CBSE Class 11 Mathematics Sets Worksheet Set 02

1. Write the set represented by A = {x : x єR, x² = 9, 2x = 4}

2. Are the following pairs of sets equal? A = {1, 2} , B = { x : x is a solution of x² + 3x +2 = 0}

3. How many subsets are there in {- 1 , 0 , 1} . List all its subsets.

4. What does the following sets represent;

i) R – Q      ii) Z₀ – N , where Z₀ is set of all non zero integers.

5. Let A = {1, 2, 3, 4, 5, 6} and B = {3, 4, 5, 6, 7, 8} , find (A – B ) ᴜ (B – A )

6. If A = {1, 2 ,3} , B = {4, 5, 6} and C = {7, 8, 9}, verify that :A U (B ∩ C) = (A U B) ∩ {A U C}

7. Verify De Morgan’s laws :-

U = { 1,2,3,4,5,6,7,8,9,10 } , A = { 1,3,4,5,7,9,10,}, B = { 1,3,4,5,7,8,10 }

 If set A = {{1, 2, 3} , {1, 2} , {1, 2,4}, 3 }then in the questions 8 to 11, insert anyone of the relevant symbols in the provided blank:є, =, ≠, ⊂, ⊄, ∉

8.Φ _____ A

9. {{1, 2}, 1} _______ A

10. {1, 3,4} _______ A

11. {{1, 2, 3} , 3} __________ A

12. Draw a venn diagram to represent the given sets with elements and shade A – B – C in it.

U = { a , b , c , d , e , f , g , h , i , j , k }

A = { c , e , f , h , i , j }, B = { a ,b , d , f , i }, C = { a ,c , e , g , h , i }.

13. For any two sets A and B

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

ii) If n(A - B) = 20 + x, n(B – A) = 3x and n(A ∩ B) = x + 1, if n(A) = n(B) then find x and n(A ∩ B).

14. The number of students who takes both mathematics and chemistry is 30. This represents 10 % of the total students taking mathematics and 12% of the total students taking chemistry. How many students takes atleast one of these two subjects?

15. If X = {4ⁿ – 3n – 1 : n є N} and Y = {9(n – 1 ), n є N }, where N is the set of natural numbers, then show that X U Y = Y

16. 150 college freshmen were interviewed, 85 were registered for a Math class, 70 were registered for an English class, 50 were registered for both Math and English

a) How many signed up only for a Math Class?

b) How many signed up only for an English Class?

c) How many signed up for Math or English?

d) How many signed up neither for Math nor English?

17. 100 students were interviewed

28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects.
a) How many students took none of the three subjects?
b) How many students took PE but not BIO or ENG?
c) How many students took BIO and PE but not ENG?

18. A school has 63 students studying Physics, Chemistry and Biology. 33 study Physics, 25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology and Chemistry
while 8 study both Physics and Biology. Equal numbers study all three subjects as those who learn none of the three.

19. An insurance company is surveying travellers, to learn how much of their summer travel is taken with an airplane, a train or a car. The following data is known; make a complete Venn Diagram with all the data. The number of people who flew was 1307. The number of people who both flew and used a train was 602. The people who used all three were 398 in number. Those who flew but didn’t drive came to a total of 599. Those who drove but did not use a train were 1097. There were 610 people who used both trains and cars. The number of people who used either a car or a train or both was 2050. Lastly, 421 people used none of these. Find

i) how many people travelled by car but used neither a train nor an airplane?
ii) how many people were in the entire survey.

20. The following information was observed during a survey of 100 television viewers:- 18 watch programme P only,23 watch programme P but not Q, 8 watch programme P and R, 26 watch programme P, 48 watch programme R, 8 watch programme Q and R , 14 watch none of these programmes. Find the number of people who watch

a) exactly two programmes   b) Only one programme   c) only Q .

ANSWERS:

1. Φ  2. No  3. 8  4. Irrational numbers, Negative integers  5. {1, 2, 7, 8}  8. ⊂9. ⊄10. ∉11.⊂13. i) 52, ii) 11; 1214. 520. 18. 319. 787; 2866 20. a) 10 b) 73 c) 20

Please click on below link to download CBSE Class 11 Mathematics Sets Worksheet Set B