Sets, Functions & Relations Part - 3

11) Let R is the set of real numbers,

      such that the function f : R→R and g:

     R→R are defined by f(x) = x^2+3x+1 

     and g(x) = 2x - 3. Find (fog)

    (a) 4x^2+6x+1

    (b) x^2+6x+1

    (c) 4x^2 -6x+1.

12) If f: R→R, f(x) = 2x +7, then the

      inverse of f is:

      (a) f^-1(x) = (x - 7)/2

      (b) f^-1(x) = (x + 7)/2

      (c) f^1(x) = (x - 3)/2

      (d) None

13) If A = {x: x^2 - 3x + 2 = 0},

      B = {x: x^2 + 4x - 12 =0}, then

       B - A is equal to :

     (a) {-6}

     (b) {1}

     (c) {1,2}

     (d) {2,-6}

Sets, Functions & Relations Part - 2

06) If A = {+ 2, + 3}, B = {1,4,9,} and F =

       {(2,4),(-2,4),(3,9),(-3,4)} then 'F' is 

       defined as :

      (a) One to one function from A into B.

      (b) One to one function from A onto B.

      (c) Many to one function from A onto B.

      (d) Many to one function from A into B.

07) In a group of 70 people, 45 speak Hindi,

      33speak English and 10 speak neither Hindi 

      or English. Find how many can speak both 

      English as well as Hindi:

     (a) 13

     (b) 19

     (c) 18

     (d) 28.

08) If f(x-1) = x^2-4x+8, then f(x+1)=--

     (a) x^2+8

     (b) x^2+7

     (c) x^2+4

     (d) x^2-4x

09) let f : R→R be such that f(x) =2'.

      then f(x+y) equals :

     (a) f(x) + f(y)

     (b) f(x) . f(y)

     (c) f(x)/f(y)

     (d) None of these

10) If f(x) = x^2 +x -1 and 4f(x) = f(2x)

      then find 'x'

     (a) 4/3

     (b) 3/2

     (c) -3/4

     (d) None of these

Sets, Functions & Relations Part - 2

06) If A = {+ 2, + 3}, B = {1,4,9,} and F =

       {(2,4),(-2,4),(3,9),(-3,4)} then 'F' is 

       defined as :

      (a) One to one function from A into B.

      (b) One to one function from A onto B.

      (c) Many to one function from A onto B.

      (d) Many to one function from A into B.

07) In a group of 70 people, 45 speak Hindi,

      33speak English and 10 speak neither Hindi 

      or English. Find how many can speak both 

      English as well as Hindi:

     (a) 13

     (b) 19

     (c) 18

     (d) 28.

08) If f(x-1) = x^2-4x+8, then f(x+1)=--

     (a) x^2+8

     (b) x^2+7

     (c) x^2+4

     (d) x^2-4x

09) let f : R→R be such that f(x) =2'.

      then f(x+y) equals :

     (a) f(x) + f(y)

     (b) f(x) . f(y)

     (c) f(x)/f(y)

     (d) None of these

10) If f(x) = x^2 +x -1 and 4f(x) = f(2x)

      then find 'x'

     (a) 4/3

     (b) 3/2

     (c) -3/4

     (d) None of these

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 " "