In expansion of {left( {x - frac{3}{{{x^2}}}} right)^9}, term independent of x is

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7.Binomial Theorem

easy

In the expansion of ${\left( {x - \frac{3}{{{x^2}}}} \right)^9},$ the term independent of $x$ is

A

Non existent

B

$^9{C_2}$

C

$2268$

D

$-2268$

Solution

(d) ${T_{r + 1}} = {\,^9}{C_r}{(x)^{9 – r}}{\left( { – \frac{3}{{{x^2}}}} \right)^r}$

= $^9{C_r}{( – 3)^r}{(x)^{9 – 3r}}$

For term independent of $x$, $9 – 3r = 0 \Rightarrow r = 3$

${T_4} = {\,^9}{C_3}\,{( – 3)^3} = – 2268$.

Standard 11

Mathematics

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