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7.Binomial Theorem
medium
If the sum of the coefficients in the expansion of ${(1 - 3x + 10{x^2})^n}$ is $a$ and if the sum of the coefficients in the expansion of ${(1 + {x^2})^n}$ is $b$, then
A
$a = 3b$
B
$a = {b^3}$
C
$b = {a^3}$
D
None of these
Solution
(b) We have $a =$ sum of the coefficient in the expansion of ${(1 – 3x + 10{x^2})^n} = {(1 – 3 + 10)^n} = {(8)^n}$
==> ${(1 – 3x + 10{x^2})^n} = {(2)^{3n}}$, [Putting $x = 1$] .
Now, $b =$ sum of the coefficients in the expansion of ${(1 + {x^2})^n} = {(1 + 1)^n} = {2^n}$. Clearly, $a = {b^3}$
Standard 11
Mathematics
