The middle term in the expansion of ( x 10 + 10 x ) 10 is

General term = T r + 1 = 10 C r ( x 10 ) 10 − r ( 10 x ) r Here n = 10 , which is an even number. Now, [ 2 10 + 1 ] th term i.e. 6 th term is the middle term. Hence, middle term = T 6 T 5 + 1 = 10 C 5 ( x 10 ) 10 − 5 ( 10 x ) 5 = 10 C 5 ( x 10 ) 5 ( 10 x ) 5 = 10 C 5 .

Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremGeneralEasy2 minPYQ_2023

MathematicsEasysingle choice

The middle term in the expansion of $(\frac{10}{x} + \frac{x}{10})^{10}$ is

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Solution:

General term $= T_{r + 1}$
$=^{10} C_{r} (\frac{10}{x})^{10 - r} (\frac{x}{10})^{r}$
Here $n = 10$ , which is an even number.
Now, $[\frac{10}{2} + 1]^{th}$ term i.e. $6^{th}$ term is the middle term.
Hence, middle term $= T_{6}$
$T_{5 + 1} =^{10} C_{5} (\frac{10}{x})^{10 - 5} (\frac{x}{10})^{5}$
$=^{10} C_{5} (\frac{10}{x})^{5} (\frac{x}{10})^{5} =^{10} C_{5}$ .

Stream:BITSATSubject:MathematicsTopic:Binomial TheoremSubtopic:General

⏱ 2mℹ️ Source: PYQ_2023

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