First slide

Binomial theorem for positive integral Index

Question

If, in the binomial expansion of $(a - b)^{n}, n \geq 5$ he sum of 5th and 6th term is zero, then value of $\frac{a}{b}$ is

Moderate

A

$\frac{n - 5}{6}$
B

$\frac{6}{n - 4}$
C

$\frac{n - 4}{5}$
D

$\frac{5}{n - 4}$

Solution

$\begin{array}{l} ^{n} C_{4} a^{n - 4} (- b)^{4} +^{n} C_{5} a^{n - 5} (- b)^{5} = 0 \\ \Rightarrow^{n} C_{4} a^{n - 4} b^{4} =^{n} C_{5} a^{n - 5} b^{5} \\ \Rightarrow \frac{a^{n - 4} b^{4}}{a^{n - 5} b^{5}} = \frac{^{n} C_{5}}{^{n} C_{4}} \Rightarrow \frac{a}{b} = \frac{n - 4}{5} \end{array}$

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