Question

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

A
999x
B
1001x
C
i
D
x1001

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$$=^{14}C_{10}x^{4}\left(\dfrac{1}{\sqrt x}\right)^{10}=^{14}C_{10}x^4\cdot \dfrac{1}{x^5}=\dfrac{^{14}C_{10}}{x}=\dfrac{1001}{x}$$ Maths

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