Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is q^p. Statement 2: The total number of selections of p different objects out of q objects is ^qC_p.

JEE Main 2012 Mathematics question

Statement 1: If A and B be two sets having p and q elements respectively, where q > p. Then the total number of functions from set A to set B is . Statement 2: The total number of selections of p different objects out of q objects is .

(1)Statement 1 is true, Statement 2 is false.
(2)Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.Correct
(3)Statement 1 is false, Statement 2 is true
(4)Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

Answer: (2)

Solution

Each of the p elements of A can be mapped to any of the q elements of B, giving functions — Statement 1 true. The number of selections of p objects from q is — Statement 2 true. But counting

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Question ID VK-103520