JEE Main 2026 — Jan 24, Shift 1 — Mathematics solution

JEE Main2026Jan 24, Shift 1Mathematics

The mean and variance of a data of 10 observations are 10 and 2, respectively. If an observations $α$ in this data is replaced by $β$ , then the mean and variance become 10.1 and 1.99, respectively. Then $α + β$ equals.

A
$10$
B
$15$
C
$5$
D
$20$

Solution

For 10 observations with mean 10 and variance 2:

$\sum x_{i} = 100$ , $\frac{\sum x _{i}^{2}}{10} - 100 = 2 \Rightarrow \sum x_{i}^{2} = 1020$ .

After replacing $α$ with $β$ , the new sum is $101$ , so $β - α = 1$ .

New variance: $\frac{1020 - α ^{2} + β ^{2}}{10} - (10.1)^{2} = 1.99$

$\Rightarrow 1020 - α^{2} + β^{2} = 10 (1.99 + 102.01) = 1040$

$\Rightarrow β^{2} - α^{2} = 20$ .

Factoring: $(β - α) (β + α) = 20$ . Since $β - α = 1$ :

$α + β = 20$ .

← Back to full paper

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →