The coefficient of x^(28) in the expansi...

The coefficient of `x^(28)` in the expansion of `(1+x^3-x^6)^(30)` is `1` b. `0` c. `^30 C_6` d. `^30 C_3`

`.^(30)C_(6)`

`.^(30)C_(3)`

Text Solution

Verified by Experts

The correct Answer is:

`(1+x^(3)-x^(6))^(30)`
`= {1+x^(3)(1-x^(3))}^(30)`
`=.^(30)C_(0) + .^(30)C_(1)x^(3)(1-x^(3))+.^(30)C_(2)x^(6)(1-x^(3))^(2) + "…."`
Obviously, each term will contain `x^(3m), m in N`. But 28 is not divisible by 3. Therefore ther will be no term containing `x^(28)`.

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