Title Chapter test-1 (Sets, Relations & Functions)(2).pdf ✅

1 Marking Scheme: (i) Each question is allotted 4 (four) marks for each correct response. (ii) 1⁄4 (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. –––––––––––––––––––––––––––––––––––––––––––––––– Q.1 If A = {5, 6, 7, 8}; B = {3, 9, 8, 10} and S = {1, 2, 3, 4....... 10} then, (A) (A ∪ B)′ = {1, 2, 3, 4} (B) (A ∩ B)′ = {8} (C) (A′ ∩ B)′ = (A ∩ B)′ (D) None of these is true Q.2 Find period of f (x) = – (A) 2π(B) π (C) 3π(D) 4π Q.3 Find the correct option among following. (A) {x : x2 = 3, x Q} is a pair set. (B) A = {x : x Z and x2 ≤ 3} and B = {x : x R and x2 – 3x + 2 = 0} are equal sets. (C){x : x is people of India speaking Hindi} is an infinite set (D) The set of prime numbers less than 99 is finite set. Q.4 Choose the correct options among the following for any sets A and B. (1) P(A) ∪ P(B) may be equal to P(A) (2) P(A) ∪ P(B) may be equal to P(A ∪ B) (3) P(A) ∪ P(B) must be a subset of P(A ∪ B) (4) P(A) ∪ P(B) must be equal to P(A ∪ B) (A) 1, 2 are true (B) 1, 2, 3 are true (C) 1, 3 are true (D) All are correct Q.5 Let A = {(x, y) : ax = ay; a > 0 and a ≠ 1; a, x, y R} B ={(x, y) : xy = 1; x, y Ro} Choose the correct statements amongst the following. (A) A ∩ B = B (B) A ∩ B = A (C) n (B) > n (A) (D) A and B are non-comparable Q.6 Find the domain and range of the function f (x) = 2 2 x x 1 x x 1 + + − + . (A) R, [1/3, 3] (B) R, [1/3, 2] (C) R, [1/3, 5] (D) R, [1/2, 3] Q.7 Choose the correct matching – Column (A) Column (B) (a) A = {x:x is prime, x∈ E } (i) Finite set but not void set (b) B = {(x, y} : y2 = 4x, (ii) Pair set x, y ∈ R} (c) C = {(x, y} : y2 = 4x, (iii) Singleton set x ∈ I, 0 < x < 5} (d) D = Set of all Muslim (iv) Void set Indian Prime Ministers (e) E = Set of all Positive (v) Infinite set integers less than 3 (A) (a)–(ii); (b)–(v); (c)–(iii); (d)–(iv); (e)–(i) (B) (a)–(iii); (b)–(v); (c)–(i); (d)–(iv); (e)–(ii) (C) (a)–(iii); (b)–(v); (c)–(i); (d)–(ii); (e)–(iv) (D) (a)–(ii); (b)–(v); (c)–(i); (d)–(iv); (e)–(iii) Q.8 Suppose A1,A2,...A30 are thirty sets each with five elements and B1, B2......Bn are n sets each with three elements such that 30 n A B i j i 1 j 1 S = = = = . If each element S belongs to exactly ten of the Bi’s and exactly nine of the Bj 's, then the value of n is (A) 15 (B) 135 (C) 45 (D) 90 Q.9 Choose the correct order of true (T) / false (F) for the following statements – (1) Every set has at least one proper subset. (2) If A is a finite, non-void set, having n proper subsets and m subsets then n – m N. (3) A = {φ, {φ}} then cardinal number of P(A) is 4. (4) a ⊆ {a,{b},{c}} (5) 'Set of all squares in a plane' is a subset of 'all rectangles in the same plane'. (A) TFFFF (B) FFTFT (C) FFFTT (D) TTTFT Q.10 Find the domain of the function f (x), if f (x) = 0.5 log x . (A) x ∈ (0, 2] (B) x ∈ (1, 1] (C) x ∈ (0, 1] (D) x ∈ (2, 1] Q.11 If f (x) = 1 sin 2x + is a periodic function, then find its period. (A) 2π(B) 3π (C) 5π(D) π Q.12 In a pollution study of 1500 Indian rivers the following data were reported, 520 were polluted by sulphur compounds, 335 were polluted by phosphates, 425 were polluted by crude oil. 100 were polluted by both crude oil and sulphur compounds, 180 were polluted by both sulphur compounds and phosphates, 150 were polluted by both phosphates and crude oil and 28 were polluted by sulphur compounds, phosphates and crude oil. How many of rivers were polluted by atleast one of the three impurties? How many rivers were polluted by exactly one of the three impurties? (A) 878, 504 (B) 478, 304 (C) 818, 554 (D) (A) 472, 104 Q.13 Which of the following is an empty set? (A) {x : x is a real number and x2 – 1 = 0} (B) {x : x is a real number and x2 + 1 = 0} (C) {x : x is a real number and x2 – 9 = 0} (D) {x : x is a real number and x2 = x + 2}