{"id":19210,"date":"2021-02-23T14:32:59","date_gmt":"2021-02-23T09:02:59","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=19210"},"modified":"2021-02-23T14:32:59","modified_gmt":"2021-02-23T09:02:59","slug":"mcq-questions-for-class-12-maths-chapter-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/mcq-questions-for-class-12-maths-chapter-1\/","title":{"rendered":"MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Relations and Functions Class 12 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 12 Maths Chapter 1 Relations and Functions Objective Questions.<\/p>\n

Relations and Functions Class 12 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Relations and Functions Multiple Choice Questions of Class 12 Maths to know different concepts. Practicing the MCQ Questions on Relations and Functions Class 12 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Relations and Functions Class 12 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nLet R be the relation in the set (1, 2, 3, 4}, given by:
\nR = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
\nThen:
\n(a) R is reflexive and symmetric but not transitive
\n(b) R is reflexive and transitive but not symmetric
\n(c) R is symmetric and transitive but not reflexive
\n(d) R is an equivalence relation.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) R is reflexive and transitive but not symmetric<\/p>\n<\/details>\n

\n

Question 2.
\nLet R be the relation in the set N given by : R = {(a, b): a = b – 2, b > 6}. Then:
\n(a) (2, 4) \u2208 R
\n(b) (3, 8) \u2208 R
\n(c) (6, 8) \u2208 R
\n(d) (8, 7) \u2208 R.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) (6, 8) \u2208 R<\/p>\n<\/details>\n

\n

Question 3.
\nLet A = {1, 2, 3}. Then number of relations containing {1, 2} and {1, 3}, which are reflexive and symmetric but not transitive is:
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 1<\/p>\n<\/details>\n

\n

Question 4.
\nLet A = (1, 2, 3). Then the number of equivalence relations containing (1, 2) is
\n(a) 1
\n(b) 2
\n(c) 3
\n(d) 4.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) 2<\/p>\n<\/details>\n

\n

Question 5.
\nLet f: R \u2192 R be defined as f(x) = x4<\/sup>. Then
\n(a) f is one-one onto
\n(b) f is many-one onto
\n(c) f is one-one but not onto
\n(d) f is neither one-one nor onto.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) f is neither one-one nor onto.<\/p>\n<\/details>\n

\n

Question 6.
\nLet f : R \u2192 R be defined as f(x) = 3x. Then
\n(a) f is one-one onto
\n(b) f is many-one onto
\n(c) f is one-one but not onto
\n(d) f is neither one-one nor onto.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) f is one-one onto<\/p>\n<\/details>\n

\n

Question 7.
\nIf f: R \u2192 R be given by f(x) = (3 – x\u00b3)1\/3<\/sup>, then fof (x) is
\n(a) x1\/3<\/sup>
\n(b) x\u00b3
\n(c) x
\n(d) 3 – x\u00b3.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) x<\/p>\n<\/details>\n

\n

Question 8.
\nLet f: R – {-\\(\\frac { 4 }{3}\\)} \u2192 R be a function defined as: f(x) = \\(\\frac { 4x }{3x+4}\\), x \u2260 –\\(\\frac { 4 }{3}\\). The inverse of f is map g : Range f \u2192 R -{-\\(\\frac { 4 }{3}\\)} given by
\n(a) g(y) = \\(\\frac { 3y }{3-4y}\\)
\n(b) g(y) = \\(\\frac { 4y }{4-3y}\\)
\n(c) g(y) = \\(\\frac { 4y }{3-4y}\\)
\n(d) g(y) = \\(\\frac { 3y }{4-3y}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) g(y) = \\(\\frac { 4y }{4-3y}\\)<\/p>\n<\/details>\n

\n

Question 9.
\nLet R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
\n(a) Reflexive and symmetric
\n(b) Transitive and symmetric
\n(c) Equivalence
\n(d) Reflexive, transitive but not symmetric.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) Transitive and symmetric<\/p>\n<\/details>\n

\n

Question 10.
\nSet A has 3 elements and the set B has 4 elements. Then the number of injective mappings that can be defined from A to B is:
\n(a) 144
\n(b) 12
\n(c) 24
\n(d) 64<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) 24<\/p>\n<\/details>\n

\n

Question 11.
\nLet f: R \u2192 R be defined by f(x) = sin x and g : R \u2192 R be defined by g(x) = x\u00b2, then fog is
\n(a) x\u00b2 sin x
\n(b) (sin x)\u00b2
\n(c) sin x\u00b2
\n(d) \\(\\frac { sin x }{x^2}\\)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) sin x\u00b2<\/p>\n<\/details>\n

\n

Question 12.
\nLet f: R \u2192 R be defined by f(x) = x\u00b2 + 1. Then pre-images of 17 and – 3 respectively, are
\n(a) \u00f8, {4,-4}
\n(b) {3, -3}, \u00f8
\n(c) {4, -4}, \u00f8
\n(d) {4, -4}, {2,-2}.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) {4, -4}, $<\/p>\n<\/details>\n

\n

Question 13.
\nLet f: R \u2192 R be defined by
\nf(x)= \\(\\left\\{\\begin{array}{lr}
\n2 x ; & x>3 \\\\
\nx^{2} ; & 1<x<3 \\\\
\n3 x ; & x \\leq 1
\n\\end{array}\\right.\\)
\n(a) 9
\n(b) 14
\n(c) 5
\n(d) None of these.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 9<\/p>\n<\/details>\n

\n

Question 14.
\nThe domain of the function f (x) = \\(\\frac { 1 }{\\sqrt{|x|-x}}\\) is
\n(a) (-\u221e, \u221e)
\n(b) (0, \u221e)
\n(c) (-\u221e, 0)
\n(d) (-\u221e, \u221e) – {0}.<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) (-\u221e, 0)
\nHint:
\nf(x) = \\(\\frac { 1 }{\\sqrt{|x|-x}}\\)
\nf(x) is defined if |x| – x > 0
\nif |x| > x
\nif x < 0.
\nHence, Df<\/sub> = (-\u221e, 0).<\/p>\n<\/details>\n

\n

Question 15.
\nIf a \u2208 R and the equation
\n-3(x – [x] )2 + 2 (x – [x]) + a\u00b2 = 0,
\nwhere [x] denotes the greatest integer (\u2264 x) has no integral solution, then all possible values of a lie in the interval:
\n(a) (1, 2)
\n(b) (-2, -1)
\n(c) (-\u221e, -2) \u222a(2, \u221e)
\n(d) (-1, 0) \u222a (0, 1).<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) (-1, 0) \u222a (0, 1).
\nHint:
\nPut x – [x] = t.
\nThen – 3t\u00b2 + 2t + a\u00b2 = 0
\n\u21d2 a\u00b2 = 3t\u00b2 – 2t.
\nFor non-integral solutions, 0 < a\u00b2 < 1.
\nHence, as (- 1, 0) \u222a (0, 1).<\/p>\n<\/details>\n

\n

Fill in the Blanks<\/span><\/p>\n

Question 1.
\nLet A = {1, 2, 3}. Then the number of equivalence relations containing (1, 2) is ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 2.<\/p>\n<\/details>\n

\n

Question 2.
\nIf A = {0, 1, 3}, then the number of relations on A is ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 9.<\/p>\n<\/details>\n

\n

Question 3.
\nA bijective function is both ……………….. and ………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: one-one, onto.<\/p>\n<\/details>\n

\n

Question 4.
\nLet R be a relation defined on A = { 1, 2, 3) by R = {(1, 3), (3, 1), (2, 2)}, R is ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: symmetric.<\/p>\n<\/details>\n

\n

Question 5.
\nIf f be the greatest integer function defined as f(x) = [x] and g be the modulus function defined as g(x) = |x|, then the value of gof (\\(\\frac { -5 }{4}\\)) is ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 2.
\nHint:
\ngof (\\(\\frac { -5 }{4}\\)) = g (f(\\(\\frac { -5 }{4}\\)))
\n= g(-2) = |-2| = 2.<\/p>\n<\/details>\n

\n

Question 6.
\nIf f : R \u2192 R is defined by 3x + 4, then f(f(x)) is …………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: 9x + 16.
\nHint:
\nf(f (x)) = f(3x + 4)
\n= 3f(x) + 4
\n= 3 (3x + 4) + 4
\n= 9x + 16.<\/p>\n<\/details>\n

\n

Question 7.
\nIf f(x) = ex<\/sup> and g(x) = log x, then gof is ……………….<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: x.
\nHint:
\ngof (x) = g(f(x) = g (ex<\/sup>)
\n= log ex<\/sup> = x log e = x(1) = x.<\/p>\n<\/details>\n

\n

Question 8.
\nThe domain of the function f (x) = \\(\\frac { x }{|x|}\\) is ………………..<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: R – {0}.
\nHint:
\nf is defined for all x \u2208 R except at x = 0.<\/p>\n<\/details>\n

\n

Question 9.
\nLet f: R – {-\\(\\frac { 4 }{3}\\)} \u2192 R be a function defined as: f(x) = \\(\\frac { 4x }{3x+4}\\), x \u2260 –\\(\\frac { 4 }{3}\\)
\nThen inverse of f is map g : Range f \u2192 R – {-\\(\\frac { 4 }{3}\\)} given by …………………<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: g(y) = \\(\\frac { 4x }{3x+4}\\)
\nHint:
\nLet y = f(x)= \\(\\frac { 4x }{3x+4}\\)
\n\u21d2 3xy + 4y = 4x
\n\u21d2 (4 – 3y)x = 4y
\n\u21d2 x = \\(\\frac { 4y }{4-3y}\\)<\/p>\n<\/details>\n

\n

We believe the knowledge shared regarding NCERT MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download has been useful to the possible extent. If you have any other queries regarding CBSE Class 12 Maths Relations and Functions MCQs Multiple Choice Questions with Answers, feel free to reach us via the comment section and we will guide you with the possible solution.<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can access the NCERT MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. Students …<\/p>\n

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Use MCQ Questions for Class 12 Maths with Answers during preparation and score maximum marks in the exam. 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