Free Printable PRE-GTU EXAM

1.

Enter your Enrollment no. and Branch name:

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2.

Enter your Name:

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3.

If a finite set S has 9 elements then power set of S has _____elements.

a)

18

b)

$2^9$

c)

$9^2$

d)

81

4.

If A and B are non empty finite sets then $\left|A\cup B\right|=$ _________. Where $\left|X\right|$ denotes the cardinality of set X .

a)

b)

c)

d)

5.

If A and B are two sets such that $\left(A\cap B\right)\subset A\$ then $A\cup\left(A\cap B\right)=$ ________

a)

B

b)

A

c)

$\phi$

d)

$A\cap B$

6.

If A and B are two sets such that $A\subset B$ then $A\cap B^c=_{ }$ _______

a)

A

b)

$\phi$

c)

B

d)

$A\cup B$

7.

Let A and B be two finite sets. Then the size of $A\times B$ is

a)

$2^{\left|A\right|\left|B\right|}$

b)

$\left|A\right|^2\left|B\right|^2$

c)

$\left|A\right|\left|B\right|$

d)

$2^{\left|A\right|}2^{\left|B\right|}$

8.

If real function $f\left(x\right)=\left(x+1\right)^2$ and $g\left(x\right)=x^2+1$ then $\left(fog\right)\left(-3\right)=$ _________

a)

121

b)

112

c)

211

d)

111

9.

Let $P\left(A\right)$ denote the power set of A. If $P\left(A\right)\subseteq B$ then

a)

$2^{\left|A\right|}\le\left|B\right|$

b)

$2^{\left|A\right|}\ge\left|B\right|$

c)

$2^{\left|A\right|}\le2^{\left|B\right|}$

d)

$2^{\left|A\right|}\ge2^{\left|B\right|}$

10.

The function $f:R\rightarrow R,\ \ \ f\left(x\right)=x^2$ then the function f is

a)

one -one and onto

b)

one -one but not onto

c)

not one -one but onto

d)

neither one-one nor onto

11.

$f:\ N\rightarrow N,\ f\left(n\right)=\left(n+1\right)^2$ then the function f is

a)

neither one-one nor onto

b)

onto but not one-one

c)

one-one but not onto

d)

one one and onto

12.

The relation R on set $A=\left\{1,2,3\right\}$ is $R=\left\{\left(1,1\right),\left(2,2\right),\left(3,3\right)\right\}$ . Then R is

a)

an Eqivalence relation

b)

only symmetric relation

c)

only transitive relation

d)

only reflexive relation

13.

Let $S=\left\{\left(1,2\right)\right\}$ be a relation on set $A=\left\{1,2,3\right\}$ then

a)

S is reflexive

b)

S is symmetric

c)

S is transitive

d)

S is an equivalence

14.

In the poset $\left(Z^+,\ D\right)$ which of the following pairs of integers are incomparable? Where $D$ denotes the divides relation.

a)

2, 3

b)

3, 12

c)

4, 16

d)

1, 2

15.

The number of subsets of a set of order four is

a)

2

b)

16

c)

8

d)

4

16.

Let $A=\left\{1,2,3,4\right\}$ then the total number of distinct relations that can be defined over A is

a)

$2^9$

b)

$2^{10}$

c)

$2^{16}$

d)

$2^4$

17.

The symmetric difference of $A=\left\{1,2,3\right\}$ and $B=\left\{2,3,4\right\}$ is

a)

$\left\{1,4\right\}$

b)

$\left\{1,2\right\}$

c)

$\left\{2,3\right\}$

d)

$\left\{1,2,3,4\right\}$

18.

The difference of set $\left\{1,2,3,4,5\right\}$ and set $\left\{2,3,4,5\right\}$ is

a)

$\left\{1\right\}$

b)

$\left\{2\right\}$

c)

$\left\{3\right\}$

d)

$\left\{4\right\}$

19.

The power set of singleton set has exactly__________subsets

a)

0

b)

1

c)

2

d)

3

20.

The set of even integers is________.

a)

Finite

b)

Empty

c)

Infinite

d)

None of these

21.

The universal relation $A\times A$ on A is

a)

Anti-symmetric

b)

an equivalence relation

c)

A partial ordering relation

d)

not symmetric not anti symmrtiric

22.

The number of elements in the power set of the set $\left\{\left\{1,2\right\},\ 3\right\}$ is

a)

2

b)

4

c)

6

d)

8

23.

Which of the following is null set?

a)

$\left\{1\right\}$

b)

$\phi$

c)

$\left\{0\right\}$

d)

$\left\{\phi\right\}$

24.

Let $A=\left\{1,2,3,4\right\}$ which ordered pair are in the relation $R=\left\{\left(a,b\right)\ :\ a\ divides\ b\right\}$

a)

(2,3)

b)

(2,1)

c)

(4,2)

d)

(2,4)

25.

A relation R on set X is said to be reflexive if

a)

$xRx\ \ \forall x\in X$

b)

$xRx\ \ \ for\ \ some\ \ x\in X$

c)

$xRy\ \ \forall\ x,\ y\in X$

d)

$x\ R\ y\ \ \ for\ some\ x,\ y\in X$

26.

Let $A=\left\{1,2,3,4\right\}$ relation R is given by $R=\left\{\left(2,2\right),\left(3,3\right),\left(4,4\right),\ \left(1,2\right)\right\}$ then R is ______relation

a)

reflexive

b)

symmetric

c)

Transitive

d)

none of these

27.

In the poset $\left(P\left(S\right),\ \subseteq\right)$ the greatest element is

a)

S

b)

P(s)

c)

$\phi$

d)

not exist

28.

$\sim p\wedge q$ is logically equivalent to

a)

$p\Longrightarrow q$

b)

$q\Longrightarrow p$

c)

$\sim\left(p\Longrightarrow q\right)$

d)

$\sim\left(q\Longrightarrow p\right)$

29.

If $p\Longrightarrow\left(\sim p\vee q\right)$ is false, the truth values of p and q are respectively

a)

F, T

b)

F, F

c)

T, T

d)

T, F

30.

Consider the subset $S=\left\{2,3,6\right\}$ of the poset $\left(\left\{1,2,3,4,5,6\right\},\ D\right).$ where $D$ denotes the divides relation . Then the upper bounds and lower bounds of S are respectively

a)

6 , 2

b)

6 , 1

c)

6 , 3

d)

6 and 1, 2

31.

The relation $R=\left\{\left(4,5\right),\left(1,4\right),\left(4,6\right),\left(7,6\right),\left(3,7\right)\right\}$ then $R^{-1}o\ R$ =

a)

$\left\{\left(1,1\right),\left(4,4\right),\ \left(7,4\right),\left(4,7\right),\left(7,7\right)\right\}$

b)

$\left\{\left(1,1\right),\left(4,4\right),\ \left(7,4\right),\left(4,7\right),\left(3,3\right)\right\}$

c)

$\left\{\left(1,5\right),\left(1,6\right),\left(3,6\right)\right\}$

d)

None of these

32.

For any finite two sets A and B, $A-\left(A\cap B\right)=$

a)

$A\cup B$

b)

$A\cap B$

c)

$\phi$

d)

$A-B$

33.

Consider a weighted

undirected graph with positive edge weights and let (u, v) be an edge in the

graph. It is known that the shortest path from source vertex s to u has

weight 53 and shortest path from s to v has weight 65. Which statement is

always true ?

a)

Weight (u, v) <= 12

b)

Weight (u, v) = 12

c)

Weight (u, v) >= 12

d)

Weight (u, v) > 12

34.

Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to

a)

3

b)

4

c)

5

d)

6

35.

Which of the

following statement is false ?

a)

G is connected and is circuitless.

b)

G is connected and has n edges

c)

G is minimally connected graph

d)

G is circuitless and has n-1 edges

36.

The number of circuits that can be created by adding an edge between any two vertices in a tree is ?

a)

Two

b)

Exactly one

c)

At least two

d)

None

37.

In a tree between every pair of vertices there is ?

a)

Exactly one path

b)

A self loop

c)

Two circuits

d)

n number of paths

38.

If for some positive integer k, degree of vertex d(v)=k for every vertex v of the graph G, then G is called...

a)

K graph

b)

K-regular graph

c)

Empty graph

d)

None

39.

If the origin and terminus of a walk are same, the walk is known as...

a)

Open

b)

Closed

c)

Path

d)

None

40.

Eccentricity of a vertex denoted by e(v) is defined by....

a)

max { d(u,v): u belongs to v, u does not equal to v : where d(u,v) is the distance between u&v}

b)

min { d(u,v): u belongs to v, u does not equal to v }

c)

Both

d)

None

41.

The complete graph K, has... different spanning trees.

a)

n^n-2

b)

n*n

c)

nⁿ

d)

n²

42.

A tour of G is a closed walk of graph G which includes every edge G at least once. A ..... tour of G is a tour which includes every edge of G exactly once .

a)

Hamiltonian

b)

Planar

c)

Isomorphic

d)

Euler

43.

Which of the following is not a type of graph?

a)

Euler

b)

Hamiltonian

c)

Path

d)

Tree

44.

A path in graph G,

which contains every vertex of G once and only once ?

a)

Euler path

b)

Hamiltonian path

c)

Euler cycle

d)

Hamiltonian cycle

45.

A tree having a main node, which has no predecessor is....

a)

Spanning tree

b)

Rooted tree

c)

Weighted tree

d)

None

46.

In a tree between every pair of vertices there is ___

a)

Exactly one path

b)

A self loop

c)

Two circuits

d)

n number of paths

47.

Which of the following is true?

a)

Prim’s algorithm can also be used for disconnected graphs

b)

Kruskal’s algorithm can also run on the disconnected graphs

c)

Prim’s algorithm is simpler than Kruskal’s algorithm

d)

In Kruskal’s sort edges are added to MST in decreasing order of their weights

48.

How many child nodes does each node of K-ary Tree contain?

a)

2

b)

3

c)

more than k

d)

at most k

49.

Which of the following is the name of the node having child nodes?

a)

Brother

b)

Sister

c)

Mother

d)

Parents

50.

What is the Height of the root node of K-ary tree?

a)

1

b)

2

c)

3

d)

0

51.

In full binary search tree every internal node has exactly two children. If there are 100 leaf nodes in the tree, how many internal nodes are there in the tree?

a)

25

b)

49

c)

99

d)

101

52.

Suppose a complete binary tree has height h>0. The minimum no of leaf nodes possible in term of h is___

a)

2^h -1

b)

2^{h -1} + 1

c)

2^{h -1}

d)

2^h +1

53.

In a full binary tree, every internal node has exactly two children. A full binary tree with 2n+1 nodes contains

a)

n leaf node

b)

n internal nodes

c)

n-1 leaf nodes

d)

n-1 internal nodes

54.

Let G be a complete undirected graph on 6 vertices. If vertices of G are labeled, then the number of distinct cycles of length 4 in G is equal to

a)

15

b)

30

c)

90

d)

360

55.

Which of the following statements is/are TRUE for undirected graphs?

P: Number of odd degree vertices is even.

Q: Sum of degrees of all vertices is even.

a)

P only

b)

Q only

c)

Both P and Q

d)

None

56.

What is the identity element In the group G = {2, 4, 6, 8) under multiplication modulo 10?

a)

5

b)

6

c)

9

d)

12

57.

Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?

a)

(Z, *) is a monoid

b)

(Z, *) is an abelian group

c)

(Z, *) is a group

d)

None of these

58.

The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is

a)

0

b)

1

c)

-1

d)

12

59.

Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then

a)

A is closed under * but < A, * > is not a semi group

b)

< A, * > is a semi group but not a monoid

c)

< A, * > is a monoid but not a group

d)

< A, * > is a group but not an abelian group

60.

If the binary operation * is defined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals

a)

(74,40)

b)

(32,40)

c)

(23,11)

d)

(7,11)

61.

A graph with n vertices will definitely have a parallel edge or self loop if the

a)

Greater than n-1

b)

less than n(n–1)

c)

greater than n(n–1)/2

d)

less than 1

62.

Which of the following is not a group under binary operation addition?

a)

N, the set of natural number

b)

Z, the set of integers

c)

Q, the set of rational

d)

R, the set of reals

PRE-GTU EXAM

Total questions: 62

Worksheet time: 3hrs 6mins

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