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Question

The $$11$$th term in the expansion of $${ \left( x+\cfrac { 1 }{ \sqrt { x }  }  \right)  }^{ 14 } $$ is


A
999x
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B
1001x
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C
i
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D
x1001
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Solution

The correct option is B $$\cfrac { 1001 }{ x } $$
We know that $$(r+1)$$th term in the expansion of $$(x+y)^n$$ is given by $$^nC_rx^{n-r}y^r$$.
Hence $$11$$th term in the expansion of given given binomial is given by
$$=^{14}C_{10}x^{4}\left(\dfrac{1}{\sqrt x}\right)^{10}=^{14}C_{10}x^4\cdot \dfrac{1}{x^5}=\dfrac{^{14}C_{10}}{x}=\dfrac{1001}{x}$$ 

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