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The term independent of x in the expansi...

The term independent of `x` in the expansion of `((1)/(60)-(x^(8))/(81)).(2x^(2)-(3)/(x^(2)))^(6)` is equal to:

A

36

B

-72

C

-36

D

-108

Text Solution

Verified by Experts

The correct Answer is:
C
`(1/60-(x^(8))/81)(2x^(2)-3/(x^(2)))^(6)`
`T_(r+1)=.^(6)C_(2)(2x^(2))^(6-r)(-3/(x^(2)))^(4)=.^(6)C_(4)2^(6-r)(-3)^(4)x^(12-4r)`
Constant term in expansion of `(2x^(2)-3/(x^(2)))^(6)=.^(6)C_(2)2^(3)(-3)^(3)`
Coefficient of `x^(-8)` in the expansioni of `(2x^(2)-3/(x^(2)))^(6)=.^(6)C_(5)(2)(-3)^(5)`
Term independent of `x=(.^(6)C_(3)xx2^(3)(-3)^(3))/60+(.^(6)C_(5)xx2xx3^(5))/80=-72+6xx6=-36`
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