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KCET2010MathematicsBinomial Theorem

The number (49²-4 ) (49³-49 ) is divisible by

Options

  1. A7 !
  2. B9 !
  3. C6 !
  4. D5 !

Correct answer

D. 5 !

Step-by-step solution

aligned & Given, (49²-4 ) (49³-49 ) & = [(49)²-(2)² ] [(49)²-1 ] 49 &=(49+2)(49-2)(49+1)(49-1) 49 &=51 47 50 48 49 &=(51 50 49 48 47) aligned Which is the product of five consecutive integers and hence it divisible by 5 !.

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