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The number of distinct terms in the expa...

The number of distinct terms in the expansion of is `(x^(3)+(1)/(x^(3))+1)^(n)` is (a) 2n (b) 3n (c) 2n+1 (d) 3n+1

A

`2n`

B

`3n`

C

`2n+1`

D

`3n+1`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `(1+x^(3)+(1)/(x^(3)))^(200)`
`=1+^(200)C_(1)(x^(3)+(1)/(x^(3)))+^(200)C_(2)(x^(3)+(1)/(x^(3)))^(2).......^(200)C_(200)(x^(3)+(1)/(x^(3)))^(200)`
The `R.H.S` is of the form
`k_(0)+k_(1)x^(3)+k_(2)(x^(3))^(2)+....k_(200)(x^(3))^(200)+(l_(1))/(x^(3))+(l_(2))/((x^(3))^(2))+....(l_(200))/((x^(3))^(200))`
where `k_(0),k_(1),.....,l_(1),l_(2),....` are all real constants
`:.` Number of terms `=1+200+200=401`
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