First slide

Binomial theorem for positive integral Index

Question

$If the 5^{th} term is 24 times the 3^{rd} term in the expansion of (1 + x)^{11} the x =$

Moderate

A

$\pm 4$
B

$\pm 2$
C

$\pm 3$
D

$\pm 8$

Solution

$\begin{array}{l} 5^{th} term = 24 \\ (3^{rd} term) \Rightarrow^{11} C_{4} x^{4} = 24 (^{11} C_{2} x^{2}) \\ \Rightarrow x^{2} = 24 \cdot \frac{^{11} C_{2}}{^{11} C_{4}} \\ = 24 \cdot \frac{11!}{2! 9!} \times \frac{4! 7!}{11!} = 4 \Rightarrow x = \pm 2 \end{array}$

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