BCA Family An online BCA community

### Sets

In a class of 50 students 18 take music, 26 take art and 2 take both of art and music. How many students in this class are not enrolled in either music or art [2013]

6

8

10

12

In a certain zoo, there are 42 animals in one sector, 34 in the second sector and 20 in th third sector. Out of this, 24 graze in sector one and also in sector two. 10 graze in sector two and sector three, 12 graze in sector one and sector three. These figures also includes four animals grazing in all the three sectors are now transported to another zoo, find the total number of animal [2012]

38

56

54

None of these

In a legislative body of 200 people, the number of democrats is 50 less than 4 times the number of Republicans. If one fifth of the legislators are neither Republicans nor democrats, how many of the legislators are republicans? [2011]

71

50

42

150

If in a certain school 20 students are taking math and 10 are taking history and 7 are taking both. How many students are there? [2011]

30

23

37

27

If A ∪ B = B ∪ A, the set operation law is known as [2009]

Commutative

Distributive

Associative

De-Morgan's

The set with three element has a number of subsets equal to [2009]

21

22

23

24

In a certain school 20 Students are taking Math and 10 are taking history and 7 are taking both, how many students are taking math only [2009]

20

14

13

7

If A = {1,2,3,4,....,15}, B = {2,4,6,8,10,..., 22} and C = {1,3,5,7,...25} what is A ∩ B ∩ C? [2008]

{2,4,6,8,10,12,14}

{1,3,5,7,9}

{6,8,10,12}

{}

If in a certain school 20 students are taking Math and 10 are taking History and 7 are taking both, How many students are there? [2008]

17

27

23

37

If A = {1,3,5,7,....,21}, B = {1,2,3,4,...20} and C = {2,4,6,8,...20} what is A ∩ B ∩ C? [2007]

{20,30}

{30}

{40}

If A = {1,2,3,...9} and B = {2,4,6,7,8} and C = {3,4,5,8,9,10...20}. What is A ∪ B ∪ C = ? [2006]

{1,2,3,.....10}

{1,3,5,7,9}

{2,4,6,8,10}

{1,3,5,8,9,10}

A math class had 27 students in it.out of those students 14 are also enrolled in History and 17 are enrolled in English, What is the minimum percentage of the students in math class who are enrolled in History and English ?

15%

22%

49%

63%

If A = {a,b,c,d,e,f,g,h,i} and B = {b,d,f,g,h} and C = {c,d,e,h,i,j} then (A - B) ∪ C is [2004]

{a,c,d,e,h,i,j}

{a,c,d,e,f,g}

{c,d,e,f,g,h,i}

{e,f,g,h,i,j}

In a locality with 70 households it has been observed that 37 subscribe Gorkhapatra, 52 subscribe Kantipur and each household subscribe at least one of the two papers, how many of the households in the locality subscribe both Gorkhapatra and Kantipur? [2003]

15

19

21

23

In a group of 70 people, 37 like coffee, 52 like tea and each person like at least one of the two drinks. How many people like both tea and coffee?[2002]

15

19

21

23

##### Other Questions

If A = {a,b,c,d} then n(A) is

4

5

6

3

If A and B are two sets, then (A-B)⋃B is _____

A

B

A ⋃ B

A ⋂ B

If A and B are two sets, then (A-B) ∩ B is _______

A

B

A ⋃ B

{}

What is the cardinality of the set of odd positive integers less than 10?

10

5

3

20

Solutions

The odd of positive less then 10 is {1,3,5,7,9} there for cardinality of set of odd numbers are 5

The set of positive integers is ____

Infinite

Finite

Subset

Empty

If U = {1,2,3,4,5} and A = {2,4} then A' should be

{2,4,5}

{2,4}

{1,2,3,4,5}

{1,3,5}

If X = {1, 2, 3, 4, 5} and Y = {2, 4, 5, 6, 8} then Y - X equals to

{4, 5}

{1, 6}

{6, 8}

{1, 3}

If A = {1, 2, 3, 4} and B = {4, 5, 6, 7} then A∪B should be

{2, 3, 4, 5, 6, 7}

{1, 2, 3, 4, 5, 6, 7}

{4}

{1, 2, 3, 5, 6, 7}

Set N = {1, 2, 3, 4, 5.....} is known as

set of odd numbers

set of whole numbers

set of natural numbers

set of even numbers

Set N = {2, 3, 5, 7, 11, 13, 17.....} is known as

set of prime numbers

set of natural numbers

set of whole numbers

set of odd numbers

(A ∪ B) ∪ C =

A ∩ (B ∪ C)

A ∪ (B ∩ C)

A ∩ ( B ∩ C)

A ∪ ( B ∪ C)

If P = {a,b,c,d,e}, Q = {a,c,e,d,t} and R = { t,d,c,b,e}, then the intersection of P, Q and R is

{a,c}

{a,c,e}

{c,d}

{c,d,e}

The union of the sets {1, 2, 5} and {1, 2, 6} is the set _____

{1, 2, 6, 1}

{1, 2, 5, 6}

{1, 2, 1, 2}

{1, 5, 6, 3}

The intersection of the sets {1, 2, 5} and {1, 2, 6} is the set _____

{1, 2}

{5, 6}

{2, 5}

{1, 6}

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

Union

Difference

Intersection

Complement

Which of the following two sets are disjoint?

{1, 3, 5} and {1, 3, 6}

{1, 2, 3} and {1, 2, 3}

{1, 3, 5} and {2, 3, 4}

{1, 3, 5} and {2, 4, 6}

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

{1}

{5}

{3}

{2}

The complement of the set A is _______

A – B

U – A

A – U

B – A

Which sets are not empty?

{x: x is a even prime greater than 3}

{x : x is a multiple of 2 and is odd}

{x: x is an even number and x+3 is even}

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

Subset of the set A= { } is:

A

{}

All of the mentioned

If set A = { 2,9,5,2}, then the number of subsets which can be formed from A is

If set A = { 2,9,5,2}, then the number of subsets which can be formed from A is

3

4

8

16

The cardinality of A = { 5,6,3,2,3, 2} is

6

5

4

3

If the universal set U = {2, 4, 6, 8, 10} and F = { 4,10}, t hen F ' is

{1,3,5,7,9}

{2,6,8}

{4,6,8,10}

{5,7,9}

If P = {p: p is a prime numbers less than 10}, then P is

{2,3,5,7}

{ 1,2,3,5,7}

{2,3,5,7,9}

{1,2,3,5,7,9}

In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, those whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?

19

41

21

57

Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B).

10

12

16

8

If n(A - B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B).

52

46

53

50

In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea?

8

6

9

12

In a group of 90 students 65 students like tea and 35 students like coffee then how many students like both tea and coffee.

40

20

30

10

In a group of 1500 people 800 people talk in Nepali and 900 people talk in English then how many people speak both Nepali and English.

200

400

300

600

How many members are present in any power set?

0

1

2

How many subset of an empty set?

0

1

2

None of these

In a group of 60 students. 45 students speak Nepali and 25 students can speak English and Nepali both then how many students can speak only English.

25

35

45

15

In a group of 50 people 35 people eat mango and 5 people eat mango and banana both then how many people eat only banana?

35

40

20

25

In a school 400 students speak Nepali 200 can speak English 200 can speak both Nepali and English then find the total number of students in That school.

500

200

400

700

I there is