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JEE Main 202624 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
24 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Statistics

JEE Main 2026 · 24 January · Evening Shift · Mathematics · Statistics

Let X=\ x ∈ ~N: 1 ≤ x ≤ 19\ and for some a, b ∈ ℝ, Y=\ a x+b: x ∈...

Let X={x∈ N:1≤x≤19}\mathrm{X}=\{x \in \mathrm{~N}: 1 \leq x \leq 19\} and for some a,b∈R,Y={ax+b:x∈X}a, b \in \mathbb{R}, \mathrm{Y}=\{a x+b: x \in \mathrm{X}\}. If the mean and variance of the elements of Y are 30 and 750, respectively, then the sum of all possible values of bb is

Options

  1. A60
  2. B100
  3. C80
  4. D20

Correct answer

A. 60

Step-by-step solution

Mean of X=1+192=10X = \frac{1+19}{2} = 10, Variance of X=192−112=30X = \frac{19^2-1}{12} = 30.
For Y=aX+bY = aX + b: Mean of Y=10a+b=30Y = 10a + b = 30 and Variance of Y=a2⋅30=750Y = a^2 \cdot 30 = 750.
a2=25⇒a=5a^2 = 25 \Rightarrow a = 5 or a=−5a = -5.
If a=5a = 5: b=30−50=−20b = 30 - 50 = -20.
If a=−5a = -5: b=30+50=80b = 30 + 50 = 80.
Sum of all possible values of b=−20+80=60b = -20 + 80 = 60.
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