Sets Problems with solutions for Class 11 Maths

Sets Problems with solutions for Class 11 Maths

Q1. Write the following sets in the roster form.

(i) A = {x : x is a positive integer less than 10 and 2x – 1 is an odd number}

Ans: {1,2,3,4,5,6,7,8,9}

(ii) C = {x : x2 + 7x – 8 = 0, x ∈ R}

Ans: C = {– 8, 1}

Q2. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5}.

Find A′, B′, A′ ∩ B′, A ∪ B and hence show that ( A ∪ B )′ = A′∩ B′.

Q3. Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {3, 5} and C = {1, 2, 4, 7}, find

(i) A′ ∪ (B ∩ C′)

(ii) (B – A) ∪ (A – C)

Q3. In a class of 60 students, 23 play Hockey,15 Play Basketball, and 20 play cricket. 7 play Hockey and Basketball, 5 play cricket and Basketball, 4 play Hockey and Cricket, and 15 students do not play any of these games. Then

A. 4 plays Hockey, Basketball and Cricket

B. 20 plays Hockey but not Cricket

C. 1 plays Hockey and Cricket but not Basketball

D. All of the above are correct

Ans: C)

CBSE All In One Mathematics Class 11 2022-23 Edition

5.0 out of 5 stars Very very nice superb quality book. Can be used for JEE Main. Giving 5 🌟 due to its content.

Q4. In a group of 50 students 15 are playing hockey, 17 are playing cricket, 13 are playing football, 5 are playing hockey and cricket both, 4 are playing football and hockey both 9 are playing cricket and football both, 3 are playing all sports.Find how many of them play at least one of three games.

Ans: 30

Q5. In a group of children 35 play football out of which 20 play football only, 22 play hockey; 25 play cricket out of which 11 play cricket only. Out of these 7 play cricket and football but not hockey, 3 play football and hockey but not cricket and 12 play football and cricket both. How many play all the three games?

Ans: 5

Q6. Out of 800 boys in a school, 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey 24 played all three games. Find the number of boys who did not play any games.

Ans: 160

Q7. Let U = {x : x ∈ N, x ≤ 9}; A = {x : x is an even number, 0 < x < 10}; B = {2, 3, 5, 7}. Write the set (A U B)’.

Ans: {1, 9}

Q8.  In a survey of 600 students in a school, 150 students were found to be drinking Tea and 225 drinking Coffee, 100 were drinking both Tea and Coffee. Find how many students were drinking neither Tea nor Coffee.

Ans: 325

Q9. Are set C = { x : x – 5 = 0} and E = {x : x is an integral positive root of the equation x2 – 2x – 15 = 0} equal?

Q10. If X and Y are two sets such that n(X)=19, n(Y)=37, n(X⋂Y)=12 find n(X⋃Y).

Q11. Write { x : –3 ≤ x <7} as interval.

Q12. Are sets A = {1,2,3,4}, B = { x : x ϵ N and 5 ≤ x ≤ 7} disjoint? Why?

Q13. If A={1,3,5}, how many elements are there in P(A)?

Q14. Write down the power set of A where A = {1, 2, 3}

Q15. Write the set B={3,9,27,81} in set-builder form.

Q16. Given L= {1,2, 3,4}, M= {3,4, 5, 6} and N= {1,3,5} Verify that L-(M⋃N) = (L-M)⋂(L-N)

Q17. Out of 100 students; 15 passed in English, 12 passed in Mathematics, 8 in Science,6 in English and Mathematics, 7 in Mathematics and Science; 4 in English and Science; 4 in all three. Find how many passed

(i) in English and Mathematics but not in Science

Ans: 2

(ii) in Mathematics and Science but not in English

Ans: 3

(iii) in Mathematics only

Ans: 3

(iv) in more than one subject only

Ans: 9

Q18. List all the element of the set A = { x : x is an integer x2 ≤ 4}

Ans. {-2, -1, 0, 1, 2}

Q19. Write the solution set of the equation x2+x-2=0 in roster form.

Ans: {1,-2}

Q20. Write the set {x:x is a positive integer and x2<40}

Ans: {1,2,3,4,5,6}

Q21. Write the set A={1,4,9….} in set builder form.

Q22. There are 200 individuals with a skin disorder, 120 had been exposed to the chemical c1, 50 to the chemical c2, and 30 to both the chemicals c1 and c2. Find the number of individuals exposed to:

a) chemical c1 but not chemical c2

Ans: 90

b) chemical c2 but not c1

Ans: 20

c) chemical c1 or chemical c2

Ans: 140

Q23. In a survey of 400 students in a school, 100 are listed as taking apple juice, 150 as taking orange juice, and 75 were listed as taking both apples as well as orange juice. Find how many students were taking “Neither apple nor orange juice”

Ans: 225

Q24. In a class of 35 students, 24 likes to play cricket and 16 like football also each student like to play at least one of two games. How many students like both cricket and football?

Ans: 5

Q25. In a class of 70, all like to play kabaddi and Kho-Kho. 45 like to play kabaddi and 52 Kho-Kho. How many students like to play kabaddi or Kho-Kho?

Ans: 27

Q26. In a school, there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and Mathematics. How many teach physics?

Ans: 12

Q27. A market research group conducted a survey of 1000 consumers and reported that 720 consumers like product A and 450 consumers like product B. What is the least number of consumers that must have liked both products?

Ans: 170

Q28. A college awarded 38 medals in football, 15 in basketball, and 20 in cricket. If these medals went to a total of 58 men and only three men got medals in all three sports. Then the number of students who received medals in exactly two of the three sports is

A. 18

B. 15

C. 9

D. 6

Ans: C

Q29. In a group of students, 100 students know Hindi,50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group?

Ans: 125

Q30. In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Ans: 11