JEE Advanced 2026 · Paper 2 · Mathematics Q12

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MathematicsNumerical+4Question 12 of 54

Consider a data consisting of 10 observations $x_1,x_2,\dots,x_{10}$ , whose mean is $5$ and variance is $7$ . If the mean and the variance of the first $8$ observations $x_1,x_2,\dots,x_8$ are $4$ and $3.5$ , respectively, and $x_9<x_{10}$ , then the value of $3x_9+2x_{10}$ is ________.

Your answer

Answer and worked solution

Official answer: 44

All ten. $\sum x_i=50$ , and $\frac{\sum x_i^2}{10}-25=7$ gives $\sum x_i^2=320$ .

First eight. $\sum=32$ , $\sum x_i^2=8(3.5+16)=156$ .

So $x_9+x_{10}=18$ and $x_9^2+x_{10}^2=164$ , giving $x_9x_{10}=\frac{324-164}2=80$ . The roots of $t^2-18t+80=0$ are 8 and 10; with $x_9<x_{10}$ , $x_9=8$ , $x_{10}=10$ .
$3x_9+2x_{10}=24+20=44.$

Topics:Variance and standard deviation Measures of central tendency

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JEE Advanced 2026 · Paper 2, Mathematics question 12