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Question
If the expansion of `(x - 1/x^2)^(2n)` contains a term independent of x, then n is a multiple of 2.
Options
True
False
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Solution
This statement is False.
Explanation:
The given expression is `(x - 1/x^2)^(2n)`
Tr+1 = `""^(2n)C_r (x)^(2n - r) (- 1/x^2)^r`
= `""^(2n)C_r (x)^(2n - r) (-1)^r * 1/x^(2r)`
= `""^(2n)C_r (x)^(2n - r - 2r) (-1)^r`
= `""^(2n)C_r (x)^(2n - 3r) (-1)^r`
For the term independent of x, 2n – 3r = 0
∴ r = `(2n)/3` which not an integer and the expression is not possible to be true
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