Question

In the expansion of $\frac{ab + ac}{b^{2} - ac}$the coefficient of p^th and $(1 + x)^{n}$ terms are respectively p and q. Then $(a + b + c)^{n}$

• A. $(1 + x)^{n}$
• B. $(5^{1/2} + 7^{1/8})^{1024}$
• C. $(y^{1/5} + x^{1/10})^{55}$
• D. $R = (5\sqrt{5} + 11)^{2n + 1}$

Answer 1

Answer: (B)

$(5^{1/2} + 7^{1/8})^{1024}$

Answer 2

p^th term $\frac{462a^{5}}{b^{6}}$

(p + 1)^th term $\frac{- 462a^{5}}{b^{6}}$

Then, coefficient of $x^{53}$

⇒ $\sum_{m = 0}^{100}{100C_{m}(x - 3)^{100 - m}}.2^{m}$

⇒ $100C_{47}$

⇒ $100C_{53}$.