Question

If in the expansion of $\left( 2a - \frac{a^{2}}{4} \right)^{9}$; the sum of middle terms is S, then which of the following is/are true–

• A. S = $\left( \frac{63}{32} \right)$a¹⁴ (a + 8)
• B. S = $\left( \frac{63}{32} \right)$a¹⁴(a – 8)
• C. S = $\left( \frac{63}{32} \right)$a¹³ (a – 8)
• D. S = $\left( \frac{63}{32} \right)$a¹³( 8 – a)

Answer 1

Answer: (D)

S = $\left( \frac{63}{32} \right)$a¹³( 8 – a)

Answer 2

There are two middle terms T₅ and T₆

So S = ⁹C₄ (2a)⁵ $\left( - \frac{a^{2}}{4} \right)^{4}$+ ⁹C₅ (2a)⁴ $\left( - \frac{a^{2}}{4} \right)^{5}$

S = $\frac{9!}{4!5!}$ (2a)⁴ $\left\lbrack \left( - \frac{a^{2}}{4} \right)^{4}\left( 2a - \frac{a^{2}}{4} \right) \right\rbrack$

S = $\frac{63}{32}$a¹³ (8 – a)