Question

If \( a \) is the coefficient of \( x^7 \) and \( b \) is the term independent of \( x \) in the expansion of \( \left( \frac{3x^4}{4} - \frac{4}{3x^3} \right)^7 \), then \( \frac{b}{a} = \)

• A. \( -1 \)
• B. \( 1 \)
• C. \( -\frac{16}{9} \)
• D. \( \frac{16}{9} \)

Hint:

To simplify coefficients of the form \( (x/y)^k \cdot (y/x)^m \), combine them into \( (x/y)^{k-m} \) to avoid large intermediate calculations.

Answer 1

The Correct Option is C