Term independent of x in expansion of {left( {{x^2} - frac{{3√ 3 }}{{{x^3}}}} right)^{10}} is

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7.Binomial Theorem

easy

The term independent of $x$ in the expansion of ${\left( {{x^2} - \frac{{3\sqrt 3 }}{{{x^3}}}} \right)^{10}}$ is

A

$153090$

B

$150000$

C

$150090$

D

$153180$

Solution

(a) ${T_{r + 1}} = {}^{10}{C_r}{({x^2})^{10 – r}}{\left( {\frac{{ – 3\sqrt 3 }}{{{x^3}}}} \right)^r}$

For term independent of $x$, $20 – 2r – 3r = 0 \Rightarrow r = 4$

$\therefore {T_{4 + 1}} = {}^{10}{C_4}{( – 3)^4}{(\sqrt 3 )^4} = 153090.$

Standard 11

Mathematics

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