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NDA 1 2024 Maths, question 30

Topic: Algebra

Q30

What is the coefficient of x10x^{10} in the expansion of (1−x2)20(2−x2−1x2)−5(1-x^{2})^{20}(2-x^{2}-\frac{1}{x^{2}})^{-5} ?

  1. (a) −1-1Correct answer
  2. (b) 11
  3. (c) 1010
  4. (d) Coefficient of x10x^{10} does not exist

Solution.

Answer: (a) −1-1

  1. Use 2−x²−x⁻²=−(1−x²)²/x².
  2. The expression simplifies to −x¹⁰(1−x²)¹⁰ wherever the original is defined.
  3. Its x¹⁰ coefficient is −1, from the constant term of the remaining factor.