QJEEM24Ma4813: JEE Main 2024 Mathematics - Class 11 JEEM24Ma4813 Solution: If A denotes the sum of all the coefficients in the expansion…

Question

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If A denotes the sum of all the coefficients in the expansion of

\left(1-3 x+10 x^2\right)^{\mathrm{n}}

and B denotes the sum of all the coefficients in the expansion of

\left(1+x^2\right)^n

, then :

Accepted Answer

Sum of coefficients in the expansion of $\left(1-3 \mathrm{x}+10 \mathrm{x}^2\right)^{\mathrm{n}}=\mathrm{A}$

then $A=(1-3+10)^n=8^n$ (put $x=1$ )

and sum of coefficients in the expansion of

$\begin{aligned}& \left(1+x^2\right)^n=B \\& \text { then } B=(1+1)^n=2^n \\& A=B^3\end{aligned}$

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