, Shift 1.

Same topic

Other ideas in Functions and Domain

Functions and Domain has 20 ideas JEE Main has asked; 8 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas