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Worksheets

51-100

Total questions: 50

Worksheet time: 25mins

Name
Class
Date
1.

Find correct disjunctive normal form of (p v q) ^ (¬p v r)

a)

b)

c)

None of mentioned

d)

2.

The conjunction p ⋀ r is true if and only if

a)

only one of them is true.

b)

p and q have the same truth values.

c)

either p or q is true.

d)

none of the mentioned

e)

both p and q are true.

3.

Find the equivalence

a)

{... — 34, -17, 0, 17, 34...}

b)

all positive numbers

c)

all negative numbers

d)

{-17,17}

e)

None of mentioned.

4.

Solve the system of congruences.

a)

None of the mentioned.

b)

47+24k

c)

58 + 462k

d)

87+462k

e)

80 + 462k

5.

Find the GCD of 612 and 912.

a)

12

b)

18

c)

6

d)

None of the mentioned.

6.

Find the prime decomposition of 1001.

a)

7 • 113 • 13

b)

None of the mentioned.

c)

7 • 11 • 13

d)

73 • 11 • 13

e)

72 • 11 • 13

7.

In the given sequence 5, 8, 11, 14, 17, 20, ..., 50 find the number of terms

a)

11

b)

15

c)

14

d)

None of the mentioned.

e)

13

8.

Find the GCD of 666 and -846.

a)

12

b)

None of the mentioned.

c)

-18

d)

36

e)

9

9.

The quotient and remainder when -983 is divided by -23 are

a)

q = 42; r = 17

b)

None of the mentioned.

c)

q = -43: r = 6

d)

q = -42;r = 17

e)

q = 43 ;r = 6

10.

Find all solutions in integers of 11x + 23y = 6.

a)

x= 6-11k; y=-12+23k

b)

x＝-12-11k; y=6+23k

c)

x = -12 + 23k; y = 6 - 11k;

d)

None of the mentioned.

e)

x = 12 + 23k; y = 6 - 11k

11.

For the given arithmetic progression find the position of first negative term?

50, 47,44,41,...

a)

20

b)

18

c)

17

d)

19

e)

None of mentioned.

12.

In which case can mathematical induction method be used in its proof?

a)

(0, 1) is uncountable

b)

c)

n2 + n + 41 is not always prime for any positive integer n.

d)

The number of choosing 2 balls from 5 different balls is 10.

13.

Find the remainder when

a)

17

b)

15

c)

None of the mentioned.

d)

13

e)

18

14.

The quotient and remainder when -818 is divided by -31 are

a)

q = 26; r = 12

b)

q = -27:r = 19

c)

None of the mentioned.

d)

q = -26; r = 12

e)

q = 27;r = 19

15.

Solve the system of congruences

a)

13 + 30k

b)

17 + 30k

c)

11 + 30k

d)

None of the mentioned.

e)

19 + 30k

16.

There are five apples of different sizes, three oranges of different sizes and four bananas of different sizes in a box. How many ways are there to choose two fruits?

a)

60

b)

66

c)

132

d)

12

e)

None of mentioned

17.

Evaluate P(8, 4).

a)

70

b)

None of mentioned.

c)

40320

d)

1680

e)

840

18.

A bag contains 20 balls such as 9 balls are red, 7 are white and 4 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one

ball of each colour?

a)

17

b)

12

c)

20

d)

14

e)

4

19.

Select one

a)

not reflexive, symmetric, not transitive, antisymmetric

b)

not reflexive, not symmetric, not transitive, not antisymmetric

c)

not reflexive, symmetric, transitive, not antisymmetric

d)

reflexive, symmetric, not transitive, not antisymmetric

e)

not reflexive, symmetric, not transitive, not antisymmetric

20.

Which of these options is incorrect for sets A and B?

a)

b)

c)

d)

None of mentioned

21.

is logically equavalent to

a)

b)

c)

None of mentioned

d)

e)

22.

The implication p → q is false if and only if

a)

both p and q are false.

b)

None of the mentioned.

c)

p and q have the same truth values.

d)

either p or q is false.

e)

only one of them is false.

23.

If a, b, c, d are distinct prime numbers with a as the smallest prime then a • b • c • d is:

a)

Odd number.

b)

Square number.

c)

Even number.

d)

None of the mentioned.

e)

Prime number

24.

Solve the system of congruences.

a)

None of the mentioned.

b)

17 + 188k

c)

58 + 462k

d)

97 + 198k

e)

215 + 24k

25.

Select one

a)

b)

c)

None of mentioned

d)

e)

26.

How many arrangements are there of all letters in DALBASA?

a)

1680

b)

5040

c)

2520

d)

None of mentioned

e)

840

27.

Evaluate

a)

210

b)

151200

c)

3628800

d)

None of mentioned.

e)

5040

28.

In how many ways can 10 identical pens distributed among five children?

a)

1001

b)

30240

c)

None of mentioned.

d)

2002

e)

252

29.

A drawer contains 12 red and 12 blue socks, all unmatched. A person takes socks out at random in the dark. How many socks must he take out to be sure that he has at least two blue socks?

a)

13

b)

12

c)

14

d)

3

e)

24

30.

For integers a and b define an equivalence relation a ~ b if and only if 3a + 4b is divisible by 7. What is the equivalence class of 2 with respect to this relation?

a)

{... - 9, -2, 5, 12, 19,..}

b)

all numbers which are divisible by 14

c)

{.. - 12, - 5,2,9, 16,...}

d)

None of mentioned

e)

all numbers which are divisible by 7

31.

In how many ways can we place four numbered balls into nine numbered boxes if boxes may contain more than one ball?

a)

6561

b)

151210

c)

126

d)

None of mentioned.

e)

3024

32.

In how many ways can we place four numbered balls into eleven numbered boxes so that each box contains at most one ball?

a)

330

b)

364

c)

1663200

d)

None of mentioned.

e)

7920

33.

Which of the following graphs is Hamiltonian?

a)

K 6,5

b)

K 5,5

c)

K 2,3

d)

K 4,5

e)

K 4,3

34.

Define a function from N to N by f(x) = x + 3. Determine whether f is 1 - 1 and whether f is onto.

a)

1-1 and onto

b)

not 1-1 and not onto

c)

1-1 and not onto

d)

not 1-1 and onto

e)

Impossible to determine

35.

Select one

a)

None of mentioned

b)

1, 1, 1, 1, 1

c)

4,3,3,3,3

d)

5, 1, 1, 1, 1

e)

4, 4, 3, 3, 3, 3

36.

Select one

a)

reflexive, not symmetric, transitive, not antisymmetric

b)

not reflexive, not symmetric, not transitive, not antisymmetric

c)

reflexive, not symmetric, not transitive, not antisymmetric

d)

reflexive, symmetric, not transitive, not antisymmetric

e)

reflexive, not symmetric, not transitive, antisymmetric

37.

Select one

a)

p-True, q-True

b)

None of the mentioned.

c)

p-False, q-True

d)

p-False, q-False

e)

 p-True, q-False

38.

Select one

a)

None of mentioned

b)

c)

d)

e)

39.

Determine the number of positive integers n where 1 ≤ n ≤ 400 and n is relatively prime to 100.

a)

4

b)

160

c)

183

d)

217

e)

None of mentioned.

40.

Which of the following sequences can be the degree sequence of a pseudograph?

a)

3,3,3,2,2

b)

3,3,3,3,1

c)

3,3,3,3

d)

3,3,3,3,3

e)

3,2,2,2,2

41.

What do you have to assume in mathematical induction?

a)

The case n = 1 is true.

b)

None of the mentioned.

c)

The case n = 0 is true.

d)

The case n = k is true.

e)

The case n = k + 1 is true.

42.

The disjunction p∨q is false if and only if

a)

both p and q are false.

b)

p and q have the same truth values.

c)

only one of them is false.

d)

either p or q is false.

e)

none of the mentioned.

43.

The quotient and remainder when 983 is divided by -23 are

a)

q= -43; r=6

b)

q=42; r=17

c)

q = -42; r= 17

d)

q=43; r=6

e)

None of the mentioned.

44.

A bag contains 25 balls such as 10 balls are red, 7 are white and 8 are blue. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

a)

4

b)

25

c)

19

d)

18

e)

3

45.

What is the largest number of edges that a graph with 20 vertices can have?

a)

361

b)

400

c)

380

d)

200

e)

190

46.

Which of the following graphs is Hamiltonian?

a)

K 8,9

b)

K 7,2

c)

K 6,5

d)

a connected graph with the degree sequence 3, 2, 2, 2, 2, 2, 2, 1

e)

a connected graph with the degree sequence 2, 2, 2, 2, 2, 2, 2, 2

47.

Which of these functions defines one-to-one correspondence from (-3, 4) to (0, 1)?

a)

2+3

b)

None of the mentioned

c)

-x + 1

d)

x + 3/7

e)

x + 4

48.

Which of these sets is uncountable?

a)

Z × Z

b)

N× N

c)

N

d)

2Z

e)

(2,5)

49.

Let V = {1, 2, 3, 4}. How many graphs are there with vertex set V?

a)

64

b)

32

c)

None of mentioned

d)

60

e)

4

50.

Select one

a)

b)

None of mentioned

c)

d)

e)

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