68 practice questions on Relations and Functions, sorted Easy → Hard. Try each one first, then open its answer page for the worked explanation. Want the full theory first? Read the Relations and Functions notes.
📐 Mathematics · Class 11 · JEE
Relations and Functions - Practice Questions with Answers
68 free MCQs on Relations and Functions, each with its own worked answer and explanation. Ordered pairs, Cartesian products, types of relations and functions, domain and range. Foundation for calculus and Class 12 algebra.
Take the timed Relations and Functions chapterwise test →Easy - 20 questions
Q1.
The domain of f(x) = 1/(x - 3) is:
- A All real numbers
- B All real numbers except 0
- C All real numbers except 3
- D Only positive real numbers
Q2.
A function f: A to B is called onto (surjective) if:
- A Every element of A maps to a unique image in B
- B Every element of B has at least one pre-image
- C f is one-one, meaning distinct inputs give distinct outputs
- D f(a) = a holds true for every single value of a
Q3.
A function f is called one-one (injective) if:
- A f(x) = f(y) implies x = y
- B f(x) = f(y) implies x is not equal to y
- C Every element of B is mapped
- D f is onto
Q4.
The range of f(x) = x² for x belonging to R is:
- A All real numbers
- B All non-negative real numbers
- C All positive real numbers
- D [-1, 1]
Q5.
The notation f: A to B means:
- A A equals B
- B B is the domain
- C f maps A to B
- D f is a subset of A
Q6.
Two ordered pairs (a, b) and (c, d) are equal if and only if:
- A a = c and b = d
- B a = d and b = c
- C a + b = c + d
- D ab = cd
Q7.
The Cartesian product A × B is the set of all ordered pairs (a, b) with a ∈ A and b belonging to:
- A A
- B B
- C A ∩ B
- D A ∪ B
Q8.
If set A has 3 elements and set B has 2 elements, then A × B has how many elements?
- A 6
- B 5
- C 8
- D 9
Q9.
A relation from set A to set B is a subset of:
- A A × B
- B A ∪ B
- C A ∩ B
- D B × B
Q10.
The domain of a relation is the set of all:
- A first components
- B second components
- C ordered pairs
- D subsets
Q11.
The range of a relation is the set of all:
- A first components
- B second components
- C ordered pairs
- D empty sets
Q12.
A function is a relation in which every element of the domain has:
- A exactly one image
- B more than one image
- C no image
- D at least two images
Q13.
The function f(x) = x is called the:
- A identity function
- B constant function
- C zero function
- D square function
Q14.
A function that assigns the same value c to every input is a:
- A constant function
- B identity function
- C linear function
- D modulus function
Q16.
The number of functions from a set with 2 elements to a set with 3 elements is:
- A 9
- B 6
- C 8
- D 5
Q17.
A function that is both one-one (injective) and onto (surjective) is called:
- A bijective
- B only injective
- C only surjective
- D constant
Q18.
For the modulus function f(x) = |x|, the value f(−5) is:
- A 5
- B −5
- C 0
- D 25
Medium - 20 questions
Q21.
In a class of 40 students, 20 play cricket, 15 play football, and 8 play both. How many play neither?
- A 13
- B 12
- C 15
- D 17
Q23.
If f(x) = 3x - 2 is bijective, find f inverse(x).
- A (x+2)/3
- B (x-2)/3
- C 3x+2
- D (3x-2)/3
Q25.
If f: R to R is defined by f(x) = |x|, then f is:
- A Injective but not surjective
- B Surjective but not injective
- C Both injective and surjective
- D Neither injective nor surjective
Q26.
The domain of f(x) = sqrt(4 - x²) is:
- A [-2, 2]
- B (-2, 2)
- C [0, 2]
- D All reals
Q27.
If fog(x) = f(g(x)) where f(x) = x + 1 and g(x) = 2x, then fog(3) =
- A 6
- B 8
- C 9
- D 7
Q28.
A relation R = {(1,1),(2,2),(3,3)} on {1,2,3} is:
- A Reflexive alone, since transitivity and symmetry both supposedly fail
- B Symmetric alone, assuming no pair (a,a) is actually present
- C Reflexive, symmetric and transitive
- D Transitive alone, assuming reflexivity is taken not to hold
Q29.
If n(A) = 3 and n(B) = 4, the maximum number of elements in A ∪ B is:
- A 3
- B 4
- C 7
- D 12
Q30.
A function f: A to B is bijective if and only if:
- A f is one-one, but not necessarily onto
- B f is onto, but not necessarily one-one
- C f is both one-one and onto
- D f has an inverse defined somewhere in B
Q31.
If f(x) = (x - 1)/(x + 1), the value of f(f(x)) is:
- A x
- B 1/x
- C -1/x
- D 1-x
Q32.
If A and B are disjoint sets, n(A) = 5, n(B) = 6, then n(A ∩ B) =
- A 0
- B 1
- C 11
- D 30
Q33.
The range of f(x) = sin x for x belonging to R is:
- A R
- B [0, 1]
- C [-1, 1]
- D (0, 1)
Q34.
Which function has an inverse?
- A f(x) = x²
- B f(x) = |x|
- C f(x) = sin x (domain R)
- D f(x) = 2x + 5
Q35.
If A = {x : x is a multiple of 3} and B = {x : x is a multiple of 6}, then:
- A A is subset of B
- B A = B
- C A and B are disjoint
- D B is subset of A
Q36.
For sets A, B, C: A ∩ (B ∪ C) =
- A (A ∩ B) ∩ C
- B (A ∩ B) ∪ (A ∩ C)
- C (A ∪ B) ∩ C
- D A ∩ B ∩ C
Q37.
The number of relations from A = {1,2} to B = {a,b,c} is:
- A 6
- B 8
- C 64
- D 36
Q38.
f: N to N defined by f(n) = n + 1 is:
- A Bijective
- B Injective but not surjective
- C Surjective but not injective
- D Neither
Q39.
The Cartesian product A × B where A = {1,2} and B = {a,b} has how many elements?
- A 2
- B 4
- C 6
- D 8
Q40.
If f(x) = 2x + 3 and g(x) = x², then the composite (f ∘ g)(x) = f(g(x)) equals:
- A 2x² + 3
- B (2x + 3)²
- C 2x² + 3x
- D 4x² + 9
Hard - 28 questions
Q41.
Let f: R to R, f(x) = (x² + x + 5)/(x² + x + 1). The range of f is:
- A [1, 7/3]
- B (1, 7/3]
- C [1, 7/3)
- D (0, 7/3)
Q42.
If f(x) = (x + 1)/(x - 1) and g(x) = (x + 3)/(x - 1), then (fog)(x) =
- A (x+3)/(x-1)
- B (2x+2)/(4)
- C (x+3)/(2)
- D (2x+2)/(x-1+x-1)
Q43.
A = {1,2,3,...,n}. The number of bijections from A to A is:
- A n
- B n²
- C n!
- D 2<sup>n</sup>
Q44.
If f: R to R satisfies f(x + y) = f(x) + f(y) and f(1) = 2, then f(n) for natural number n =
- A n
- B n²
- C 2<sup>n</sup>
- D 2n
Q45.
Let A have m elements and B have n elements (m < n). The number of injective functions from A to B is:
- A m<sup>n</sup>
- B n<sup>m</sup>
- C nPm
- D nCm
Q46.
In a survey of 100 people, 60 read newspaper A, 40 read B, 20 read both. How many read neither?
- A 10
- B 20
- C 30
- D 40
Q47.
f(x) = sqrt(log(2 - log(x² + 4x + 5))). The domain of f is:
- A [-5, 1]
- B [-3, 1]
- C [-5, -1]
- D (-5, 1)
Q48.
If f(x) = x/(1 + |x|), the function f: R to (-1,1) is:
- A Injective but not surjective
- B Surjective but not injective
- C Bijective
- D Neither
Q49.
The number of onto functions from a set of 3 elements to a set of 2 elements is:
- A 4
- B 6
- C 8
- D 3
Q50.
A = {x : |x - 2| < 3}. In interval notation, A is:
- A (-1, 5)
- B [-1, 5]
- C (0, 5)
- D (-3, 3)
Q51.
The relation R = {(a,b) : a divides b} on Z+ is:
- A Equivalence relation
- B Partial order only
- C Both equivalence and partial order
- D Neither
Q52.
f: [0, ∞) to [0, ∞) defined by f(x) = x/(1+x). The function is:
- A Bijective
- B Injective but not surjective
- C Surjective but not injective
- D Neither
Q54.
For all sets A, B, C: A − (B ∪ C) equals:
- A (A − B) ∪ (A − C)
- B (A − B) ∩ (A − C)
- C (A − B) ∪ C
- D (A ∪ B) − C
Q55.
Let f(x) = x² - 4x + 3. Find the set of values of x for which f(x) < 0.
- A (1, 3)
- B [1, 3]
- C (-inf, 1)
- D (3, inf)
Q56.
f(x) = log₂(x² - 1). Domain of f is:
- A (-∞, -1) ∪ (1, ∞)
- B (-1, 1)
- C [-1, 1]
- D All reals except 0
Q58.
f: R to R defined by f(x) = x³ is:
- A Injective but not surjective
- B Surjective but not injective
- C Bijective
- D Neither
Q59.
If f(x) = (2x - 3)/(3x - 2), find f inverse(x) and verify.
- A (2x-3)/(3x-2)
- B (2x+3)/(3x+2)
- C (3x-2)/(2x-3)
- D (x-1)/(x+1)
Q60.
The inverse of the function f(x) = (x − 3)/2 is:
- A 2x + 3
- B 2x − 3
- C (x + 3)/2
- D x/2 + 3
Q61.
The function f: R → R given by f(x) = x² is:
- A injective only
- B surjective only
- C bijective
- D neither injective nor surjective
Q62.
The number of onto functions from a 4-element set to a 3-element set is:
- A 24
- B 36
- C 64
- D 81
Q63.
The range of the function f(x) = x/(1 + |x|) is:
- A (−1, 1)
- B [−1, 1]
- C R
- D (0, 1)
Q64.
If f(x) = 2x + 3 and g(x) = x² − 1, then (f ∘ g)(2) equals:
- A 7
- B 9
- C 11
- D 15
Q65.
The inverse of the bijection f(x) = x³ + 1 on R is:
- A (x − 1)<sup>1/3</sup>
- B (x + 1)<sup>1/3</sup>
- C x<sup>1/3</sup> − 1
- D (1 − x)<sup>1/3</sup>
Q66.
The number of one-one functions from a 3-element set to a 4-element set is:
- A 12
- B 24
- C 64
- D 81
Q67.
For f(x) = (4x + 3)/(6x − 4), x ≠ 2/3, the composition f(f(x)) equals:
- A x
- B 1/x
- C −x
- D (6x − 4)/(4x + 3)
Q68.
The function f(x) = |x − 1| + |x − 2| fails to be differentiable at how many points?
- A 1
- B 2
- C 3
- D 0
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