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If the coefficient of $(2 r+1)$ th term and $(r+2)$ th term in the expansion of $(1+x)^{43}$ are equal, then $r$ is equal to :
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The correct answer is:
14
Given that,
Coefficient of $(2 r+1)$ th term $=$ co-efficient of $(r+2)$ th term
$\Rightarrow \quad{ }^{43} C_{2 r}={ }^{43} C_{r+1}$
$\Rightarrow \quad 2 r+(r+1)=43$
or $\quad 2 r=r+1$
$\Rightarrow \quad r=14$ or $r=1$
thus $r=14$
Coefficient of $(2 r+1)$ th term $=$ co-efficient of $(r+2)$ th term
$\Rightarrow \quad{ }^{43} C_{2 r}={ }^{43} C_{r+1}$
$\Rightarrow \quad 2 r+(r+1)=43$
or $\quad 2 r=r+1$
$\Rightarrow \quad r=14$ or $r=1$
thus $r=14$
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