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If ${ }^n C_{r-1}=36,{ }^n C_r=84$ and ${ }^n C_{r+1}=126$, then the value of $r$ is
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The correct answer is:
$3$
Here $\frac{{ }^n C_{r-1}}{{ }^n C_r}=\frac{36}{84}$ and $\frac{{ }^n C_r}{{ }^n C_{r+1}}=\frac{84}{126}$.
$\Rightarrow 3 n-10 r=-3$ and $4 n-10 r=6$
On solving, we get $n=9, r=3$.
$\Rightarrow 3 n-10 r=-3$ and $4 n-10 r=6$
On solving, we get $n=9, r=3$.
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