JEE Main 2021 · MathsNumerical answerNumerical valueHardCalculation

JEE Main 17 March 2021, Shift 2, Maths Q84

Question 84 of 90 in this shift, Maths question 24 of 30, Section B.

Consider 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

numbers is 3. A new set is constructed by adding 1 into each of first

2n

numbers, and subtracting 1 from each of the remaining

n

numbers. If the variance of the new set is k, then

9k

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
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
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

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.