The coefficient of the term independent of x in x2-1-x9 is

The correct option is D 84 T_r+1 = ^9C_r(x^2)^9 r ( 1/x)^r = ^9C_r( 1)^r x^18 3r For term, independent of x, 18 3r = 0 ⇒ r = 6 ∴ term independent of x = ...

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Byju's Answer

Standard XII

Mathematics

Sum of Product of Binomial Coefficients

The coefficie...

Question

The coefficient of the term independent of x in $(x^{2} - \frac{1}{x})^{9}$ is

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Solution

The correct option is D
84

$T_{r + 1} =^{9} C_{r} (x^{2})^{9 - r} (\frac{- 1}{x})^{r}$

= $^{9} C_{r} (- 1)^{r} x^{18 - 3 r}$

For term, independent of x,

18 - 3r = 0 $\Rightarrow$ r = 6

$∴$ term independent of x = $^{9} C_{6} (- 1)^{6}$ = 84.

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The coefficient of the term independent of x in (x2−1x)9 is

The correct option is D 84 Tr+1=9Cr(x2)9−r(−1x)r = 9Cr(−1)rx18−3r For term, independent of x, 18 - 3r = 0 ⇒ r = 6 ∴ term independent of x = 9C6(−1)6 = 84.

The coefficient of the term independent of x in $(x^{2} - \frac{1}{x})^{9}$ is

The correct option is D
84

$T_{r + 1} =^{9} C_{r} (x^{2})^{9 - r} (\frac{- 1}{x})^{r}$

= $^{9} C_{r} (- 1)^{r} x^{18 - 3 r}$

For term, independent of x,

18 - 3r = 0 $\Rightarrow$ r = 6

$∴$ term independent of x = $^{9} C_{6} (- 1)^{6}$ = 84.