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For a positive integer n, if the expanis...

For a positive integer n, if the expanison of
`(5/x^(2) + x^(4))` has a term independent of x, then n can be

A

18

B

27

C

36

D

45

Text Solution

Verified by Experts

The correct Answer is:
a, b, c, d
Let (r + 1)th term of `(5/x^(2) + x^(4))^(n)` be independent
of x. We have, `T_(r+1) = "" ^(n) C_(r) (5/x^(2))^(n-r) (x^(4))^(r) = ^(n) C_(r) cdot 5^(n-r) cdot x ^(6r-2n)`
For this term to be independent of x,
`6r-2n= 0 or n = 3r`
For `r= 6, 9, 12, 15,`
`n= 18, 27, 36, 45.`
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