Q35 / 90 · JEE Main 2012 (12 May Online) · Mathematics

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 ${ }^q \mathrm{C}_p$.

  • A
    Statement 1 is true, Statement 2 is false.
  • B
    Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.
  • C
    Statement 1 is false, Statement 2 is true
  • Correct answer
    D
    Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation of Statement 1.

Solution

Statement-1: $n(A)=p, n(B)=q, q>p$ Total number of functions from $A \rightarrow B=q^p$ It is a true statement. Statement - 2 : The total number of selections of $p$ different objects out of $q$ objects is ${ }^q \mathrm{C}_p$. It is also a true statement and it is a correct explanation for statement $-1$ also.

Hence, the correct answer is option: 'D'.

Relevant Questions