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Let the eleven letters .....,K denote an arbitrary permutation of the integers (1, 2,.....11), then  left parenthesis A minus 1 right parenthesis left parenthesis B minus 2 right parenthesis left parenthesis C minus 3 right parenthesis horizontal ellipsis. left parenthesis K minus 11 right parenthesis

  1. Necessarily zero
  2. Always odd
  3. Always even
  4. None of these

The correct answer is: Always even


    Given set of numbers is {1, 2,....11} in which 5 are even six are odd, which demands that in the given product it is not possible to arrange to subtract only even number from odd numbers. There must be at least one factor involving subtraction of an odd number form another odd number. So at least one of the factors is even. Hence product is always even

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