# Topic: Chapter 1: Sets, Relations and Functions (Test 1)

Topic: Chapter 1: Sets, Relations and Functions
Q.1
Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is
A. reflexive
B. symmetric
C. transitive
D. equivalence
Answer : Option B
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Q.2
The range of the function 1 / 1-2 sin x is
A. B. C. D. Answer : Option D
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Q.3
The range of the function f(x) = |└ x┘- x| , x R is
A. [0, 1]
B. [0, ∞)
C. [0, 1)
D. (0, 1)
Answer : Option C
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Q.4
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
A. R,R
B. R, (0, ∞)
C. (0, ∞),R
D. [0, ∞), [0, ∞)
Answer : Option D
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Q.5
The number of constant functions from a set containing m elements to a set containing n elements is
A. mn
B. m
C. n
D. m + n
Answer : Option C
Explaination / Solution:
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Q.6
The function f : [0, 2π] → [-1, 1] defined by f(x) = sin x is
A. one-to-one
B. onto
C. bijection
D. cannot be defined
Answer : Option B
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Q.7
If the function f : [-3, 3] → S defined by f(x) = x2 is onto, then S is
A. [-9, 9]
B. R
C. [-3, 3]
D. [0, 9]
Answer : Option D
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Q.8
Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is
A. an one-to-one function
B. an onto function
C. a function which is not one-to-one
D. not a function
Answer : Option D
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Q.9
The inverse of f(x) = A. B. C. D. Answer : Option A
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Q.10
Let f : R → R be defined by f(x) = 1 - |x|. Then the range of f is
A. R
B. (1,∞)
C. (-1, ∞)
D. (-∞, 1]
Answer : Option D
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