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Question

In the expansion of $${ \left( 1+x \right)  }^{ n }$$, the coefficients of $$p^{th}$$ and $$(p+1)^{th}$$ terms are respectively $$p$$ and $$q$$, then $$p+q=$$


A
n+3
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B
n+2
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C
n
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D
n+1
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Solution

The correct option is D $$n+1$$
Given, $$p^{th}$$ and $$(p+1)^{th}$$ terms are $$p$$ and $$q$$
$${ n }_{ { c }_{ p }-1 }=p,{ n }_{ { c }_{ p } }=q\quad $$
$$\Rightarrow \cfrac { q }{ p } =\cfrac { { n }_{ { c }_{ p } } }{ { n }_{ { c }_{ p }-1 } } =\cfrac { n-p+1 }{ p }$$
$$ \Rightarrow p+q=n+1$$

Mathematics

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