JEE Main 2021 · MathsNumerical answerNumerical valueMediumMulti-step

JEE Main 27 August 2021, Shift 2, Maths Q90

Question 90 of 90 in this shift, Maths question 30 of 30, Section B.

An 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 variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If

\mu

is the average marks of girls and

\sigma^2

is the variance of marks of 50 candidates, then

\mu + \sigma^2

is equal to __________.

Official answer

NTA final key.

Chapter: Statistics
Topic: Variance and SD
Idea tested: Combined Variance of Two Sets

Same idea in other shifts

Asked 7× in all

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
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
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
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
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
17 Mar 2021, Shift 2 · Q84Consider a set of $3n$ numbers having variance 4. In this set, the mean of first $2n$ numbers is 6 and the mean of the remaining $n$ …HardNumerical 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.