The middle term of expnsion of 10- x - x -1010A- 7 C5B- 8 C 5C- 9 C 5D- 10 C 5

The correct option is D ^10C_5Total number of terms in the expansion of nbsp;(10x+x10)^10 is 11, so the middle term is 6^th term ∴ t_6=^10C_6 1(10x)^6 1(x10) ...

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Standard XII

Mathematics

Middle Terms

The middle te...

Question

The middle term of expnsion of ${(\frac{10}{x} + \frac{x}{10})}^{10}$

^{7} C_{5}

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^{8} C_{5}

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^{9} C_{5}

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^{10} C_{5}

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Solution

The correct option is D $^{10} C_{5}$
Total number of terms in the expansion of ${(\frac{10}{x} + \frac{x}{10})}^{10}$ is $11$ , so the middle term is $6^{t h}$ term
$∴ t_{6} =^{10} C_{6 - 1} {(\frac{10}{x})}^{6 - 1} {(\frac{x}{10})}^{10 - 6 + 1} =^{10} C_{5}$

Suggest Corrections

The middle term of expnsion of (10x+x10)10

The correct option is D 10C5Total number of terms in the expansion of (10x+x10)10 is 11, so the middle term is 6th term ∴t6=10C6−1(10x)6−1(x10)10−6+1=10C5

The middle term of expnsion of ${(\frac{10}{x} + \frac{x}{10})}^{10}$

The correct option is D $^{10} C_{5}$
Total number of terms in the expansion of ${(\frac{10}{x} + \frac{x}{10})}^{10}$ is $11$ , so the middle term is $6^{t h}$ term
$∴ t_{6} =^{10} C_{6 - 1} {(\frac{10}{x})}^{6 - 1} {(\frac{x}{10})}^{10 - 6 + 1} =^{10} C_{5}$