JEE Mains · Maths · STD 11 - 7. binomial theoram
If \(\sum\limits_{r = 0}^{25} {\left\{ {^{50}{C_r}.{\,^{50 - r}}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} \), then \(K\) is equal to
- A \((25)^2\)
- B \(2^{25} -1\)
- C \(2^{24}\)
- D \(2^{25}\)
Answer & Solution
Correct Answer
(B) \(2^{25} -1\)
Step-by-step Solution
Detailed explanation
\(\sum\limits_{r = 1}^{25} {\frac{{\left| {50} \right.}}{{\left| r \right.\left| {50} \right. - r}} \times \frac{{\left| {50 - r} \right.}}{{\left| {25 - r\left| {25} \right.} \right.}}} \)…
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