Verified Solution • 2025–26 Session moderate

QJEEM23Maec85: JEE Main 2023 Mathematics - Class 11 JEEM23Maec85 Solution: The mean and variance of 5 observations are 5 and 8…

The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1, 3, 5, then the sum of cubes of the remaining two observations is :

Multiple Choice Options

  • A 1792
  • B 1216
  • C 1456
  • D 1072

Step-by-Step Verified Solution

Let observation 1,3,5,a,b1,3,5, a, b

amp; Mean =9+a+b5=5amp; Variance =a2+b2+355−25=8amp;⇒a+b=16 and a2+b2=130amp;∴a and b are 7 and 9amp;∴a3+b3=73+93=1072\begin{aligned}& \text { Mean } = \frac{9+a+b}{5}=5 \\\\& \text { Variance } = \frac{a^{2}+b^{2}+35}{5}-25=8 \\\\& \Rightarrow a+b=16 \text { and } a^{2}+b^{2}=130 \\\\& \therefore a \text { and } b \text { are } 7 \text { and } 9 \\\\& \therefore a^{3}+b^{3}=7^{3}+9^{3}=1072\end{aligned}

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