NCERT Class 12/MCQ Questions for Class 12 Maths Chapter 1 Relations and Functions Sample Test,Sample questions

Question:
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)


Question:
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


Question:
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


Question:
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


Question:
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}


Question:
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


Question:
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


Question:
he period of sin² θ is

1.π²

2.π

3.2π

4.π2


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


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

1.8

2.10

3.16

4.20


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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)


Question:
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


Question:
Let f: [0, 1| → [0, 1| be defined by

1. Constant

2. 1 + x

3.x

4.None of the above


Question:
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, ∞)


Question:
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


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

1.Reflexive

2.Symmetric

3.Transitive

4.Anti-symmetric


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


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

1.[1, 9]

2.[-1, 9]

3. [-9, 1]

4.[-9, -1]


Question:
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


Question:
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


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

1.1

2.2

3.3

4.5


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


Question:
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


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

1.only symmetric

2.only transitive

3.only reflexive

4.equivalence


Question:
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


Question:
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


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