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JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    Let the eleven letters \[A,B\].....,K denote an arbitrary permutation of the integers (1, 2,.....11), then \[(A-1)(B-2)(C-3).....(K-11)\] [Orissa JEE 2005]

    A) Necessarily  zero

    B) Always odd

    C) Always even

    D) None of these

    Correct Answer: C

    Solution :

    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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