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Consider the expansion (x^(2)+(1)/(x))^(...

Consider the expansion `(x^(2)+(1)/(x))^(15)`.
Consider the following statements:
1. There are 15 terms in the given expansion.
2. The coefficient of `x^(12)` is equal to that of `x^(3)`.
Which of the above statements is/are correct ?

A

1 only

B

2 only

C

Both 1 and 2

D

Neither 1 nor 2

Text Solution

Verified by Experts

The correct Answer is:
B
1. W e know that, `(a+b)^(n)` have total (n + 1) number of terms
So, `(x^(2)+(1)/(x))^(15)` have 16 terms.
Hence, Statement 1 is false.
2. For coefficient of `x^(12)`
`30-3r = 12 rArr r = 6 rArr .^(15)C_(6)`
and for coefficient of `x^(3)`,
`30 - 3r = 3 rArr r = 9 rArr .^(15)C_(9) .^(15)C_(6) = .^(15)C_(9)`
Hence, statement 2 is correct.
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