Free Printable DM MODEL EXAM 1

1.

Express the statement " Good food is not cheap"in symbolic form

a)

$\sim p\rightarrow q$

b)

p\rightarrow\sim q

c)

$\sim p\rightarrow\sim q$

d)

$p\rightarrow q$

2.

If the premises P,Q,R are inconsistent ,then

\sim R

is a conclusion from P and Q

a)

True

b)

False

3.

Let P(x) be the statement x< 2 give counter example to the statement

\forall xP\left(x\right)

where the set f all real number is the universe

a)

x=3

b)

x=4

c)

x=-3

d)

x=-4

4.

Give an indirect proof of the theorem if 3n+2 is odd, then n is

a)

Even

b)

Odd

c)

Nne of the above

5.

if\ \left(R\rightarrow S\right)\vee\sim\left(R\rightarrow S\right)\ is\

a)

Contradiction

b)

Tautology

c)

Contigency

d)

Nne of the above

6.

$\left(P\rightarrow Q\right)\wedge\sim\left(P\vee Q\right)\ is\$

a)

Tautology

b)

Contradiction

c)

Contigency

d)

None of the above

7.

How many bit string of length 10 either begin with three 0's or end with two 0's

a)

342

b)

352

c)

423

d)

243

8.

How many number not exceeding 100 are divisible by 4 or 6

a)

33

b)

32

c)

31

d)

30

9.

A coin is tossed 10 times where each toss comes up with a head od taill . how many possible outcomes contain at most 3 tails

a)

180

b)

167

c)

176

d)

186

10.

What is the number of permutation of the letter of the word PEPPER

a)

60

b)

59

c)

61

d)

58

11.

In an exam a minimum is to be secured in each of 8 subject for a pass , in how many ways can a student fail

a)

525

b)

255

c)

552

d)

155

12.

A number lock consist of three rings each marked with the 10 different digits 0,1,2,3,........9 find the number of unsuccessful to open the lock

a)

999

b)

989

c)

899

d)

998

13.

Find the number of edges and degree of each vertex in the complete graph k(5)

a)

(10,4)

b)

(4,10)

c)

(3,9)

d)

(9,3)

14.

Which is correct regular graph

a)

its vertices are of the same degree

b)

its vertices are of the equal degree

c)

its vertices are of the not equal degree

15.

Can a simple graph with 8 vertices have edges

a)

18

b)

28

c)

08

d)

38

16.

What is the maximum number of edge of a simple graph with 10 vertices

a)

44

b)

55

c)

54

d)

45

17.

The degree of each vertex of a graph G if it has a hamilton circuit atleast

a)

n/2

b)

n

c)

n(n-1)/2

d)

n(n-1)(n-2)/2

18.

How many non isomorphic connected simple graphs are there with 3 vertices

a)

3

b)

2

c)

1

d)

4

19.

In an abelian group G then $\left(a\cdot b\right)^2$

a)

$a^2\cdot b^2$

b)

$b^2\cdot a^2$

c)

$a^2$

d)

$b^2$

20.

G={1,1,i,-1}is a group under usual multiplication H={1,-1} is a subset of G

a)

H is subgroup

b)

H is normal subgroup

c)

All the above

21.

The following semi group which is not a group

a)

(2z, . )

b)

(z,.)

c)

(2z,+)

d)

(z,-)

22.

Any group of prime order is cyclic

a)

Yes

b)

No

23.

The inverse of an element in a group G is

a)

Unique

b)

equal

c)

same

d)

None of the above

24.

Semi group homomorphism preserves the property of

a)

Idempotency law

b)

Demorgan law

c)

Absorption law

d)

Identity law

25.

If a poset has a least element , then it is

a)

same

b)

unique

c)

equal

d)

All the above

26.

Is the lattice of divisors of 32 a boolean algebra

a)

yes

b)

no

27.

The boolean algebra (B,*,+,',0,1) given B=(0,1) then

a)

0'=1

b)

1'=0

c)

all the above

28.

In a boolean algebra B, then

a)

a(a+b)=a

b)

a+(a.b)=a

c)

a(a.b)=a

d)

a+(a+b)=a

29.

a lattice that is not distributive and not

a)

Modular

b)

chain

c)

cycle

d)

none of the above

30.

In the lattice has LUB AND GLB IS

a)

1,0

b)

0,1

c)

1,1

d)

0,0

31.

PDNF of $\sim P\vee Q$

a)

$\left(\sim P\wedge Q\right)\vee\left(\sim P\wedge\sim Q\right)\vee\left(P\wedge Q\right)$

b)

$\left(\sim P\vee Q\right)\wedge\left(\sim P\vee\sim Q\right)\wedge\left(P\vee Q\right)$

32.

Let p(x,,y) denote the statement x=y+3 ,what are the truth values of the proposition p(1,2)

a)

true

b)

false

33.

Symbolise the expression for any x and y , if x is taller than y, then y is not taller than x.

a)

$\forall x\forall y\left(T\left(x,y\right)\rightarrow T\left(y,x\right)\right)$

b)

$\exists x\exists y\left(T\left(x,y\right)\rightarrow T\left(y,x\right)\right)$

34.

The generating function for the sequence $1,a,a^2,a^3........$

a)

1/1-ax

b)

1/1-x

c)

a/1-x

d)

1/1-a

35.

Find the minimum number of students needed to make sure that 5 of them take the same engineering course ECE ,CSE ,EEE and MECH

a)

18

b)

17

c)

15

d)

16

36.

How many positive integers not exceeding 1000 are divisible by 7 or 11

a)

222

b)

110

c)

220

d)

111

37.

Does there exists a simple graph of oeder 4 and size 7

a)

simple graph

b)

digraph

c)

sub graph

d)

none of the above

38.

A regular graph G has 10 edges and degree of any vertex is 5 find the number of vertices

a)

5

b)

4

c)

3

d)

2

39.

Does there exist a simple graph with the degree sequence 3,3,3,3,2

a)

graph

b)

sub graph

c)

simple graph

d)

normal graph

40.

When is a graph (G ,*) called abelian

a)

a+b=b+a

b)

a.b=b.a

c)

a*b=b*a

d)

a-b=b-a

41.

The permutation $f=\left(\frac{1\ 2\ 3\ 4\ 5\ 6\ 7\ 8}{2\ 5\ 7\ 8\ 6\ 1\ 4\ 3}\right)$ is

a)

even

b)

odd

c)

neither odd nor even

42.

Any group of prime order is

a)

cyclic

b)

semi group

c)

normal group

d)

none of the above

43.

In a bolean algebra show that ab'+a'b=0 iff

a)

a=a

b)

a=b

c)

b=a

d)

b=b

44.

In a boolean algebra B , then ab'+bc'+ca'=

a)

a'b+b'c+c'a

b)

ab+bc+ca

c)

ab'+bc'+ca'

d)

b'c+c'b+a'c

45.

Every distributive lattice is

a)

modular

b)

cyclic

c)

Complete lattice

d)

none of the above

DM MODEL EXAM 1

Total questions: 45

Worksheet time: 3600secs

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