Sets Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. Let A and B be two sets then  is equal to
(a) A '
(b) A
(c) B '
(d) None of these
2. Let A = {(n, 2n) : n  N} and B = {(2n, 3n) : n  N}. What is A n B
equal to ?
(a) {(n, 6n) : n  N}
(b) {(2n, 6n) : n  N}
(c) {(n, 3n) : n  N}
(d)
3. If aN = {ax : x ? N} and bN n cN = dN, where b, c ? N are relatively
prime, then
(a) d = bc
(b) c = bd
Page 2


PART-I (Single Correct MCQs)
1. Let A and B be two sets then  is equal to
(a) A '
(b) A
(c) B '
(d) None of these
2. Let A = {(n, 2n) : n  N} and B = {(2n, 3n) : n  N}. What is A n B
equal to ?
(a) {(n, 6n) : n  N}
(b) {(2n, 6n) : n  N}
(c) {(n, 3n) : n  N}
(d)
3. If aN = {ax : x ? N} and bN n cN = dN, where b, c ? N are relatively
prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None of these
4. In a class of 55 students, the number of students studying different
subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in
Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in
Physics and Chemistry and 4 in all the three subjects. The number of
students who have taken exactly one subject is
(a) 6
(b) 9
(c) 7
(d) All of these
5. A set A has 3 elements and another set B has 6 elements. Then
(a) 3 = n (A ? B) = 6
(b) 3 = n (A ? B) = 9
(c) 6 = n (A ? B) = 9
(d) 0 = n (A ? B) = 9
6. At a certain conference of 100 people, there are 29 Indian women and
23 Indian men. Of these Indian people 4 are doctors and 24 are either
men or doctors. There are no foreign doctors. How many foreigners and
women doctors are attending the conference?
(a) 48, 1
(b) 34, 3
(c) 46, 4
(d) 42, 2
7. Let X and  Y be two  non-empty sets such that
X n A = Y n A = f and X ? A = Y ? A for some non-empty set A.
Then
(a) X is a proper subset of Y
Page 3


PART-I (Single Correct MCQs)
1. Let A and B be two sets then  is equal to
(a) A '
(b) A
(c) B '
(d) None of these
2. Let A = {(n, 2n) : n  N} and B = {(2n, 3n) : n  N}. What is A n B
equal to ?
(a) {(n, 6n) : n  N}
(b) {(2n, 6n) : n  N}
(c) {(n, 3n) : n  N}
(d)
3. If aN = {ax : x ? N} and bN n cN = dN, where b, c ? N are relatively
prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None of these
4. In a class of 55 students, the number of students studying different
subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in
Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in
Physics and Chemistry and 4 in all the three subjects. The number of
students who have taken exactly one subject is
(a) 6
(b) 9
(c) 7
(d) All of these
5. A set A has 3 elements and another set B has 6 elements. Then
(a) 3 = n (A ? B) = 6
(b) 3 = n (A ? B) = 9
(c) 6 = n (A ? B) = 9
(d) 0 = n (A ? B) = 9
6. At a certain conference of 100 people, there are 29 Indian women and
23 Indian men. Of these Indian people 4 are doctors and 24 are either
men or doctors. There are no foreign doctors. How many foreigners and
women doctors are attending the conference?
(a) 48, 1
(b) 34, 3
(c) 46, 4
(d) 42, 2
7. Let X and  Y be two  non-empty sets such that
X n A = Y n A = f and X ? A = Y ? A for some non-empty set A.
Then
(a) X is a proper subset of Y
(b) Y is a proper subset of X
(c) X = Y
(d) X and Y are disjoint sets
8. Let A and B are two sets in a universal set U. Then which of these is/are
correct ?
(a) A – B = A’ – B’
(b) A – (A – B) = A n B
(c) A – B = A’ n B’
(d) A ? B = (A – B) ? (B–A) ? (A n B)
9. In a town of 10,000 families, it was found that 40% families buy
newspaper A, 20% families buy newspaper B and 10% families buy
newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy
A and C. If 2% families buy all the newspapers, then
(a) 3,300 families buy A only
(b) 1,400 families buy B only.
(c) 4000 families buy none of A, B and C
(d) All are correct
10. Let n (U) = 700, n (A) = 200, n (B) = 300, n (A n B) = 100, then n (A’
n B’) is equal to
(a) 400
(b) 600
(c) 300
(d) None of these
11. Each student in a class of 40, studies at least one of the subjects
English, Mathematics and Economics. 16 study English, 22 Economics
and 26 Mathematics, 5 study English and Economics, 14 Mathematics
and Economics and 2 study all the three subjects. The number of
students who study English and Mathematics but not Economics is
(a) 7
(b) 5
Page 4


PART-I (Single Correct MCQs)
1. Let A and B be two sets then  is equal to
(a) A '
(b) A
(c) B '
(d) None of these
2. Let A = {(n, 2n) : n  N} and B = {(2n, 3n) : n  N}. What is A n B
equal to ?
(a) {(n, 6n) : n  N}
(b) {(2n, 6n) : n  N}
(c) {(n, 3n) : n  N}
(d)
3. If aN = {ax : x ? N} and bN n cN = dN, where b, c ? N are relatively
prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None of these
4. In a class of 55 students, the number of students studying different
subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in
Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in
Physics and Chemistry and 4 in all the three subjects. The number of
students who have taken exactly one subject is
(a) 6
(b) 9
(c) 7
(d) All of these
5. A set A has 3 elements and another set B has 6 elements. Then
(a) 3 = n (A ? B) = 6
(b) 3 = n (A ? B) = 9
(c) 6 = n (A ? B) = 9
(d) 0 = n (A ? B) = 9
6. At a certain conference of 100 people, there are 29 Indian women and
23 Indian men. Of these Indian people 4 are doctors and 24 are either
men or doctors. There are no foreign doctors. How many foreigners and
women doctors are attending the conference?
(a) 48, 1
(b) 34, 3
(c) 46, 4
(d) 42, 2
7. Let X and  Y be two  non-empty sets such that
X n A = Y n A = f and X ? A = Y ? A for some non-empty set A.
Then
(a) X is a proper subset of Y
(b) Y is a proper subset of X
(c) X = Y
(d) X and Y are disjoint sets
8. Let A and B are two sets in a universal set U. Then which of these is/are
correct ?
(a) A – B = A’ – B’
(b) A – (A – B) = A n B
(c) A – B = A’ n B’
(d) A ? B = (A – B) ? (B–A) ? (A n B)
9. In a town of 10,000 families, it was found that 40% families buy
newspaper A, 20% families buy newspaper B and 10% families buy
newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy
A and C. If 2% families buy all the newspapers, then
(a) 3,300 families buy A only
(b) 1,400 families buy B only.
(c) 4000 families buy none of A, B and C
(d) All are correct
10. Let n (U) = 700, n (A) = 200, n (B) = 300, n (A n B) = 100, then n (A’
n B’) is equal to
(a) 400
(b) 600
(c) 300
(d) None of these
11. Each student in a class of 40, studies at least one of the subjects
English, Mathematics and Economics. 16 study English, 22 Economics
and 26 Mathematics, 5 study English and Economics, 14 Mathematics
and Economics and 2 study all the three subjects. The number of
students who study English and Mathematics but not Economics is
(a) 7
(b) 5
(c) 10
(d) 4
12. In a class of 80 students numbered a to 80, all odd numbered students
opt of Cricket, students whose numbers are divisible by 5 opt for
Football and those whose numbers are divisible by 7 opt for Hockey.
The number of students who do not opt any of the three games, is
(a) 13
(b) 24
(c) 28
(d) 52
13. In a class of 60 students, 23 play Hockey 15 Play Basket-ball and 20
play cricket. 7 play Hockey and Basket-ball, 5 play cricket and Basket-
ball, 4 play Hockey and Cricket and 15 students do not play any of
these games. Then
(a) 4 play Hockey, Basket-ball and Cricket
(b) 20 play Hockey but not Cricket
(c) 1 plays Hockey and Cricket but not Basket-ball
(d) All above are correct
14. The set (A \ B) ? (B \ A) is equal to
(a)
(b)
(c)
(d)
15. If A is the set of the divisors of the number 15, B is the set of prime
numbers smaller than 10 and C is the set of even numbers smaller than
9, then (A  C)  B is the set
(a) {1, 3, 5}
(b) {1, 2, 3}
(c) {2, 3, 5}
(d) {2, 5}
Page 5


PART-I (Single Correct MCQs)
1. Let A and B be two sets then  is equal to
(a) A '
(b) A
(c) B '
(d) None of these
2. Let A = {(n, 2n) : n  N} and B = {(2n, 3n) : n  N}. What is A n B
equal to ?
(a) {(n, 6n) : n  N}
(b) {(2n, 6n) : n  N}
(c) {(n, 3n) : n  N}
(d)
3. If aN = {ax : x ? N} and bN n cN = dN, where b, c ? N are relatively
prime, then
(a) d = bc
(b) c = bd
(c) b = cd
(d) None of these
4. In a class of 55 students, the number of students studying different
subjects are 23 in Mathematics, 24 in Physics, 19 in Chemistry, 12 in
Mathematics and Physics, 9 in Mathematics and Chemistry, 7 in
Physics and Chemistry and 4 in all the three subjects. The number of
students who have taken exactly one subject is
(a) 6
(b) 9
(c) 7
(d) All of these
5. A set A has 3 elements and another set B has 6 elements. Then
(a) 3 = n (A ? B) = 6
(b) 3 = n (A ? B) = 9
(c) 6 = n (A ? B) = 9
(d) 0 = n (A ? B) = 9
6. At a certain conference of 100 people, there are 29 Indian women and
23 Indian men. Of these Indian people 4 are doctors and 24 are either
men or doctors. There are no foreign doctors. How many foreigners and
women doctors are attending the conference?
(a) 48, 1
(b) 34, 3
(c) 46, 4
(d) 42, 2
7. Let X and  Y be two  non-empty sets such that
X n A = Y n A = f and X ? A = Y ? A for some non-empty set A.
Then
(a) X is a proper subset of Y
(b) Y is a proper subset of X
(c) X = Y
(d) X and Y are disjoint sets
8. Let A and B are two sets in a universal set U. Then which of these is/are
correct ?
(a) A – B = A’ – B’
(b) A – (A – B) = A n B
(c) A – B = A’ n B’
(d) A ? B = (A – B) ? (B–A) ? (A n B)
9. In a town of 10,000 families, it was found that 40% families buy
newspaper A, 20% families buy newspaper B and 10% families buy
newspaper C. 5% families buy A and B, 3% buy B and C and 4% buy
A and C. If 2% families buy all the newspapers, then
(a) 3,300 families buy A only
(b) 1,400 families buy B only.
(c) 4000 families buy none of A, B and C
(d) All are correct
10. Let n (U) = 700, n (A) = 200, n (B) = 300, n (A n B) = 100, then n (A’
n B’) is equal to
(a) 400
(b) 600
(c) 300
(d) None of these
11. Each student in a class of 40, studies at least one of the subjects
English, Mathematics and Economics. 16 study English, 22 Economics
and 26 Mathematics, 5 study English and Economics, 14 Mathematics
and Economics and 2 study all the three subjects. The number of
students who study English and Mathematics but not Economics is
(a) 7
(b) 5
(c) 10
(d) 4
12. In a class of 80 students numbered a to 80, all odd numbered students
opt of Cricket, students whose numbers are divisible by 5 opt for
Football and those whose numbers are divisible by 7 opt for Hockey.
The number of students who do not opt any of the three games, is
(a) 13
(b) 24
(c) 28
(d) 52
13. In a class of 60 students, 23 play Hockey 15 Play Basket-ball and 20
play cricket. 7 play Hockey and Basket-ball, 5 play cricket and Basket-
ball, 4 play Hockey and Cricket and 15 students do not play any of
these games. Then
(a) 4 play Hockey, Basket-ball and Cricket
(b) 20 play Hockey but not Cricket
(c) 1 plays Hockey and Cricket but not Basket-ball
(d) All above are correct
14. The set (A \ B) ? (B \ A) is equal to
(a)
(b)
(c)
(d)
15. If A is the set of the divisors of the number 15, B is the set of prime
numbers smaller than 10 and C is the set of even numbers smaller than
9, then (A  C)  B is the set
(a) {1, 3, 5}
(b) {1, 2, 3}
(c) {2, 3, 5}
(d) {2, 5}
16. Two finite sets have m and n elements. The number of subsets of the
first set is 112 more than that of the second set. The values of m and n
are, respectively,
(a) 4, 7
(b) 7, 4
(c) 4, 4
(d) 7, 7
17. The number of students who take both the subjects mathematics and
chemistry is 30. This represents 10% of the enrolment in mathematics
and 12% of the enrolment in chemistry.  How many students take at
least one of these two subjects?
(a) 520
(b) 490
(c) 560
(d) 480
18. If n(A) = 1000, n(B) = 500 and if n(A n B) = 1 and n(A ? B) = p, then
(a) 500 = p = 1000
(b) 1001 = p = 1498
(c) 1000 = p = 1498
(d) 1000 = p = 1499
19. Let A, B, C be finite sets. Suppose that n (A) = 10, n (B) = 15, n (C) = 20,
n (AnB) = 8 and  n (BnC) = 9. Then the possible value of n
(A ?B ?C) is
(a) 26
(b) 27
(c) 28
(d) Any of the three values 26, 27, 28 is possible
20. The value of (A ? B ? C) n (A n B
c
 n C
c
)
c
 n C
c
,
 
is
(a) B n C
c
(b) B
c
 n C
c