Types of Relations and Functions Quiz - CBSE Class 12 Mathematics
Free practice quiz: Types of Relations and Functions (CBSE Class 12 Mathematics). 17 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
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Which of the following is a function?
- y = x^2
- y^2 = x
- x = y^2
- y^3 = x
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Answer: A. y = x^2
A function is a relation in which each input from the domain has exactly one output in the range. y = x^2 is a function as every x corresponds to exactly one y.
Determine the identity function from the options below.
- f(x) = x + 1
- f(x) = 2x
- f(x) = x
- f(x) = -x
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Answer: C. f(x) = x
The identity function is of the form f(x) = x. Here, f(x) = x represents the identity function where the output is the same as the input.
Which of the following sets of ordered pairs is a function?
- {(1, 2), (2, 3), (1, 4)}
- {(1, 2), (2, 3), (3, 4)}
- {(1, 2), (2, 3), (2, 4)}
- {(1, 2), (3, 4), (5, 6)}
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Answer: B. {(1, 2), (2, 3), (3, 4)}
In a function, each input should map to exactly one output. The set {(1, 2), (2, 3), (3, 4)} ensures each input has one unique output.
Identify the bijective function among the options.
- f(x) = x^2
- f(x) = x^3
- f(x) = |x|
- f(x) = sin(x)
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Answer: B. f(x) = x^3
A bijective function is both injective and surjective. f(x) = x^3 is bijective as it is one-one (each y has a unique x) and onto (covers all reals).
If a function f: A → B is defined such that it is surjective but not injective, what can you infer about the cardinality of A and B?
- |A| < |B|
- |A| = |B|
- |A| > |B|
- Cannot determine
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Answer: C. |A| > |B|
If f is surjective, every element in B is mapped to by some element in A. If not injective, some elements in A map to the same element in B, implying |A| > |B|.