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Jee Main 2025Medium JEE math MCQ

Let \( x_1, x_2, \ldots, x_{10} \) 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 \( 2(x_1 - 1) + 4\beta, \) \( 2(x_2 - 1) + 4\beta, \ldots, 2(x_{10} - 1) + 4\beta, \) then \( \frac{\partial \mu}{\partial \beta} \) is equal to
  1. A. 100
  2. B. 120
  3. C. 110
  4. D. 90

Solution

The correct option is **A**. (A. 100)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let x1,x2,,x10 x_1, x_2, \ldots, x_{10} be ten observations such that i=110(xi2)=30, \sum_{i=1}^{10} (x_i - 2) = 30, i=110(xiβ)2=98,β>2, \sum_{i=1}^{10} (x_i - \beta)^2 = 98, \beta > 2, and their variance is 45. \frac{4}{5}. If μ \mu and σ2 \sigma^2 are respectively the mean and the variance of 2(x11)+4β, 2(x_1 - 1) + 4\beta, 2(x21)+4β,,2(x101)+4β, 2(x_2 - 1) + 4\beta, \ldots, 2(x_{10} - 1) + 4\beta, then μβ \frac{\partial \mu}{\partial \beta} is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep