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JEE Math Practice Question

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 :

  1. A.224
  2. B.225$$-$$ 1
  3. C.225
  4. D.(25)2

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