### CBSE 11 Mathematics

### Practice Paper 01 Set

**1. Which of the following are sets? Justify your answer**

**(a) The collection of all months of a year beginning with the letter A.**

**(b) The collection of best Indian cricketer.**

**(c) The collection of most difficult question in Math.**

**(d) The collection of prime numbers less than 50.**

**(e) The collection of all Indian women football player.**

**2. Write the following sets in roster form.**

**(a) A = {x: x is a natural number less than 9}**

**(b) B = {x: x is a two digit natural number such that the sum of its digit is 7}**

**(c) C = {x: x is a prime number which is a divisor of 24}**

**(d) D = Set of all letters in the word Mathematics**

**(e) P = Set of all letters in the word Theory**

**3. Write the following sets in the set-builder form.**

**(a) {2, 4, 8, 16, 32}**

**(b) {-1, 1, 3, 5, 7}**

**(c) {4, 8, 12, 16, 20}**

**(d) {2, 4, 8, 16, 32}**

**(e) {1, 7, 17, , 31, 49}**

**4. List all the elements of the following sets.**

**(a) A = {x: x is an integer, -1/4 < x < 9/4}**

**(b) B = {x: x is an odd natural number}**

**(c) C = {x: x is a vowel in English alphabet}**

**(d) D = {x: x is an odd number less than 20}**

**(e) E = {x: x is a letter in word "BEAUTIFUL"}**

**5. Which of the following are examples of the null set?**

**(a) Set of odd natural numbers divisible by 2.**

**(b) Set of even prime numbers.**

**(c) Set of prime number less than 2.**

**(d) {x: x is an integer, 7<x<6}**

**(e) Set of even number divisible by 3.**

**6. Which of the following sets are finite or infinite?**

**(a) The set of months of a year.**

**(b) {1, 2, 3 …}**

**(c) The set of lines which are parallel to the x-axis.**

**(d) The set of all prime numbers less than 100.**

**(e) The number of lines drawn from a point.**

**7. In the following, state whether A = B or not.**

**(a) A = {a, b, c, d}; B = {d, c, b, a}**

**(b) C = {4, 8, 12, 16}; D = {8, 4, 16, 18}**

**(c) S = {a, e, i, o, u}, T = {x: x is a vowel in English alphabet}**

**(d) A = {2, 4, 6, 8, 10}, B= {x: x is even numbers less than 100}**

**(e) A = {10, 20, 30, 40, 49}, C={x: x is a multiple of 5}**

**8.Write down all the subsets of the following sets:**

(a) {a}

(b) {a, b}

(c) {1, 2, 3}

(d) {}

(e) {0, 1,2,3,4}

9. Write the following as intervals:

(a) {x: x ? R, –4 < x = 6}

(b) {x: x ? R, –12 < x < –10

**9.**

**If A = {3, 5, 7, 9, 11}, B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17}; find**

**(a) A n B**

**(b) B n C**

**(c) A n C n D**

**(d) A n C**

**(e) B n D**

10. If A = {x: x is a natural number}, B ={x: x is an even natural number} C = {x: x is an odd natural number} and D = {x: x is a prime number}, find

(a) A n B

(b) A n C

(c) A n D

(d) B n C

(e) B n D

(f) C n D

11. Which of the following pairs of sets are disjoint?

(a) {1, 2, 3, 4} and {x: x is a natural number and 4 = x = 6}

(b) {a, e, i, o, u}and {c, d, e, f}

12. If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},

**C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find**

**(a) A – B**

**(b) A – C**

**(c) A – D**

**(d) (B - C)'**

**(e) (A U C)'**

**13. If R is the set of real numbers and Q is the set of rational numbers, then what is R – Q?**

**14. 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**

**(a) A’**

**(b) B’**

**(c) (A U C)’**

**(d) (B - C)'**

**(e) (A – B)'**

**14. If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:**

**(a) A = {a, b, c}**

**(b) B = {d, e, f, g}**

**15. Taking the set of natural numbers as the universal set, write down the complements of the following sets:**

**(a) {x: x is an even natural number}**

**(b) {x: x is an odd natural number}**

**(c) {x: x is a positive multiple of 3}**

**(d) {x: x is a prime number}**

**16. If U = {1, 2, 3, 4, 5,6,7,8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that**

**(a) (A U B)’ = A’∩B’**

**(b) (A n B)’ = A’ U B’**

**17. Draw an appropriate Venn diagram for each of the following:**

**(a) (A U B)’**

**(b) A’ n B’**

**(c) (A n B)’**

**(d) A’ U B’**

**18. Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60°, what is A’?**

**19.**

**If A and B are two sets such that n(A) = 23, n(B) = 52 and n(A∪B) = 70. Find n(A∩B).**

**20. In a group there are 650 people, 360 speaks Tamil and 420 can speak Hindi. How many people can speak both Tamil and Hindi?**

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