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NCERT Solutions for class 12 Maths | Chapter 1 - Relations and Functions

Questions
1 The period of sin² θ is
A π²
B π
C
D π/2

Answer:π
2 Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
A onto function
B one-one, onto function
C one-one, into function
D many-one into function

Answer:many-one into function
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3 Let A = {1, 2}, how many binary operations can be defined on this set?
A 8
B 10
C 16
D 20

Answer:16
4 The range of the function f(x) = Relations and Functions is
A [-2, 2]
B [0, 1]
C [1, 3]
D None of these

Answer:[1, 3]
5 A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
A reflexive
B symmetric and transitive
C equivalence
D None of these

Answer:equivalence
6 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?
A Many-one onto
B Constant function
C one-one onto
D into

Answer:one-one onto
7 If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
A 1
B 2
C 3
D 4

Answer:2
8 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?
A into
B one-one onto
C many-onto
D constant function

Answer:one-one onto
9 If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
A reflexive
B transitive
C symmetric
D None of these

Answer:transitive
10 Let A = {1, 2,3,…. n} and B = { a, b}. Then the number of surjections from A into B is
A nP2
B 2n – 2
C 2n – 1
D None of these

Answer:2n – 2
11 Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
A (x + 5)1/3
B (x -5)1/3
C (5 – x)1/3
D 5 – x

Answer:(x -5)1/3
12 Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
A 31
B 40
C 43
D None of these

Answer:31
13 If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
A many one
B one-one onto
C onto
D one-one

Answer:one-one
14 What type of relation is ‘less than’ in the set of real numbers?
A only symmetric
B only transitive
C only reflexive
D equivalence

Answer:only transitive
15 A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
A {(1, 1), (2, 2), (3, 3)}
B {(1, 2), (2, 1), (3, 1)}
C {(1, 3), (3, 2), (2, 1)}
D {(1, 2), (2, 3), (3, 1)

Answer:{(1, 2), (2, 1), (3, 1)}
16 Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
A R
B [1, ∞)
C [4, ∞)
D [5, ∞)

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

Answer:f-1 o g-1
18 Which one of the following relations on R is an equivalence relation?
A aR1b ⇔ |a| = |b|
B aR2b ⇔ a ≥ b
C aR3b ⇔ a divides b
D aR4b ⇔ a < b

Answer:aR1b ⇔ |a| = |b|
19 If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
A A = B
B A = C
C B = C
D A ∩ B = d

Answer:B = C
20 If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
A 12
B 28
C 61
D None of these

Answer:61

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