CBSE Class 12 Mathematics Relations And Functions Assignment Set 01

Question. Set A has 3 elements and set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
Answer : C

Question. Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is
(a) reflexive and symmetric
(b) symmetric and transitive
(c) equivalence relation
(d) symmetric
Answer : D

Question. Which of the following functions from Z into Z are bijective?
(a) f(x) = x³
(b) f(x) = x + 2
(c) f(x) = 2x + 1
(d) f(x) = x² + 1
Answer : B

Question. Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x)=(x−2)/(x−3). Then,
(a) f is bijective
(b) f is one-one but not onto
(c) f is onto but not one-one
(d) None of these
Answer : A

Question. Let f: R → R is defined as f(x) = 3x then f is
a) f is one-one and onto
b) f is one-one but not onto
c) f is many-one
d) f is neither one-one nor onto
Answer : A

Question. The function f : R → R given by f(x) = x3 – 1 is
(a) a one-one function
(b) an onto function
(c) a bijection
(d) neither one-one nor onto
Answer : C

Question. Let f : R → R be a function defined by f(x) = x3 + 4, then f is
(a) injective
(b) surjective
(c) bijective
(d) none of these
Answer : C

Question. Set A has 3 elements and the set B has 4 elements. Then the number of injective functions that can be defined from set A to set B is
(a) 144
(b) 12
(c) 24
(d) 64
Answer : C

Question. If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is
(a) one-one onto
(b) one-one into
(c) many-one onto
(d) None of these
Answer : B

Question. The mapping f : N → N is given by f(n) = 1 + n2, n ∈ N when N is the set of natural numbers is
(a) one-one and onto
(b) onto but not one-one
(c) one-one but not onto
(d) neither one-one nor onto
Answer : C

Question. The relation R on the set A ={1,2,3} given by R = {(1,1), (1,2), (2,2), (2,3), (3,3)} is
a) Reflexive
b) Symmetric
c) Transitive
d) Equivalence
Answer : A

Question. Given set A ={1, 2, 3} and a relation R = {(1, 2), (2, 1)}, the relation R will be
(a) reflexive if (1, 1) is added
(b) symmetric if (2, 3) is added
(c) transitive if (1, 1) is added
(d) symmetric if (3, 2) is added
Answer : C

ASSERTION AND REASON

Read Assertion and reason carefully and write correct option for each question
(a) Both A and R are correct; R is the correct explanation of A.
(b) Both A and R are correct; R is not the correct explanation of A.
(c) A is correct; R is incorrect.
(d) R is correct; A is incorrect.

Question. Assertion (A) if n (A) = p and n(B) = q The number of relation from set A to B is 𝑝𝑞
Reason (R) The number of subset of A X B is 2𝑝𝑞
Answer : D

Question. Assertion (A) Let A and B be sets. Show that f : A × B →B × A such that f (a, b) = (b, a) is bijective function
Reason (R) f is said to equivalence relation if f is reflexive , symmetric and transitive
Answer : B

Question. Assertion (A)A function f : X →Y is said to be one-one and onto (or bijective)
Reason (R) if f is both one-one and onto.
Answer : A

Question. Assertion (A) Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Then f is one-one.
Reason (R) f is bijective function
Answer : C

Question. Assertion (A) The function f :N→N, given by f (x) = 2x, is not onto
Reason (R) The function f is onto, for f (x) = f (y) ⇒2x = 2y⇒x = y.
Answer : C

Question. Assertion (A) the function f :N→N, given by f (1) = f (2) = 1 and f (x) = x – 1, for every x > 2, is onto but not one-one.
Reason (R) fis not one-one, as f (1) = f (2) = 1. But f is onto, as given any y ∈N, y ≠1, we can choose x as y + 1 such that f (y + 1) = y + 1 – 1 = y. Also for 1 ∈N, we have f (1) = 1.
Answer : A

Question. Assertion (A) Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function From A to B. Then f is one-one.
Reason (R) Since the function f : N→N, given by f (x) = 2x, is not onto
Answer : B

Question. Assertion (A)Let L be the set of all lines in a plane and R be the relation in L defined as R = {(L1, L2) : L1 is perpendicular to L2}. R is not equivalence realtion.
Reason (R)R is symmetric but neither reflexive nor transitive
Answer : A

Question. Assertion (A)The relation R in the set Z of integers given by R = {(a, b) : 2 divides a – b} is reflexive and symmetric
Reason (R) R is reflexive, as 2 divides (a – a) for all a ∈Z.
Answer : B

Question. Assertion (A) The number of all one-one functions from set A = {1, 2, 3} to itself is 6
Reason (R) if n (A) = p and n(B) = q The number of function from set A to B is 𝑝𝑞
Answer : C

Case Based Questions

Raji visited the Exhibition along with her family.
The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by y =  x₂.

Answer the following questions using the above information:

Question. Let f: {1, 2, 3,...} → {1, 4, 9, ...} be defined by f(x) =  x₂ is _______ .
(a) Bijective
(b) Surjective but not injective
(c) Injective but Surjective
(d) Neither Surjective nor Injective
Answer : A

Question. Let f : R → R be defined by f(x) =  x₂ is ____
(a) Neither Surjective nor Injective
(b) Surjective
(c) Injective
(d) Bijective
Answer : A

Question. Let : N → R be defined by f(x) = x₂. Range of the function among the following is ______
(a) {1, 4, 9, 16, ...}
(b) {1, 4, 8, 9, 10,...}
(c) {1, 4, 9, 15, 16,...}
(d) {1, 4, 8, 16,...}
Answer : A

Question. Let f : N → N be defined by f(x) =  x₂ is _____
(a) Surjective but not Injective
(b) Surjective
(c) Injective
(d) Bijective
Answer : C

Question. The function f : Z → Z defined by f(x) =  x₂ is ________
(a) Neither Injective nor Surjective
(b) Injective
(c) Surjective
(d) Bijective
Answer : A

Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1, 2, 3, 4, 5, 6}. Let A be the set of players while B be set of all possible outcomes. A = {S, D}, B = {1, 2, 3, 4, 5, 6}

Based on the above information answer the following:

Question. Raji wants to know the number of relations possible from A to B. How many numbers of relations are possible?
(a) 6²
(b) 2⁶
(c) 6^!
(d) 2¹²
Answer :D

Question. Let R : B → B be defined by R = {(x, y) : y is divisible by x} is
(a) Reflexive and transitive but not symmetric
(b) Reflexive and symmetric but not transitive
(c) Not reflexive but symmetric and transitive
(d) Equivalence
Answer : A

Question. Let R be a relation on B defined by R = {(1, 2), (2, 2), (1, 3), (3, 4), (3, 1), (4, 3), (5, 5)}. Then R is
(a) Symmetric
(b) Reflexive
(c) Transitive
(d) None of these three
Answer : D

Question. Raji wants to know the number of functions from A to B. How many number of functions are possible?
(a) 6²
(b) 2⁶
(c) 6^!
(d) 2¹²
Answer : A

Question. Let R : B → B be defined by R = {(1, 1), (1, 2), (2, 2)(3, 3), (4, 4), (5, 5), (6, 6)}, then R is
(a) Symmetric
(b) Reflexive and Transitive
(c) Transitive and symmetric
(d) Equivalence
Answer : B

1 marks question

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