Median of $^{2 n} C_{0},^{2 n} C_{1},^{2 n} C_{2}, . . . .,^{2 n} C_{n}$ (when $n$ is even) is

^{2 n} C_{\frac{n - 1}{2}}

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^{2 n} C_{\frac{n}{2}}

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^{2 n} C_{\frac{n + 1}{2}}

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None of these

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Solution

The correct option is A $^{2 n} C_{\frac{n}{2}}$
Given observations $^{2 n} C_{0},^{2 n} C_{1},^{2 n} C_{2}, . . . .,^{2 n} C_{n}$
Here number of terms $= n + 1$ ....(odd)
Median $= (\frac{n}{2} + 1)$ th term
$=^{2 n} C_{\frac{n}{2}}$

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Similar questions

(1 + x)^{n} = C_{0} + C_{1} x + \dots . . + C_{n} x^{n}

\sum \sum 0 \leq r < s \leq n C_{r} C_{s}

^{2 n} C_{1} +^{2 n} C_{3} +^{2 n} C_{5} + . . . . . +^{2 n} C_{n - 1} = 2^{2 n - 1}

^{2 n} C_{1} +^{2 n} C_{3} +^{2 n} C_{5} + . . . . . +^{2 n} C_{n - 1} = 2^{2 n - 2}

(1 + x)^{n} = C_{0} + C_{1} x + C_{2} x^{2} + \dots + C_{n} x^{n},

\sum \sum 0 \leq r < s \leq n {(C_{r} + C_{s})}_{r}^{2}

\frac{1}{2}

The middle term in the expansion of $(x + \frac{1}{x})^{2 n}$ is:

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