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

 

TGT/PGT CS Course in "S P SHARMA CLASSES" APP

 TGT/PGT CS Course in "S P SHARMA CLASSES" APP

This is a crash course for TGT, PGT CS very help full for DSSSB, KVS, NVS, APS, HTET, BSTET, UP-LT, UP Polytechnic Lecturer and All Computer Science Exams for the post of TGT, PGT and Equivalent.

Content of the Course - 338 Videos 

Video Duration 30 Min to 90 Mins

C LANGUAGE - 21 VIDEOS

C++ LANGUAGE - 12 VIDEOS

C and C++ MIX - 21 VIDEOS

DBMS - 40 VIDEOS

NETWORKING - 46 VIDEOS

PYTHON - 55 VIDEOS

JAVA - 10 VIDEOS

OPERATING SYSTEM - 18 VIDEOS

DIGITAL ELECTRONICS - 22 VIDEOS

GENERAL COMPUTER - 18 VIDEOS

DATA STRUCTURE - 23 VIDEOS

COMPUTER SYSTEM ARCHITECTURE - 14 VIDEOS

ASP & VB NET - 2 VIDEOS

TOC - 5 VIDEOS

WEB DESIGNING - 07 VIDEOS

UNIX, LINUX, MS-DOS - 08 VIDEOS

BUSINESS COMPUTING - 1 VIDEO

DISCRETE (ENGINEERING) MATHEMATICS - 16 VIDEOS

Set Theory Assignment - 2

 

1.     The complement of the set A is _____________

A).   A – B

B).   U – A

C).   A – U

D).   B – A

 

2.     The set difference of the set A with null set is __________

A).   A

B).   null

C).   U

D).   B

 

3.     The difference of {1, 2, 3} and {1, 2, 5} is the set ____________

A).   {1}

B).   {5}

C).   {3}

D).   {2}

 

4.     Two sets are called disjoint if there _____________ is the empty set.

A).   Union

B).   Difference

C).   Intersection

D).   Complement

 

5.     Which of the following two sets are disjoint?

A).   {1, 3, 5} and {1, 3, 6}

B).   {1, 2, 3} and {1, 2, 3}

C).   {1, 3, 5} and {2, 3, 4}

D).   {1, 3, 5} and {2, 4, 6}

 

6.     Two sets are called disjoint if there _____________ is the empty set.

A).   Union

B).   Difference

C).   Intersection

D).   Complement

 

7.     The union of the sets {1, 2, 5} and {1, 2, 6} is the set _______________

A).   {1, 2, 6, 1}

B).   {1, 2, 5, 6}

C).   {1, 2, 1, 2}

D).   {1, 5, 6, 3}

 

8.     The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____________

A).   {1, 2}

B).   {5, 6}

C).   {2, 5}

D).   {1, 6}

 

9.     In which of the following sets A – B is equal to B – A?

A).   A = {1, 2, 3}, B = {2, 3, 4}

B).   A = {1, 2, 3}, B = {1, 2, 3, 4}

C).   A = {1, 2, 3}, B = {2, 3, 1}

D).   A = {1, 2, 3, 4, 5, 6}, B = {2, 3, 4, 5, 1}

 

10.  If A has 4 elements B has 8 elements then the minimum and maximum number of elements in A U B are ____________

A).   4, 8

B).   8, 12

C).   4, 12

D).   None of the mentioned

 

11.  If A is {{Φ}, {Φ, {Φ}}}, then the power set of A has how many element?

A).   2

B).   4

C).   6

D).   8

 

12.  Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the number of elements in A U B is?

A).   4

B).   5

C).   6

D).   7

 

13.  Let the set A is {1, 2, 3} and B is { 2, 3, 4}. Then number of elements in A ∩ B is?

A).   1

B).   2

C).   3

D).   4

 

14.  Let the set A is {1, 2, 3} and B is {2, 3, 4}. Then the set A – B is?

A).   {1, -4}

B).   {1, 2, 3}

C).   {1}

D).   {2, 3}

 

15.  Let A be set of all prime numbers, B be the set of all even prime numbers, C be the set of all odd prime numbers, then which of the following is true?

A).   A ≡ B U C

B).   B is a singleton set.

C).   A ≡ C U {2}

D).   All of the mentioned

 

16.  Two sets A and B contains a and b elements respectively. If power set of A contains 16 more elements than that of B, value of ‘b’ and ‘a’ are _______

A).   4, 5

B).   6, 7

C).   2, 3

D).   None of the mentioned

 

17.  Let A be {1, 2, 3, 4}, U be set of all natural numbers, then U-A’(complement of A) is given by set.

A).   {1, 2, 3, 4, 5, 6, ….}

B).   {5, 6, 7, 8, 9, ……}

C).   {1, 2, 3, 4}

D).   All of the mentioned

 

18.  Which sets are not empty?

A).   {x: x is a even prime greater than 3}

B).   {x : x is a multiple of 2 and is odd}

C).   {x: x is an even number and x+3 is even}

D).   { x: x is a prime number less than 5 and is odd}

19.     If n(A)=20 and n(B)=30 and n(A U B) = 40 then n(A ∩ B) is?

A).   20

B).   30

C).   40

D).   10

 

20.     Let A: All badminton player are good sportsperson.

B: All person who plays cricket are good sportsperson.

Let X denotes set of all badminton players, Y of all cricket players, Z of all good sportsperson. Then which of the following statements is correct?

A).   Z contains both X and Y

B).   Z contains X and Y is outside

C).   X contains Y and Z

D).   None of the mentioned

 

21.     If n(A)=10, n(B)=30,n(C)=50 and if set A, B, C are pairwise disjoint then which of the following is correct?

A).   n(A U B)=0

B).   n(B U C)=0

C).   n(A U B U C)=90

D).   All of the mentioned

 

22.     if n(A)=20,n(U)=50,n(C)=10 and n(A∩B)=5 then n(B)=?

A).   35

B).   20

C).   30

D).   10

 

23.     Let the students who likes table tennis be 12, the ones who like lawn tennis 10, those who like only table tennis are 6, then number of students who likes only lawn tennis are, assuming there are total of 16 students.

A).   16

B).   8

C).   4

D).   10