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If the sum of the coefficients in the expansion of   \left(1-3 x+10 x^2\right)^nis a and if the sum of the coefficients in the expansion of  \left(1+x^2\right)^nis b, then

 

Option: 1

a=3 b


Option: 2

a=b^3


Option: 3

b=a^3


Option: 4

None of these


Answers (1)

best_answer

We have a = sum of the coefficient in the expansion of 

\left(1-3 x+10 x^2\right)^n=(1-3+10)^n=(8)^n

\Rightarrow\left(1-3 x+10 x^2\right)^n=(2)^{3 n}, [Putting x = 1].

Now, b = sum of the coefficients in the expansion of

\left(1+x^2\right)^n=(1+1)^n=2^n.Clearly, a=b^3

Posted by

shivangi.bhatnagar

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