Relations And Functions

15 Questions | Total Attempts: 1711

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Relations And Functions

Time: 30 Minute


Questions and Answers
  • 1. 
    If f: R →R is defined by f(x) = 3x + 2, define f [f(x)].
    • A. 

      9x+5

    • B. 

      9x+8

    • C. 

      9x+4

    • D. 

      9x-4

  • 2. 
    Let f: {1, 3, 4} → {1, 2, 5} and g: {1, 2, 5} → {1, 3} be given by = {(1, 2), (3, 5), (4, 1)} and = {(1, 3), (2, 3), (5, 1)}. What will be the value of gof.
    • A. 

      Gof = {(1, 3), (3, 1), (4, 3)}

    • B. 

      Gof = {(1, 3), (3, 1), (2, 3)}

    • C. 

      Gof = {(2, 3), (3, 1), (4, 3)}

    • D. 

      Gof = {(1, 3), (3, 4), (4, 3)}

  • 3. 
    • A. 

      F is invertible

    • B. 

      F is not invertible

    • C. 

      None of the above

    • D. 

      Both A & B

  • 4. 
    For the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)), what is true about R?
    • A. 

      R is reflexive

    • B. 

      R is transitive

    • C. 

      Neither A nor B

    • D. 

      Both A & B

  • 5. 
    • A. 

      One-one

    • B. 

      Onto

    • C. 

      Neither A nor B

    • D. 

      None of these

  • 6. 
    What is true regarding the given function? f: R → R defined by f(x) = 3 − 4x
    • A. 

      Onto

    • B. 

      Bijective

    • C. 

      Neither A nor B

    • D. 

      Both A & B

  • 7. 
    The function f in  defined as  is one-one and onto. Find .
    • A. 
    • B. 
    • C. 
    • D. 
  • 8. 
    Consider f: R → R given by f(x) = 4x + 3. Find weather f is invertible. Find the inverse of f.
    • A. 

      Not invertible, (y – 3 / 4)

    • B. 

      Invertible, (y – 3 / 4)

    • C. 

      Not invertible, (y + 3 / 4)

    • D. 

      Invertible, (y + 3 / 4)

  • 9. 
    What is true regarding the given function? Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(xy): 3x − y = 0}
    • A. 

      Reflexive

    • B. 

      Symmetric

    • C. 

      Transitive

    • D. 

      None of the above

  • 10. 
    What is true regarding the given function? Relation R in the set N of natural numbers defined as R = {(xy): y = x + 5 and x < 4}
    • A. 

      Reflexive & symmetric

    • B. 

      Symmetric & transitive

    • C. 

      Both A & B

    • D. 

      None of the above

  • 11. 
    What is true regarding the given functions? 1.      f: N → N given by f(x) = x2 2.      f: Z → Z given by f(x) = x2
    • A. 

      Both functions are not injective

    • B. 

      Both functions are not subjective

    • C. 

      Both functions are not subjective

    • D. 

      Both functions are injective

  • 12. 
    • A. 

      Bijective

    • B. 

      Not bijective

    • C. 

      Onto

    • D. 

      Both B & C

  • 13. 
    Let A = R − {3} and B = R − {1}. Consider the function f: A → B defined by . What is true about ‘f’?
    • A. 

      One-one

    • B. 

      Onto

    • C. 

      One-one and onto

    • D. 

      None of these

  • 14. 
    The function f: [−1, 1] → R, given by  is one-one. Find the inverse of the function f: [−1, 1] → Range f.
    • A. 
    • B. 
    • C. 
    • D. 
  • 15. 
    Let A = N X N and * be the binary operation on A defined by (ab)*(cd) = (cd) What is true about ‘*’
    • A. 

      Commutative

    • B. 

      Associative

    • C. 

      Commutative and associative

    • D. 

      None of these