Function and Relation MCQ of Discrete Mathematics

 

1.     The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

A).   one-one

B).   Many-one

C).   Odd

D).   Even

 

2.     The smallest integer function f(x) = [x] is

A).   One-one

B).   Many-one

C).   Both (a) & (b)

D).   None of these

 

3.     The function f : R → R defined by f(x) = 3 – 4x is

A).   Onto

B).   Not onto

C).   None one-one

D).   None of these

 

4.     The number of bijective functions from set A to itself when A contains 106 elements is

A).   106

B).   (106)2

C).   106!

D).   2106

 

5.     If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x² + 7, then the value of x for which f(g(x)) = 25 is

A).   ±1

B).   ±2

C).   ±3

D).   ±4

 

6.     If f : R → R, g : R → R and h : R → R are such that f(x) = x^2, g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be

A).   0

B).   1

C).   -1

D).   π

 

7.     The number of binary operations that can be defined on a set of 2 elements is

A).   8

B).   4

C).   16

D).   64

 

8.     The maximum number of equivalence relations on the set A = {1, 2, 3} are

A).   1

B).   2

C).   3

D).   5

 

9.     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

A).   reflexive but not symmetric

B).   reflexive but not transitive

C).   symmetric and transitive

D).   neither symmetric, nor transitive

 

10.  Let us define a relation R in R as aRb if a ≥ b. Then R is

A).   an equivalence relation

B).   reflexive, transitive but not symmetric

C).   symmetric, transitive but not reflexive

D).   neither transitive nor reflexive but symmetric

 

11.  Let f : R → R be defind by f(x) = 1/x ∀ x ∈ R. Then f is

A).   one-one

B).   onto

C).   bijective

D).   f is not defined

 

12.  Which of the following functions from Z into Z are bijective?

A).   f(x) = x³

B).   f(x) = x + 2

C).   f(x) = 2x + 1

D).   f(x) = x² + 1

 

13.  Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows:

(a, b) R (c, d) iff ad = cb. Then, R is

A).   reflexive only

B).   Symmetric only

C).   Transitive only

D).   Equivalence relation

 

14.  Total number of equivalence relations defined in the set S = {a, b, c} is

A).   5

B).   3!

C).   23

D).   33

 

15.  Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defined by y = 2x⁴, is

A).   one-one onto

B).   one-one into

C).   many-one onto

D).   many-one into

 

16.  Let g(x) = x^2 – 4x – 5, then

A).   g is one-one on R

B).   g is not one-one on R

C).   g is bijective on R

D).   None of these

 

17.  Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=x−2/x−3. Then,

A).   f is bijective

B).   f is one-one but not onto

C).   f is onto but not one-one

D).   None of these

 

18.  The mapping f : N → N is given by f(n) = 1 + n^2, n ∈ N when N is the set of natural numbers is

A).   one-one and onto

B).   onto but not one-one

C).   one-one but not onto

D).   neither one-one nor onto

 

19.  The function f : R → R given by f(x) = x^3 – 1 is

A).   a one-one function

B).   an onto function

C).   a bijection

D).   neither one-one nor onto

 

20.  If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is

A).   one-one onto

B).   one-one into

C).   many-one onto

D).   None of these

 

21.  Let f : R → R be a function defined by f(x) = x^3 + 4, then f is

A).   injective

B).   surjective

C).   bijective

D).   none of these

 

22.  If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5.

A).   35

B).   30

C).   25

D).   29

 

23.  Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4.

A).   1

B).   2

C).   3

D).   4

 

24.  Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * 1/3

A).   20/3

B).   4

C).   18

D).   16/3