Question

The coefficient of \( x^{20} \) in the expansion of \( (1 + x^2)^{40} \left( x^2 + 2 + \frac{1}{x^2} \right)^{-5} \) is:

• A. \( \binom{30}{10} \)
• B. \( \binom{30}{25} \)
• C. 1
• D. None of these

Hint:

Expand each factor and find the relevant term using binomial coefficients.

Answer 1

The Correct Option is A

Step 1: Identify the term.
To find the coefficient of \( x^{20} \), expand both parts of the product and identify the term that contains \( x^{20} \). The required coefficient is \( \binom{30}{10} \).
Thus, the correct answer is (1).