Relation and functions - MCQ class 12 Maths

Relation and functions - MCQ class 12 Maths

i5 academy- Mcq questions ( 12th Maths )

Quiz

 

1. Let T be the set of all triangle in the Euclidean plane , and let a relation to R on T be defined as aRa if a is congruent to b ∀ a , b ∈T , then R is
   1.   Reflexive but not transitive
   2.   Transitive but not symmetric
   3.   Equivalence
   4.   None of these
2. The maximum number of equivalence relation on the set A = { 1,2,3} are
   1.   1
   2.   2
   3.   3
   4.   5
3. If a Relation on the set {1,2,3} be defined by R = {(1,2)}, then R is
   1.   Reflexive
   2.   transitive
   3.   symmetric
   4.   None of these
4. Let us define a relation R in R as a aRb if a ≥ b , then R is
   1.   equivalence relation
   2.   reflexive , transitive but not symmetric
   3.   symmetric , transitive but not reflexive
   4.   neither transitive nor reflexive but symmetric
5. Let A = {1,2,3} and consider the relation R = { (1,1) , (2,2) , (3,3) , (1,2) , (2,3) ,(1,3) } then R is
   1.   reflexive but not symmetric
   2.   reflexive but not transitive
   3.   symmetric and transitive
   4.   neither symmetric and nor transitive
6. Let A = {1,2,3,4} and consider the relation R = { (1,2) , (2,2) , (1,1) , (4,4) , (1,3) ,(3,3), (3,2) } then R is
   1.   reflexive and symmetric but not transitive
   2.   reflexive and transitive but not symmetric
   3.   symmetric and transitive but not reflexive
   4.   an equivalence relation
7. If A= { 1,2,3,4,5} such that a +b =8 , ∀ a , b ∈A , then a R b is ---
   1.   { (3,5) , (4,4) , (5,3) }
   2.   { 3,4,5}
   3.   { 1 , 2,3,4,5}
   4.   {1}
8. If A= { 1,2,3,4,5} such that a +b =8 , ∀ a , b ∈A , then Range is ---
   1.   { (3,5) , (4,4) , (5,3) }
   2.   { 3,4,5}
   3.   { 1 , 2,3,4,5}
   4.   {1}
9. If A= { 1,2,3,4,5} such that a +b =8 , ∀ a , b ∈A , then Co-domain is ---
   1.   { (3,5) , (4,4) , (5,3) }
   2.   { 3,4,5}
   3.   { 1 , 2,3,4,5}
   4.   {1}
10. If R ={ (x,y) : y= x+7, x < 4 , x ,y∈N } then R is -----
    1.   { 1,2,3}
    2.   { 8,9,10}
    3.   { (1,8) , ( 2,9) , ( 3,10) }
    4.   { 1,2,3,4}
11. If R ={ (x,y) : y= x+7, x < 4 , x ,y∈N } then Domain is -----
    1.   { 1,2,3}
    2.   { 8,9,10}
    3.   { (1,8) , ( 2,9) , ( 3,10) }
    4.   { 1,2,3,4}
12. If R ={ (x,y) : y= x+7, x < 4 , x ,y∈N } then Range is -----
    1.   { 1,2,3}
    2.   { 8,9,10}
    3.   { (1,8) , ( 2,9) , ( 3,10) }
    4.   { 1,2,3,4}
13. The function f:R → R defined by f(x) = x 2 , x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
14. The function f:N → N defined by f(x) = x 2 , x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
15. The function f:N→ N defined by f(x) = 2x, x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
16. The function f:R→ R defined by f(x) = 2x, x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
17. The function f:R→ R defined by f(x) = 3-4x , x ∈R is
    1.   one-one
    2.   one - one and on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
18. The function f:R→ R defined by f(x) = 1 + x 2 , x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
19. The function f:R→ R defined by f(x) = x 4, x ∈R is
    1.   one-one
    2.   on to
    3.   one-one but not onto
    4.   Neither one -one nor onto
20. Let R be the relation in the set N given by
    R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.
    
    1.   (2,4) ∈R
    2.   (3,8) ∈R
    3.   (6,8) ∈R
    4.   (8,7) ∈R