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JEE Main 7-April-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 7-April-2025 Paper - Shift 24 Marks
MCQ
Let a random variable $X$ take values $0,1,2,3$ with $\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)=\mathrm{p}, \mathrm{P}(\mathrm{X}=2)=\mathrm{P}(\mathrm{X}=3)$ and $E\left(X^{2}\right)=2 E(X)$. Then the value of $8 p-1$ is :
  • A
    0
  • B
    2
  • C
    1
  • D
    3
✓

Answer

B. 2
$2 \mathrm{p}+2 \mathrm{q}=\frac{1}{2}$
$p+q$
$E \left( x ^2\right)=\sum_{ i =0}^3 x _{ i }^2 p \left( x _{ i }\right)=0 \cdot p +1 \cdot p +4 \cdot q +9 q$
$E(x)=\sum_{i=0}^{3} x_{i}^{2} p\left(x_{i}\right)=0 . p+1 . p+2 q+3 q=p+5 q$
$p+13 q=2(p+5 q)$
$p=3 q$
So, $q=\frac{1}{8} \& p=\frac{3}{8}$
So, $8 \mathrm{p}-1=2 $

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