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

(1) The period of sin² θ is
[A] π²
[B] π
[C] 2π
[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) = 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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