Olete.in – MCQs, Mock Tests & Government Job Prep | NCERT Class 12 MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions

If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is

1. one-one
2. one-one onto
3. onto
4. many one

✅ Correct Answer: 1

What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}

1. Reflexive
2. Transitive
3. Symmetric
4. None of the above

✅ Correct Answer: 4

If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x).

1. x−54
2. x−y5
3. x−45
4. x4 -5

✅ Correct Answer: 3

If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is

1. 12
2. 28
3. 61
4. None of the above

✅ Correct Answer: 3

Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals

1. 31
2. 40
3. 43
4. None of the above

✅ Correct Answer: 1

The range of the function f(x) = (x−1)(3−x)−−−−−−−−−−−√ is

1. [1, 3]
2. [0, 1]
3. [-2, 2]
4. None of the these

✅ Correct Answer: 1

If f: R → R defined by f(x) = 2x + 3 then f-1(x) =

1. 2x – 3
2. x−32
3. x+32
4. None of the these

✅ Correct Answer: 2

The function f(x) = log (x² + x2+1−−−−−√ ) is

1. even function
2. odd function
3. Both of the above
4. None of the above

✅ Correct Answer: 1

Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is

1. 14
2. 16
3. 12
4. 8

✅ Correct Answer: 1

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then

1. A = B
2. A = C
3. B = C
4. A ∩ B = d

✅ Correct Answer: 3

Let A = {1, 2}, how many binary operations can be defined on this set?

1. 8
2. 10
3. 16
4. 20

✅ Correct Answer: 3

If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?

1. Many-one onto
2. Constant function
3. one-one onto
4. into

✅ Correct Answer: 3

Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is

1. 2x³ + 1
2. (2x)³ + 1
3. (1 – 2x)³
4. (1+x2)1/3

✅ Correct Answer: 4

Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is

1. onto function
2. one-one, onto function
3. one-one, into function
4. many-one into function

✅ Correct Answer: 4

A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-

1. reflexive
2. symmetric and transitive
3. equivalence
4. None of the above

✅ Correct Answer: 3

If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =

1. x² – 2
2. 1
3. 13 (x – 2)²
4. None of the above

✅ Correct Answer: 3

he period of sin² θ is

1. π²
2. π
3. 2π
4. π2

✅ Correct Answer: 2

The domain of sin-1 (log (x/3)] is. .

1. [1, 9]
2. [-1, 9]
3. [-9, 1]
4. [-9, -1]

✅ Correct Answer: 1

f(x) = log2(x+3)x2+3x+2 is the domain of

1. R – {-1, -2}
2. (- 2, ∞) .
3. R- {- 1,-2, -3}
4. (-3, + ∞) – {-1, -2}

✅ Correct Answer: 4

If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is

1. 1
2. 2
3. 3
4. 4

✅ Correct Answer: 2

What type of relation is ‘less than’ in the set of real numbers?

1. only symmetric
2. only transitive
3. only reflexive
4. equivalence

✅ Correct Answer: 2

If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?

1. into
2. one-one onto
3. many-onto
4. constant function

✅ Correct Answer: 2

f: A → B will be an into function if

1. range (f) ⊂ B
2. f(a) = B
3. B ⊂ f(a)
4. f(b) ⊂ A

✅ Correct Answer: 1

If f : R → R such that f(x) = 3x then what type of a function is f?

1. one-one onto
2. many one onto
3. one-one into
4. many-one into

✅ Correct Answer: 3

If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?

1. 13 (x + 4)
2. 13 (x – 4)
3. 3x – 4
4. undefined

✅ Correct Answer: 1

A = {1, 2, 3} which of the following function f: A → A does not have an inverse function

1. {(1, 1), (2, 2), (3, 3)}
2. {(1, 2), (2, 1), (3, 1)}
3. {(1, 3), (3, 2), (2, 1)}
4. {(1, 2), (2, 3), (3, 1)

✅ Correct Answer: 2

Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a congruent to b ∀ a, b ∈ T. Then R is

1. eflexive but-not transitive
2. transitive but not symmetric
3. equivalence
4. None of the above

✅ Correct Answer: 3

Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is

1. symmetric but not transitive
2. transitive but not symmetric
3. neither symmetric nor transitive
4. both symmetric and transitive

✅ Correct Answer: 2

The maximum number of equivalence relations on the set A = {1, 2, 3} are

1. 1
2. 2
3. 3
4. 5

✅ Correct Answer: 4

If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is

1. reflexive
2. transitive
3. symmetric
4. None of the above

✅ Correct Answer: 2

Let us define a relation R in R as aRb if a ≥ b. Then R is

1. an equivalence relation
2. reflexive, transitive but not symmetric
3. neither transitive nor reflexive but symmetric
4. symmetric, transitive but not reflexive

✅ Correct Answer: 2

Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is

1. reflexive but not symmetric
2. reflexive-but not transitive
3. symmetric and transitive
4. neither symmetric, nor transitive

✅ Correct Answer: 1

The identity element for the binary operation * defined on Q ~ {0} as a * b = ab2 ∀ a, b ∈ Q ~ {0} is

1. 1
2. 0
3. 2
4. None of the above

✅ Correct Answer: 3

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

1. 720
2. 120
3. 0
4. None of the above

✅ Correct Answer: 3

Let f : R → R be defined by f (x) = 1x ∀ x ∈ R. Then f is

1. one-one
2. onto
3. bijective
4. f is not defined

✅ Correct Answer: 4

Which of the following functions from Z into Z are bijective?

1. f(x) = x³
2. f(x) = x + 2
3. f(x) = 2x + 1
4. f{x) = x² + 1

✅ Correct Answer: 2

Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is

1. (x + 5)1/3
2. (x -5)1/3
3. (5 – x)1/3
4. 5 – x

✅ Correct Answer: 2

Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,

1. f-1 o g-1
2. f o g
3. g-1 o f-1
4. g o f

✅ Correct Answer: 1

Let f: R – {35} → R be defined by f(x) = 3x+25x−3 then

1. f-1(x) = f(x)
2. f-1(x) = -f(x)
3. (f o f)x = -x
4. f-1(x) = 119 f(x)

✅ Correct Answer: 1

Let f: [0, 1| → [0, 1| be defined by

1. Constant
2. 1 + x
3. x
4. None of the above

✅ Correct Answer: 3

Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is

1. R
2. [1, ∞)
3. [4, ∞)
4. [5, ∞)

✅ Correct Answer: 2

Let f: N → R be the function defined by f(x) = 2x−12 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 32 is

1. 1
2. 0
3. 7/2
4. None of the above

✅ Correct Answer: 4

Let f : R → R be given by f (,v) = tan x. Then f-1(1) is

1. π/4
2. {nπ + π/4 : n ∈ Z}
3. does not exist
4. None of these

✅ Correct Answer: 2

The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by

1. {(2, 1), (4, 2), (6, 3),….}
2. {(1, 2), (2, 4), (3, 6),….}
3. R-1 is not defined
4. None of the above

✅ Correct Answer: 2

The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by

1. {(2, 1), (4, 2), (6, 3),….}
2. {(1, 2), (2, 4), (3, 6),….}
3. R-1 is not defined
4. None of the above

✅ Correct Answer: 2

The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

1. Reflexive but not symmetric
2. Reflexive but not transitive
3. Symmetric and transitive
4. Neither symmetric nor transitive

✅ Correct Answer: 1

The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is

1. Reflexive but not symmetric
2. Reflexive but not transitive
3. Symmetric and transitive
4. Neither symmetric nor transitive

✅ Correct Answer: 1

Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is

1. Reflexive
2. Symmetric
3. Transitive
4. Anti-symmetric

✅ Correct Answer: 2

Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is

1. Less than n
2. Greater than or equal to n
3. Less than or equal to n
4. None of the above

✅ Correct Answer: 2

For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is

1. Reflexive
2. Symmetric
3. Transitive
4. None of the above

✅ Correct Answer: 1

Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is

1. Reflexive
2. Symmetric
3. Transitive
4. None of the above

✅ Correct Answer: 4

Which one of the following relations on R is an equivalence relation?

1. aR1b ⇔ |a| = |b|
2. aR2b ⇔ a ≥ b
3. aR3b ⇔ a divides b
4. aR4b ⇔ a < b

✅ Correct Answer: 1

Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is

1. Reflexive and symmetric
2. Transitive and symmetric
3. Equivalence
4. Reflexive, transitive but not symmetric

✅ Correct Answer: 4