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Question:
The middle term of expansion of $(\frac {10}{x}+\frac {x}{10})^{10}$ is
The middle term of expansion of $(\frac {10}{x}+\frac {x}{10})^{10}$ is
Updated On: Apr 2, 2024
- $^7C_5$
- $^8C_5$
- $^9C_5$
- $^{10}C_5$
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The Correct Option is D
Solution and Explanation
Since, $n=10$ (even), so the middle term will be $\left(\frac{10+2}{2}\right)$ th term, i.e. 6 th term.
Now, $T_{6}={ }^{10} C_{5}\left(\frac{10}{x}\right)^{5}\left(\frac{x}{10}\right)^{5}={ }^{10} C_{5}$
Now, $T_{6}={ }^{10} C_{5}\left(\frac{10}{x}\right)^{5}\left(\frac{x}{10}\right)^{5}={ }^{10} C_{5}$
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Concepts Used:
Binomial Theorem
The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is
Properties of Binomial Theorem
- The number of coefficients in the binomial expansion of (x + y)n is equal to (n + 1).
- There are (n+1) terms in the expansion of (x+y)n.
- The first and the last terms are xn and yn respectively.
- From the beginning of the expansion, the powers of x, decrease from n up to 0, and the powers of a, increase from 0 up to n.
- The binomial coefficients in the expansion are arranged in an array, which is called Pascal's triangle. This pattern developed is summed up by the binomial theorem formula.
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