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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2019 · Mathematics · Binomial Theorem

What is the number of terms in the expansion of [(2 x-3 y)^2..(2...

What is the number of terms in the expansion of \left[(2 x-3 y)^2\right.\left.(2 \mathrm{x}+3 \mathrm{y})^2\right]^2 ?

Options

  1. A4
  2. B5
  3. C8
  4. D16

Correct answer

B. 5

Step-by-step solution

[(2x−3y)2(2x+3y)2]2=[(4x2−9y2)2]2=(4x2−9y2)4∴ Number of  terms =4+1=5\begin{aligned} & \quad\left[(2 \mathrm{x}-3 \mathrm{y})^2(2 \mathrm{x}+3 \mathrm{y})^2\right]^2 \\ & =\left[\left(4 \mathrm{x}^2-9 \mathrm{y}^2\right)^2\right]^2=\left(4 \mathrm{x}^2-9 \mathrm{y}^2\right)^4 \\ & \therefore \text{ Number\text{ of } terms }=4+1=5\end{aligned}
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