Question

If the ratio of the coefficient of third and fourth term in the expansion of $(\alpha^{2}x^{2} - 2\alpha\ x + 1)^{51}$ is 1 : 2, then the value of n will be.

• A. 18
• B. 16
• C. 12
• D. – 10

Answer 1

Answer: (D)

– 10

Answer 2

$4n - 5 = 9r$ and $\frac{4n - 5}{n + 1} = 3 \Rightarrow n = 8$

But according to the condition,

$\left\lbrack \because\frac{nC_{k}}{nC_{k - 1}} = \frac{n - k + 1}{k} \right\rbrack$