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Saturday, 31 October

JEE Main · Maths · Statistics

Combined Variance of Two Sets

JEE Main asked Combined Variance of Two Sets 7 times in 7 of the 108 shifts Lumi analysed, in 2021, 2023 and 2026. It belongs to Variance and SD, in Statistics (Maths). The longest wait between two years asking it was 3 years. In 2021 and 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
7
in 7 shifts
Years
3 of 8
First asked
2021
last in 2026
Pattern
Frequent
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2021, 2023 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.10.20’170’200.14’210’220.14’230’240’250.11’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 4 in 24 shifts · 2022: 0 in 24 shifts · 2023: 2 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
  • 20232 of 12
  • 20220 of 24
  • 20214 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: calculation.

  • Find unknown data from mean and variance
  • Combined variance of two sets

Difficulty

Easy 2Medium 4Hard 1

3 of the 7 questions had a numerical answer.

Every question

All 7 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 2026, Shift 2 · Q7A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1. Then, the variance of…EasySingle correct
  2. 11 Apr 2023, Shift 1 · Q18Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the variance of the…MediumSingle correct
  3. 6 Apr 2023, Shift 1 · Q17The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and…MediumSingle correct
  4. 17 Mar 2021, Shift 2 · Q84Consider a set of 3n3n numbers having variance 4. In this set, the mean of first 2n2n numbers is 6 and the mean of the remaining nn…HardNumerical value
  5. 16 Mar 2021, Shift 2 · Q86Consider the statistics of two sets of observations as follows : Size Mean Variance Observation I 10 2 2 Observation II n 3 1 If the…EasyNumerical value
  6. 25 Jul 2021, Shift 2 · Q68The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean…MediumSingle correct
  7. 27 Aug 2021, Shift 2 · Q90An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The…MediumNumerical value

Shifts: 16 Mar 2021, Shift 2, 17 Mar 2021, Shift 2, 25 Jul 2021, Shift 2, 27 Aug 2021, Shift 2, 6 Apr 2023, Shift 1, 11 Apr 2023, Shift 1, 8 Apr 2026, Shift 2.

Same topic

Other ideas in Variance and SD

Variance and SD has 20 ideas JEE Main has asked; 10 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas