Maths Class XI Chapter 1 Sets Practice Paper 1 PDF

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32 PRACTICE PAPER 01 (2023-24) CHAPTER 01 SETS SUBJECT: MATHEMATICS MAX. MARKS : 40 CLASS : XI...

KENDRIYA VIDYALAYA GACHIBOWLI, GPRA CAMPUS, HYD–32 PRACTICE PAPER 01 (2023-24) CHAPTER 01 SETS SUBJECT: MATHEMATICS MAX. MARKS : 40 CLASS : XI DURATION : 1½ hrs General Instructions: (i). All questions are compulsory. (ii). This question paper contains 20 questions divided into five Sections A, B, C, D and E. (iii). Section A comprises of 10 MCQs of 1 mark each. Section B comprises of 4 questions of 2 marks each. Section C comprises of 3 questions of 3 marks each. Section D comprises of 1 question of 5 marks each and Section E comprises of 2 Case Study Based Questions of 4 marks each. (iv). There is no overall choice. (v). Use of Calculators is not permitted SECTION – A Questions 1 to 10 carry 1 mark each. 1. The number of subsets of a set containing n elements is (a) 2n (b) 2n – 1 (c) 2n – 1 (d) nn 2. Let A = {2, 5}, then subsets of set A are ϕ, {2}, {5}, {2, 5}, i.e. 4 subsets then the number of elements its power set contains are (a) 4 (b) 42 (c) 10 (d) 2 3. The set (A ∩ B′)′ ∪ (B ∩ C) is equal to (a) A′ ∪ B ∪ C (b) A′ ∪ B (c) A′ ∪ C′ (d) A′ ∩ B 4. Let S = set of all points inside the square, T = the set of points inside the triangle and C = the set of points inside the circle. If the triangle and circle intersect each other and are contained in a square. Then (a) S ∩ T ∩ C = ϕ (b) S ∪ T ∪ C = C (c) S ∪ T ∪ C = S (d) S ∪ T = S ∩ C 5. If set A: numbers multiple of 4 and set B: numbers multiple of 6, then set A ∩ B is (a) numbers multiple of 2 (b) numbers multiple of 4 (c) numbers multiple of 12 (d) numbers multiple of 24 6. For disjoint sets A and B, n(A) = 3, n(B) = 5, then n(A ∩ B) is (a) 0 (b) 3 (c) 5 (d) 8 7. Representation of set A = {x | x ∈ Z, x2 < 20} in the roster form is (a) {1, 2, 3,..., 20} (b) {1, 2, 3, 4} (c) {0, 1, 2, 3, 4} (d) {–4, –3, –2, –1, 0, 1, 2, 3, 4} 8. The set {– 1, 1} in the set builder form can be written as (a) {–1, 1} (b) {x ∈ W : x ≤ 1} (c) {x ∈ Z : x ≤ 1} (d) {x : x is a solution of x2 = 1} For Q9 and Q10, a statement of assertion (A) is followed by a statement of reason (R). Choose the correct answer out of the following choices. (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true but R is not the correct explanation of A. (c) A is true but R is false. (d) A is false but R is true. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 1 - 9. Assertion (A): The set A = {x : x is an even prime number greater than 2} is the empty set. Reason (R): The set B = {x : x2 = 4, x is odd} is not an empty set. 10. Assertion (A): If n(A) = 3, n(B ) = 6 and A  B, then the number of elements in A  B is 9. Reason (R): If A and B are disjoint, then n(A  B ) is n(A) + n(B ). SECTION – B Questions 11 to 14 carry 2 marks each. 11. A and B are two sets such that : n(A – B) = 14 + x, n(B – A) = 3x and n(A ∩ B) = x, draw a Venn diagram to illustrate information and if n(A) = n(B) then find the value of x. 12. Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m and n. 13. A and B are two sets such that n(A) = 3 and n(B) = 6. Find (i) minimum value of n(A ∪ B) (ii) maximum value of n(A ∪ B). 14. If U = {x : x ≤ 10, x ∈ N}, A = {x : x ∈ N, x is prime}, B = {x : x ∈ N, x is even}, write A ∩ B′ in roster form. SECTION – C Questions 15 to 17 carry 3 marks each. 15. In an examination, 80% students passed in Mathematics, 72% passed in Science and 13% failed in both the subjects, if 312 students passed in both the subjects. Find the total number of students who appeared in the examination. 16. Let A, B and C be three sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C. Show that B = C. 17. Let U ={1, 2, 3, 4, 5, 6, 8}, A = {2, 3, 4}, B = {3, 4, 5}. Show that (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′ SECTION – D Questions 18 carry 5 marks. 18. In a group of 50 students, the number of students studying French, English, Sanskrit were found to be as follows : French = 17, English = 13, Sanskrit = 15 French and English = 9, English and Sanskrit = 4 French and Sanskrit = 5, English, French and Sanskrit = 3. Find the number of students who study (i) French only (ii) English only (iii) Sanskrit only (iv) English and Sanskrit but not French (v) French and Sanskrit but not English SECTION – E (Case Study Based Questions) Questions 19 to 20 carry 4 marks each. 19. In a city of 56,000 people, following is the number of fans of players Rohit (R), Virat (V) and Dhoni (D): Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 2 -  Players Number of Fans Rohit 23,000 Virat 25,000 Dhoni 18,000 Rohit and Virat 12,000 Rohit and Dhoni 10,000 Virat and Dhoni 8,000 Rohit, Virat and Dhoni 3,000 Based on the above information, answer the following: (i) How many people are fans of at least 2 players? (ii) How many people are fans of exactly 1 player? (iii) How many people are fans of exactly 2 players? (iv) How many people follow R or V but not D? 20. In class XI of one International school in Hyderabad, there are 200 students out of which 80 have taken Mathematics, 120 have taken Economics and 90 have taken Physical Education. If 50 have taken Mathematics and Economics, 60 have taken Economics and Physical Education, 40 have taken Mathematics and Economics. If 20 students have taken all three subjects then on the basis of above information answer the following: (i) Find the number of students who have taken at least one of the subjects. (ii) Find the number of students who have taken at most one of the subjects. (iii) Find the number of students who has taken none of the subject. (iv) Find the number of students who have taken exactly one subject. Prepared by: M. S. KumarSwamy, TGT(Maths) Page - 3 -