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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2020 · Mathematics · Binomial Theorem

What is the sum of the last five coefficients in the expansion of...

What is the sum of the last five coefficients in the expansion of (1+x)9(1+x)^9 when it is expanded in ascending powers of xx ?

Options

  1. A256
  2. B512
  3. C1024
  4. D2048

Correct answer

A. 256

Step-by-step solution

Expansion of (1+x)9=9C0+9C1x+9C2x2+9C3x3+9C4x4+9C5x5+9C6x6+9C7x7+9C8x8+9C9x9\begin{aligned} (1+x)^9={ }^9 C_0 & +{ }^9 C_1 x+{ }^9 C_2 x^2+{ }^9 C_3 x^3+{ }^9 C_4 x^4 \\ & +{ }^9 C_5 x^5+{ }^9 C_6 x^6+{ }^9 C_7 x^7+{ }^9 C_8 x^8+{ }^9 C_9 x^9 \end{aligned} Sum of last five co-efficient =9C5+9C6+9C7+9C8+9C9=126+84+36+9+1=256\begin{aligned} & ={ }^9 C_5+{ }^9 C_6+{ }^9 C_7+{ }^9 C_8+{ }^9 C_9 \\ & =126+84+36+9+1=256 \end{aligned}
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