Welcome to your Relations and Functions MCQs Mock Tests of 12th Class Mathematics
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Q.1 Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
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Q.2 Let A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is
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Q.3 The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is
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4. The identity element for the binary operation * defined on Q ~ {0} as a * b = ab/2 ∀ a, b ∈ Q ~ {0} is
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5. Number of binary operations on the set {a, b} are
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6. Let A = {1, 2, 3}. Then the number of relations containing (1, 2) and (1, 3), which are reflexive and symmetric but not transitive is
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7. Let f , g : R → R be defined by f(x) = 3x + 1 and g(x) = x2 – 2, ∀ x ∈ R, respectively. Then, f o g is
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Q.8 Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
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Q.9The number of commutative binary operation that can be defined on a set of 2 elements is
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Q.10 Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
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Q.11 Let R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:
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Q.12 Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is
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Q.13 Let us define a relation R in R as aRb if a ≥ b. Then R is
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Q.14 A relation S in the set of real numbers is defined as xSy ⇒ x – y+ √3 is an irrational number, then relation S is
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Q.11 The function f : R → R defined by f(x) = 3 – 4x is
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Q.15 The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
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Q.16 Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
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Q.17 The smallest integer function f(x) = [x] is
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Q.18 Let f : R → R be defined as f(x) = 3x. Then
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Q.19 The number of binary operations that can be defined on a set of 2 elements is
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Q.20Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is
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Q.21 Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.
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Q.22What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
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Q.23 Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is
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Q.24 Let A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:
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25 A relation R in a set A is called _______, if (a1, a2) ∈ R implies (a2, a1) ∈ R, for all a1, a2 ∈ A.
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26. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
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27. The maximum number of equivalence relations on the set A = {1, 2, 3} are
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28. If set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is
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29. Let f : [2, ∞) → R be the function defined by f(x) = x2 – 4x + 5, then the range of f is
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30. Let f : R → R be defined by f(x) = 1/x ∀ x ∈ R. Then f is
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31. Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is
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32. If f : R → R be defined by f(x) = 3x2 – 5 and g : R → R by g(x) = x/(x2 + 1), then g o f is
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33. Let f : R → R be given by f (x) = tan x. Then f–1(1) is
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34. If f: R → R be given by f(x) = (3 – x3)1/3, then fof(x) is
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35. Let f : A → B and g : B → C be the bijective functions. Then (g o f)–1 is
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36. Let f : R → R be defined by Then f(– 1) + f(2) + f(4) is
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37. Consider a binary operation ∗ on N defined as a ∗ b = a3 + b3. Choose the correct answer.
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38. Let f : R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are
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39. Set A has 3 elements, and set B has 4 elements. Then the number of injective mappings that can be defined from A to B is
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40. Let f : R → R be defined by f(x) = 3x – 4. Then f–1 (x) is given by
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Q.41. Let P = {(x, y) : x2+y2=1, x, y ∈ R}. Then, P is
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Q.42. Let S be the set of all real numbers. Then, the relation R = {(a, b) : 1 +ab > 0} on S is
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Q.43. The relation R = {(1,1), (2, 2), (3, 3)} on set {1, 2, 3} is:
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Q.44. If R is a relation in a set A such that (a, a) ∈ R for every a ∈ A, then the relation R is called
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Q.45. Let A = {1, 2, 3} and R={(1, 2), (2, 3)} be a relation in A. Then, the minimum number of ordered pairs may be added, so that R becomes an equivalence relation, is
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Q.46. Let f : R → R be defined as f(x) = x4, then
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Q.47. Let A={1, 2, 3} and B={a, b, c}, and let f = {(1, a), (2, b), (P, c)} be a function from A to B. For the function f to be one-one and onto, the value of P =
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Q.48. If then f (x) is
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Q.49. The function F : R → R defined by f(x) = (x-1) (x-2) (x-3) is
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Q.50. For real x, let f(x) = x3+5x+1, then
