If number of terms in the expansion of ${(1 - 2 x + x^{2})}^{n}$ , is $19$ , then $n (n \in N)$ is-

7

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9

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10

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11

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Solution

The correct option is B $9$
${(1 - 2 x + x^{2})}^{n} = {(1 - x)}^{2 n}$
Hence number of term $= 2 n + 1 = 19$
$\Rightarrow$ $n = 9$

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