The middle terms in the expansion of x-29 isA- C39 x6 23B- C49 x5 24C- C59 x4 25D- C69 x3 26

The correct options are B C49 nbsp;x5 nbsp;24 C C59 nbsp;x4 nbsp;25(x+2)9 nbsp;has nbsp;10 nbsp;terms.So nbsp;we nbsp;will nbsp;have nbsp; ...

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Standard XII

Mathematics

General Term of Binomial Expansion

The middle te...

Question

The middle term(s) in the expansion of ${(x + 2)}^{9}$ is

9 C 3 x^{6} 2^{3}

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9 C 4 x^{5} 2^{4}

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9 C 5 x^{4} 2^{5}

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9 C 6 x^{3} 2^{6}

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Solution

The correct options are
B $9 C 4 x^{5} 2^{4}$
C $9 C 5 x^{4} 2^{5}$
${(x + 2)}^{9} has 10 terms . So we will have two middle terms i . e . the 5^{th} and the 6^{th} term . So, T_{5} and T_{6} are the required middle terms . T_{r + 1} = n C r x^{n - r} y^{r} ({(r + 1)}^{th} term in the expansion of {(x + y)}^{n}) T_{5} = T_{4 + 1} = 9 C 4 x^{5} 2^{4} (n = 9; x = x; y = 2; r = 4) and T_{6} = T_{5 + 1} = 9 C 5 x^{4} 2^{5} (n = 9; x = x; y = 2; r = 5)$

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The middle term(s) in the expansion of (x+2)9is

The middle term(s) in the expansion of ${(x + 2)}^{9}$ is