JEE Main 2026 · 8 Apr · Shift 2 · Mathematics Q7

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MathematicsSingle correct+4 / -1Question 7 of 75

A 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 all these 10 observations is equal to :

5.96

6.14

6.04

6.24

Answer and worked solution

Official answer: C

Sums of squares.

First set: $\sum x^2=4(13+1)=56$ .
Second set: $\sum x^2=6(1+4)=30$ .

Combined. Mean $\tfrac{4+12}{10}=1.6$ , so
$\sigma^2=\frac{86}{10}-1.6^2=8.6-2.56=6.04.$

(C)

Topics:Variance and standard deviation

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JEE Main 2026 · 8 Apr · Shift 2, Mathematics question 7