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MCQ

True or False

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)`

T_{r+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

Concept: General and Middle Terms

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