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STD 11 - 7. binomial theoram — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 7. binomial theoram4 Marks
Question
For a positive integer $n,\left(1+\frac{1}{x}\right)^{n}$ is expanded in increasing powers of $x$. If three consecutive coefficients in this expansion are in the ratio, $2: 5: 12,$ then $n$ is equal to
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Answer

d
${ }^{ n } C _{ r -1}:{ }^{ n } C _{ r }:{ }^{ n } C _{ r +1}=2: 5: 12$

Now $\frac{{ }^{n} C_{r-1}}{{ }^{n} C_{r}}=\frac{2}{5}$

$\Rightarrow 7 r=2 n+2$

$\frac{{ }^{n} C_{r}}{{ }^{n} C_{r+1}}=\frac{5}{12}$

$\Rightarrow 17 r =5 n -12$

On solving (1)$\&(2)$

$\Rightarrow n =118$

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