If rth term in the expansion of 2 x2-1-x12 is without x- then r is equal toA- 8B- 7C- 9D- 10

The correct option is C 9 rth term in the given expansion is ^12C_r 1 (2x^2)^12 r+1 ( 1/x )^r 1 =( 1)^r 1^12C_r 1 2^13 r x^26 2r r+1 For this term to be indep ...

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Standard XII

Mathematics

Term Independent of x

If rth term i...

Question

If rth term in the expansion of ${(2 x^{2} - \frac{1}{x})}^{12}$ is without x, then r is equal to

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Solution

The correct option is C
9

rth term in the given expansion is $^{12} C_{r - 1} (2 x^{2})^{12 - r + 1} {(\frac{- 1}{x})}^{r - 1}$

$= (- 1)^{r - 1}^{12} C_{r - 1} 2^{13 - r} x^{26 - 2 r - r + 1}$

For this term to be independent of x, we must have:

27-3r=0

$\Rightarrow r = 9$

Hence, the 9th term in the expansion is independent of x.

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