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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2020 · Mathematics · Binomial Theorem

If (1+2 x-x^2)^6=a_0+a_1 x+a_2 x^2+ .+a_ 12 x^ 12 , then what is...

If (1+2x−x2)6=a0+a1x+a2x2+….+a12x12\left(1+2 x-x^2\right)^6=a_0+a_1 x+a_2 x^2+\ldots .+a_{12} x^{12}, then what is a0−a1+a2−a3+a4−….+a12a_0-a_1+a_2-a_3+a_4-\ldots .+a_{12} equal to?

Options

  1. A32
  2. B64
  3. C2048
  4. D4096

Correct answer

B. 64

Step-by-step solution

(1+2x−x2)6=a0+a1⋅x+a2⋅x2+….+a12⋅x12Putting x=−1a0−a1+a2+….+a12=(1+2(−1)−(−1)2)6=(1−2−1)12=(−2)6=64\begin{aligned} & \left(1+2 x-x^2\right)^6=a_0+a_1 \cdot x+a_2 \cdot x^2+\ldots.+a_{12} \cdot x^{12} \\ & \text{Putting } x=-1 \\ & a_0-a_1+a_2+\ldots.+a_{12} =\left(1+2(-1)-(-1)^2\right)^6 \\ & =(1-2-1)^{12}=(-2)^6=64 \end{aligned}
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