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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 :

JEE · Math · previous-year question

  1. A.$\mathrm{B}=\mathrm{A}^3$
  2. B.$3 \mathrm{A}=\mathrm{B}$
  3. C.$A=3 B$
  4. D.$\mathrm{A}=\mathrm{B}^3$correct

Answer

D. $\mathrm{A}=\mathrm{B}^3$

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 $$x=1$$) 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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