JEE Mains · Maths · STD 11 - 7. binomial theoram
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 \(\mathrm{A}=3 \mathrm{~B}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{A}=\mathrm{B}^3\)
Step-by-step Solution
Detailed explanation
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 \(B=(1+1)^n=2^n\) \(A=B^3\)
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