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CA Foundation Sets, Relations and Functions — practice questions — page 2

Explore 74 free Sets, Relations and Functions questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Sets, Relations and Functions questions and exercises with answers

Showing questions 31–60 of 74.

The finest equivalence relation on any set isRead the answer and worked solution →The empty relation on a non-empty set is vacuously symmetric and transitive but notRead the answer and worked solution →A relation that is functional and total is called aRead the answer and worked solution →A relation that is functional but not injective isRead the answer and worked solution →A relation that is neither injective nor functional isRead the answer and worked solution →A function that is both injective and surjective is calledRead the answer and worked solution →A function is injective when different inputs always giveRead the answer and worked solution →A function is surjective when its range equals itsRead the answer and worked solution →The set f(X) of all outputs of a function f is also called theRead the answer and worked solution →Who first used the functional notation f(x), in 1734?Read the answer and worked solution →A function whose domain is the set of natural numbers is called aRead the answer and worked solution →Which of these is a polynomial function of x?Read the answer and worked solution →The domain of f(x) = 1/(x - 4) over the reals is all reals exceptRead the answer and worked solution →For f(x) = sqrt(x - 3), the largest set of real inputs isRead the answer and worked solution →With f(x) = x + 2 and g(x) = x^2, the value f(g(3)) isRead the answer and worked solution →The inverse of f(x) = 3x - 6 isRead the answer and worked solution →How many functions map a 3-element set into a 2-element set?Read the answer and worked solution →How many bijections exist from a 4-element set onto itself?Read the answer and worked solution →The range of f(x) = x^2 on the domain {-2, -1, 0, 1, 2} isRead the answer and worked solution →A function is given by f(x) = 5x - 7. For which x is f(x) = 18?Read the answer and worked solution →In a partial function, an element of the domain set X mayRead the answer and worked solution →A function of n variables has a domain that is a set ofRead the answer and worked solution →Continuity of real functions is usually defined in terms ofRead the answer and worked solution →As x approaches 2, the expression (x^3 - 8)/(x - 2) tends toRead the answer and worked solution →As x grows without bound, (2x^2 + 3x)/(x^2 + 1) approachesRead the answer and worked solution →What value does 1/x approach as x tends to infinity?Read the answer and worked solution →The standard limit of sin(x)/x as x approaches 0 equalsRead the answer and worked solution →Evaluate (e^x - 1)/x as x approaches 0.Read the answer and worked solution →What is the limit of (3x^2 + 2x)/x as x tends to 0?Read the answer and worked solution →For f(x) = |x|/x, the left-hand limit at x = 0 isRead the answer and worked solution →

Worked practice questions

The finest equivalence relation on any set is

  1. the equality relation
  2. the empty relation
  3. the universal relation
  4. the divisibility relation
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Correct answer: A. the equality relation

Equality relates each element only to itself, so its classes are as small as possible.

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The empty relation on a non-empty set is vacuously symmetric and transitive but not

  1. symmetric
  2. antisymmetric
  3. reflexive
  4. transitive
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Correct answer: C. reflexive

With no pairs at all, the required pairs (a, a) are missing, so reflexivity fails.

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A relation that is functional and total is called a

  1. complement
  2. function
  3. partition
  4. power set
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Correct answer: B. function

Every domain element then has exactly one image, which is what a function requires.

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