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7.Binomial Theorem
medium
If $A$ denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^n$ and $B$ denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^n$, then :
A
$\mathrm{A}=\mathrm{B}^3$
B
$3 A=B$
C
$B=A^3$
D
$\mathrm{A}=3 \mathrm{~B}$
(JEE MAIN-2024)
Solution
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 $\left.x=1\right)$
and sum of coefficients in the expansion of $\left(1+x^2\right)^n=B$
then $B=(1+1)^n=2^n$
$A=B^3$
Standard 11
Mathematics
