SATHEE: Permutations And Combinations Question 308

Permutations And Combinations Question 308

Question: 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]

Options:

A) Necessarily zero

B) Always odd

C) Always even

D) None of these

Show Answer

Answer:

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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Permutations And Combinations Question 308

Question: 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]

Options:

Answer:

Solution:

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