Sets, relation and functions L1: 11th Elite -DPP

Q1. What is the set builder form of the set {1, 3, 7, 15, 31}?

A

B

D

C

A

B

D

C

D

Q2. Write the following set in the set-builder form: {1, 4, 9,........, 100}

Q3. Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

Q4. Let X = {x : x = n3 + 2n + 1, n ∈ N} and Y = {x : x = 3n2 + 7, n ∈ N} then

A

B

C

A

B

C

D None of these

Q5. Let A and B be two sets. The set A has 2016 more subsets than B. If A ∩ B has 3 members, then the number of members in A ∪ B is

A

B

C

A

B

C

10

12

11

D 13

Q6. Let A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}. Then A ⋂ B is given by

A

B

C

A

B

C

{3, 6, 9, …….}

{15, 30, 45,........}

{5, 10, 15, 20, ………}

D None of these

Q7. If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y).

Q8. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

Q9. In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea?

Q10. India today conducted a survey if people taking tea/coffee. Out of 9000 people, 5550 people take tea, 3600 people take coffee and 1500 people take both tea and coffee. How many people take neither tea nor coffee?

A

B

C

A

B

C

350

1120

700

D 1350

Q11. A, B, C are three sets such that n(A) = 25, n(B) = 20, n(c) = 27, n( A ∩ B) = 5, n(B ∩ C) = 7 and A ∩ C = ф then n(A ∪ B ∪ C) is equal to

A

B

C

A

B

C

60

67

65

D 72

Q12. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = (1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) B’ (ii) (A ∩ C)’

Q13. If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:

Q14. Consider the two sets:A = {m ∈ R : both the roots of x2 - (m + 1)x + m + 4 = 0 are real} and B = [-3, 5).Which of the following is not true?

A

B

C

A

B

C

A ∩ B = {-3}

A ∪ B = R

B - A = (-3, 5)

D A - B = (-∞, -3) ∪ (5, ∞)

JEE Main - 2020

Q15. If A and B be two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in A ∪ B? Find also, the maximum number of elements in A ∪ B.

Q16. If the difference between the number of subsets of the sets A and B is 120, then choose the incorrect option.

A

B

C

A

B

C

Maximum value of n(A ∩ B) = 3

Maximum value of n(A ∪ B) = 21

Minimum value of n(A ∩ B) = 0

D Minimum value of n(A ∪ B) = 7

Q17. A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, find the value of x.

Q18. In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?

Q19. In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is

A

B

C

A

B

C

10000

30000

20000

D 40000

Q20. If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics and Physics, 50 take Mathematics and Chemistry, 43 take Physics and Chemistry and 38 take Mathematics, Physics and Chemistry, then the number of students who have taken exactly one subject is

A

B

C

A

B

C

42

270

56

D 98

Q21. Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all?

Q22. In a survey of 700 students in a college, 180 were listed as drinking Limca, 275 as drinking Miranda and 95 were listed as both drinking Limca as well as Miranda. Find how many students were drinking neither Limca nor Miranda.

Q23. Each set X, contains 5 elements and each set Y, contains 2 elements and

If each element of S belongs to exactly 10 of the Xr’s and to

exactly 4 of Yr’s, then find the value of n.

Q24. Let where each Xi contains 10 elements and each Y

i

contains 5 elements. If each element of the set T is an element of exactly 20 of sets X

i’s and exactly 6 of sets Y

i’s, then n is equal to

A

B

C

A

B

C

50

30

15

D 45

JEE Main 2020

Q25. A survey of 500 viewers produced the following data. 285 watch football, 195 watch hockey, 115 watch cricket, 45 watch football and cricket, 70 watch football and hockey, 50 watch hockey and cricket and 50 do not watch any game. How many watch(a) all the 3 games?(b) exactly one of the 3 games?

Sets, Relations and Functions L1: 11th Elite -DPP Solutions

Q1. What is the set builder form of the set {1, 3, 7, 15, 31}?

A

B

D

C

A

B

D

C

D

Solution:

Q2. Write the following set in the set-builder form: {1, 4, 9,........, 100}

Solution:

Q3. Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

Solution:

Q4. Let X = {x : x = n3 + 2n + 1, n ∈ N} and Y = {x : x = 3n2 + 7, n ∈ N} then

A

B

C

A

B

C

D None of these

Solution:

Q5. Let A and B be two sets. The set A has 2016 more subsets than B. If A ∩ B has 3 members, then the number of members in A ∪ B is

A

B

C

A

B

C

10

12

11

D 13

Solution:

Q6. Let A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}. Then A ⋂ B is given by

A

B

C

A

B

C

{3, 6, 9, …….}

{15, 30, 45,........}

{5, 10, 15, 20, ………}

D None of these

Solution:

Q7. If X and Y are two sets such that n(X) = 17, n(Y) = 23 and n(X ∪ Y) = 38, find n(X ∩ Y).

Solution:

Q8. If S and T are two sets such that S has 21 elements, T has 32 elements, and S ∩ T has 11 elements, how many elements does S ∪ T have?

Solution:

Q9. In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea?

Solution:

Q10. India today conducted a survey if people taking tea/coffee. Out of 9000 people, 5550 people take tea, 3600 people take coffee and 1500 people take both tea and coffee. How many people take neither tea nor coffee?

A

B

C

A

B

C

350

1120

700

D 1350

Solution: People taking neither tea nor coffee = 1350.

Hence (D) is the correct answer.

1350Coffee

2100Tea

4050

1500

Q11. A, B, C are three sets such that n(A) = 25, n(B) = 20, n(c) = 27, n( A ∩ B) = 5, n(B ∩ C) = 7 and A ∩ C = ф then n(A ∪ B ∪ C) is equal to

A

B

C

A

B

C

60

67

65

D 72

Solution:

Q12. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = (1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (i) B’ (ii) (A ∩ C)’

Solution:

Q13. If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:

Solution:

Solution:

Q14. Consider the two sets:A = {m ∈ R : both the roots of x2 - (m + 1)x + m + 4 = 0 are real} and B = [-3, 5).Which of the following is not true?

A

B

C

A

B

C

A ∩ B = {-3}

A ∪ B = R

B - A = (-3, 5)

D A - B = (-∞, -3) ∪ (5, ∞)

JEE Main - 2020

Solution:

Q15. If A and B be two sets containing 3 and 6 elements respectively, what can be the minimum number of elements in A ∪ B? Find also, the maximum number of elements in A ∪ B.

Solution:

Solution:

Q16. If the difference between the number of subsets of the sets A and B is 120, then choose the incorrect option.

A

B

C

A

B

C

Maximum value of n(A ∩ B) = 3

Maximum value of n(A ∪ B) = 21

Minimum value of n(A ∩ B) = 0

D Minimum value of n(A ∪ B) = 7

Solution:

Q17. A survey shows that 63% of the Americans like cheese whereas 76% like apples. If x% of the Americans like both cheese and apples, find the value of x.

Solution:

Q18. In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali? How many can speak both Hindi and Bengali?

Solution:

A

B

C

A

B

C

10000

30000

20000

D 40000

Q19. In a certain town 25% families own a cell phone, 15% families own a scooter and 65% families own neither a cell phone nor a scooter. If 1500 families own both a cell phone and a scooter, then the total number of families in the town is

Solution:

20% 5% 10%

Phone Scooter 65%

Let the total population of town be x.

Q20. If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics and Physics, 50 take Mathematics and Chemistry, 43 take Physics and Chemistry and 38 take Mathematics, Physics and Chemistry, then the number of students who have taken exactly one subject is

A

B

C

A

B

C

42

270

56

D 98

Solution:

Alternate Solution

PC

Z Y

1238

X M12

5

n(M) =120X + 12 + 12 + 38 = 120X = 58

n(P) =90Y + 12 + 5 + 38 = 90Y = 35

n(C) =60Z + 12 + 5 + 38 = 60Y = 5

Required No. of students taking exactly one subject is X + Y + Z = 98

Q21. Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football and basketball and 8 play all the three games. How many members are there in all?

Solution:

Q22. In a survey of 700 students in a college, 180 were listed as drinking Limca, 275 as drinking Miranda and 95 were listed as both drinking Limca as well as Miranda. Find how many students were drinking neither Limca nor Miranda.

Solution:

Solution:

Q23. Each set X, contains 5 elements and each set Y, contains 2 elements and

If each element of S belongs to exactly 10 of the Xr’s and to

exactly 4 of Yr’s, then find the value of n.

Solution:

A

B

C

A

B

C

50

30

15

D 45

JEE Main 2020

Q24. Let where each Xi contains 10 elements and each Y

i

contains 5 elements. If each element of the set T is an element of exactly 20 of sets X

i’s and exactly 6 of sets Y

i’s, then n is equal to

Solution:

Q25. A survey of 500 viewers produced the following data. 285 watch football, 195 watch hockey, 115 watch cricket, 45 watch football and cricket, 70 watch football and hockey, 50 watch hockey and cricket and 50 do not watch any game. How many watch(a) all the 3 games?(b) exactly one of the 3 games?

(a) Let viewers who watch all the three games be x.

Viewers watch all three games = 500-50 = 450

Then, according to venn diagram

450 = 285 + 195 + 112 - 70 - 50 - 45 + x

450 - 430 = x

x = 20

20 + x

FC

H

x

75 + x

50 -x

45 -x 170 + x

70 -x

50

Solution:

(b) Viewers watching exactly one of 3 games

= (75 + x) + (20 + x) + (170 + x)

= 265 + 3x

= 265 + 60

= 325

20 + x

FC

H

x

75 + x

50 -x

45 -x 170 + x

70 -x

50

Solution:

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