If { } ( ) 25 50 50 r 50 r 25 r 25 r 0 C C K C, – – = å × = then K is equal to:

Question:
If $\sum_{r=0}^{25}\left\{{ }^{50} \mathrm{C}_{\mathrm{r}} \cdot{ }^{50-\mathrm{r}} \mathrm{C}_{25-\mathrm{r}}\right\}=\mathrm{K}\left({ }^{50} \mathrm{C}_{25}\right)$, then $\mathrm{K}$ is equal to:

$(25)^{2}$
$2^{25}-1$
$2^{24}$
$2^{25}$

Correct Option: 4

JEE Main Previous Year 1 Question of JEE Main from Mathematics Binomial Theorem and its Simple Applications chapter.

JEE Main Previous Year Jan. 10, 2019 (II)

Solution:

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