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Saturday, 31 October

JEE Main · Maths · Probability

Always Positive Condition

JEE Main asked Always Positive Condition 2 times in 2 of the 108 shifts Lumi analysed, in 2021 and 2026. It belongs to Quadratic Roots, in Probability (Maths). The longest wait between two years asking it was 5 years.

Updated 2026-10-24

Times asked
2
in 2 shifts
Years
2 of 8
First asked
2021
last in 2026
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.03’210’220’230’240’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20240 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 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.

  • Probability of quadratic positivity condition
  • Integer parameter for quadratic always positive

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. 2 Apr 2026, Shift 1 · Q23Let a,b,c∈{1,2,3,4}a, b, c \in \{1, 2, 3, 4\}. If the probability, that ax2+22 bx+c>0ax^2+2\sqrt2\,bx+c>0 for all x∈Rx \in \mathbf{R}, is mn\frac{m}{n},…MediumNumerical value
  2. 25 Feb 2021, Shift 1 · Q63The integer 'k', for which the inequality x2−2(3k−1)x+8k2−7>0x^2 - 2(3k-1)x + 8k^2 - 7 > 0 is valid for every xx in R, is :MediumSingle correct

Shifts: 25 Feb 2021, Shift 1, 2 Apr 2026, Shift 1.

Same topic

Other ideas in Quadratic Roots

Quadratic Roots has 22 ideas JEE Main has asked; 13 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas