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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Binomial Theorem

NDA 2023 · Mathematics · Binomial Theorem

How many terms are there in the expansion of (3 x-y)^4(x+3 y)^4 ?

How many terms are there in the expansion of (3x−y)4(x+3y)4(3 x-y)^4(x+3 y)^4 ?

Options

  1. A99
  2. B1212
  3. C1515
  4. D1717

Correct answer

C. 1515

Step-by-step solution

(3 x-y)^4(x+3 y)^4=[(3 x-y)(x+3 y)]^4=(3x2+8xy−3y2)4\left(3 x^2+8 x y-3 y^2\right)^4 Number of terms =(4+3−13−1)=6C2=15=\binom{4+3-1}{3-1}={ }^6 C_2=15.
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