Sets, Functions & Relations Part - 1

01)  If A ={1,2,3,4,}

       B = {2,4,6,8,}

      f(1) = 2, f(2) =4, f(3) = 6 and

      f(4) = 8, and f: A→B then f^-1 is :

   (a) {(2,1),(4,2),(6,3),(8,4)}

   (b) {(1,2),(2,4),(3,6),(4,8)}

   (c) {(1,4),(2,2),(3,6),(4,8)}

   (d) None of these

02) If R is the set of real numbers such 

     that the function f: R→R is defined

     by f(x) = (x + 1)^2, then find (fof) :

    (a) (x + 1)^2 + 1

    (b) x^2 + 1

    (c) {(x + 1)^2 + 1}^2

    (d) None

03) Out of 20 members in a family, 11

      like to take tea and 14 like coffee.

      Assume that each one likes at least 

      one of the two drinks. Find how many

     like both coffee and tea :

     (a) 2

     (b) 3

     (c) 4

     (d) 5

04) If F : A→R is a real valued function

      defined by f(x) = 1/x, then A=-------

     (a) R

     (b) R - {1}

     (c) R - {0}

     (d) R - N

05) In a survey of 300 companies, the

      number of companies using different 

     media - Newspapers (N), Ratio(R)

      and Television(T) are as follows :

     n(N) = 200, n(R) = 100, n(T) = 40,

     n(N∩R)= 50, n(R∩T) = 20,

    n(N∩T)=25 and n(N∩R∩T)=5.

     Find the numbers of companies

    using none of these media:

    (a) 20 companies

    (B) 250  " "

     (c) 30  " "

     (d) 50 " "