Term independent of x in {left[ {√{frac{ x }{3}} + frac{{√ 3 }}{{{x^2}}}} right]^{10}} is

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7.Binomial Theorem

easy

The term independent of $x$ in ${\left[ {\sqrt{\frac{ x }{3}} + \frac{{\sqrt 3 }}{{{x^2}}}} \right]^{10}}$ is

A

$\frac{2}{3}$

B

$\frac{5}{3}$

C

$\frac{4}{3}$

D

None of these

Solution

(b) Accordingly, ${(\sqrt x )^{10 – r}}{\left( {\frac{1}{{{x^2}}}} \right)^r} = {x^0} \Rightarrow r = 2$

Hence the term is $^{10}{C_2}{\left( {\frac{1}{{\sqrt 3 }}} \right)^8}.\,\,\,{(\sqrt 3 )^2} = \frac{5}{3}$.

Standard 11

Mathematics

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