First slide

Binomial theorem for positive integral Index

Question

$If the coefficients of rth term and (r + 1) th terms in the expansion of (1 + x)^{20} are in the ratio 1 : 2, then r =$

Moderate

A

6
B

7
C

8
D

9

Solution

The ratio of coefficient of rth term and (r+1)th term=1:2
$= \frac{^{20} C_{r - 1}}{\frac{\cdot^{20} C_{r}}{}} = \frac{1}{2} \Rightarrow \frac{r}{21 - r} = \frac{1}{2} \Rightarrow 2 r = 21 - r \Rightarrow r = 7$

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