Let x_1, x_2, . . ., x_{10} be ten observations such that \sum_{{i=1}}^{{10}} (x_i-2) =30, \sum_{{i=1}}^{{10}} (x_i-\beta) ^2=98, \beta>2, and their variance is \frac{4}{5}. If \mu and \sigma^2 are respectively the mean and the variance of 2 (x_1-1) +4 \beta, 2 (x_2-1) +4 \beta, . . ., 2 (x_{10}-1) +4 \beta, then \frac{\beta \mu}{\sigma^2} is equal to [29 Jan 2025 Shift 1]

JEE Main 29 Jan 2025 Shift 1 Paper

Section: Mathematics

Question : 13 of 75

Marks: +1, -0

Let x1,x2,...,x10 be ten observations such that

∑

i=1

(xi−2)=30,‌‌

∑

i=1

(xi−β)2=98,β>2, and their variance is ‌

. If µ and σ2 are respectively the mean and the variance of 2(x1−1)+4β,2(x2−1)+4β,..., 2(x10−1)+4β, then ‌

βµ

σ2

is equal to

[29 Jan 2025 Shift 1]

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