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5/25/24, 4:35 PM Best Educational ERP/LMS Solution Competishun 52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar Date: 25/05/2024 Time: 1 hour...

5/25/24, 4:35 PM Best Educational ERP/LMS Solution Competishun 52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar Date: 25/05/2024 Time: 1 hour Max. Marks: 100 Relation & Function_Maths_Chapterwise Test_2024-25 Mathematics Single Choice Question Q1 Let. Suppose is the set of all the subsets of , then the relation is : a) symmetric and reflexive only b) reflexive only c) symmetric and transitive only d) symmetric only Q2 The number of symmetric relations defined on the set which are not reflexive is a) 930 b) 960 c) 850 d) 860 Q3 Let a relation on be defined as : if and only if or Consider the two statements : (I) is reflexive but not symmetric. (II) is transitive Then which one of the following is true? a) Only (II) is correct. b) Only (I) is correct. c) Both (I) and (II) are correct. d) Neither (I) nor (II) is correct. Q4 Let A = {1, 2, 3, 4, 5, 6, 7}. Then the relation R = {(x,y) ∈ A × A : x + y =7} is a) transitive but neither symmetric nor reflexive b) reflexive but neither symmetric nor transitive c) an equivalence relation d) symmetric but neither reflexive nor transitive https://lms.tutorlog.in/export-test-paper/664db8405af5ff0e42fc21ae 1/5 5/25/24, 4:35 PM Best Educational ERP/LMS Solution Q5 Let f : N→ Z and , then: a) f(x) is bijective b) f{x) is injective but not surjective c) f(x) is not injective but surjective d) f(x) is neither injective nor surjective Q6 Which of the following is the graph of the curve is a) b) c) d) Q7 If ex + ef(x) = e, then for f(x): a) Domain is (–∞, 1) b) Range is (–∞, 1] c) Domain is (–∞, 0] d) Range is (∞, 0] Q8 If | f(x) + 6 – x2| = | f(x) | + |4 – x2| + 2, then f(x) is necessarily non–negative for: a) x ∈ [–2, 2] b) x ∈ (–∞, –2) ∪ (2, ∞) c) d) x ∈ [–5, –2] ∪ [2, 5] Q9 The domain of f(x) is (0, 1), therefore, the domain of y = f(ex) + f(In |x|) is : a) b) (–e, –1) c) d) (–e, –1) ∪ (1, e) Q10 The function, n ∈ N is : a) Odd function b) Even function c) Neither odd nor even function d) Constant function Q11 Which of the following function is periodic? a) f(x) = x – [x], where [x] denotes the greatest integer less than or equal to the real number x b) c) f[x] = x cosx d) None of these f(x) = sin for x ≠ 0, f(0) = 0 Q12 The functionf(x) = x3+ λx2+ 5x + sin 2x will bean invertible function if A belongs to theset a) (–∞,–3] b) [–3,3] c) [3,∞) d) None of these https://lms.tutorlog.in/export-test-paper/664db8405af5ff0e42fc21ae 2/5 5/25/24, 4:35 PM Best Educational ERP/LMS Solution Q13 Let f :N →N defined byf(x) = x2+ x + 1, x ∈N, then f is a) One–one onto b) Many–one onto c) One–one but not onto d) None of these Q14 Iff :[2, 3] → R is defined byf(x) = x3 + 3x –2, then the range off(x) is contained in the interval a) [1,12] b) [12,34] c) [35, 50] d) [–12,12] Q15 The inverse of the function is a) b) c) d) None of these Q16 Iff :R →R is defined by f(x) = x2– 6x –14, then f–1(2)equals to a) {–2,8} b) {–2,–8} c) {2,–8} d) None of these Q17 Total number of solutions of 2x+ 3x+ 4x– 5x = 0 is a) 0 b) 1 c) 2 d) Infinitely many Q18 If n ∈ N and period of is 4π, then n is equal to a) 4 b) 3 c) 2 d) 1 Q19 The period of the function a) 2π b) 10π c) 6π d) 12π Q20 If , the set of values of x, where f(x) ≥0, (where [.] represents the greatest integer function) is a) (–1, 3) b) [–1,3) c) (–1,3] d) [–1,3] Numerical Q21 The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is _________. Ans. 13 Q22 Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such that R = {(x, y) ∈ A×A: x – y is odd positive integer or x – y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to _____ Ans. 19 https://lms.tutorlog.in/export-test-paper/664db8405af5ff0e42fc21ae 3/5 5/25/24, 4:35 PM Best Educational ERP/LMS Solution Q23 The number of relations, on the set {1, 2, 3} containing (1, 2) and (2,3), which are reflexive and transitive but not symmetric, is____. Ans. 4 Q24 Let A={1, 2, 3, 4,.....10} and B = {0, 1, 2, 3, 4}. The number of elements in the relation R = {(a, b) ∈ A × A: 2(a – b)2 + 3(a – b) ∈ B} is______ Ans. 18 Q25 Let A= {–4, –3, –2, 0, 1, 3, 4} and R = {(a, b) ∈ A × A : b = |a| or b2 = a + 1} be a relation on A. Then the minimum number of elements, that must be added to the relation R so that it becomes reflexive and symmetric, is_____. Ans. 7 Q26 Let f : R → R be a one onto differentiable function, such that f(2) = 1 and f'(2) = 3, then the value of is – Ans. 1 Q27 The number of solutions of the equation [y + [y]] = 2cos x is : (Where y = [sin x + [sin x + [sin x]]] and [⋅] = greatest integer function) Ans. 0 Q28 Number of elements in the range set of ; (where [⋅] denotes greatest integer function) : Ans. 6 Q29 The function f(x) satisfy the equation f(1 – x) + 2f(x) = 3x x ∈ R, then |f(0)| = Ans. 1 Q30 Let , where the function f satisfies f(x + y) = f(x) f(y) for all natural numbers x, y and f(1) = 2. Then the natural number ‘a’ is : Ans. 3 https://lms.tutorlog.in/export-test-paper/664db8405af5ff0e42fc21ae 4/5 5/25/24, 4:35 PM Best Educational ERP/LMS Solution Answer Key Que. 1 2 3 4 5 6 7 8 9 10 Ans. D B B D A B A A B B Que. 11 12 13 14 15 16 17 18 19 20 Ans. A B C B A D B C D A Que. 21 22 23 24 25 26 27 28 29 30 Ans. 13 19 4 18 7 1 0 6 1 3 https://lms.tutorlog.in/export-test-paper/664db8405af5ff0e42fc21ae 5/5