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1.

Which function is shown in graph?(a) Constant(b) Modulus(c) Identity(d) Signum functionI got this question during an interview.This intriguing question originated from Functions in section Relations and Functions of Mathematics – Class 11

Answer» RIGHT answer is (b) MODULUS

To elaborate: {(-1,1), (1,1), (-2,2), (2,2), (-3,3), (3,3), ……}. This function INVOLVES relation {(X, y): y = |x|} which is involved in modulus function. So, above function is modulus function.
Discussion
2.

Let R be a relation defined on set of natural numbers {(x, y): y=2x}. Is this relation can be called a function?(a) True(b) FalseI have been asked this question by my school principal while I was bunking the class.The origin of the question is Functions in section Relations and Functions of Mathematics – Class 11

Answer»

The CORRECT choice is (a) True

Explanation: SINCE every natural number has one and only image so this relation can be CALLED a FUNCTION.
Discussion
3.

If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find domain of the relation.(a) {1,4,9}(b) {-1,1, -2,2, -3,3}(c) {1,4,8,9}(d) {-1,1, -2,2, -3,3,5}I have been asked this question during an online exam.My query is from Relations topic in section Relations and Functions of Mathematics – Class 11

Answer»

Right answer is (c) {1,4,8,9}

The best I can explain: We know, DOMAIN of a relation is the SET from which relation is DEFINED i.e. set A.

So, domain = {1,4,8,9}.
Discussion
4.

f(x) = \(\sqrt{9-x^2}\). Find the domain of the function.(a) (0,3)(b) [0,3](c) [-3,3](d) (-3,3)This question was posed to me by my college professor while I was bunking the class.My query is from Functions topic in section Relations and Functions of Mathematics – Class 11

Answer»

Right OPTION is (C) [-3,3]

To explain: We KNOW radical cannot be negative. So, 9-x,^2 ≥ 0

(3-x) (3+x) ≥ 0 => (x-3) (x+3) ≤ 0 => x∈[-3,3].
Discussion
5.

Is relation from set A to set B is always equal to relation from set B to set A.(a) True(b) FalseThe question was posed to me during an interview for a job.Question is from Relations topic in chapter Relations and Functions of Mathematics – Class 11

Answer» CORRECT option is (B) False

To elaborate: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. A relation from a non-empty set B to a non-empty set A is a subset of cartesian product B X A.

Since A X B ≠ B X A so, both relations are not equal.
Discussion
6.

If set A has 2 elements and set B has 3 elements then how many subsets does A X B have?(a) 6(b) 8(c) 32(d) 64The question was posed to me in an online quiz.My question comes from Cartesian Product of Sets in division Relations and Functions of Mathematics – Class 11

Answer»

Right choice is (d) 64

To explain: If set A has m ELEMENTS and set B has n elements then A X B has m*n elements.

We KNOW, a set has 2^r subsets if it has r NUMBER of elements.

Here, A X B has 2*3 = 6 elements. So, number of subsets of A X B will be 2^6 i.e. 64.
Discussion
7.

Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the domain.(a) {1,2,3,4,5}(b) {2,3,4,5}(c) {1,2,3,4}(d) {1,2,3,4,5,6}The question was asked in an international level competition.My enquiry is from Relations in division Relations and Functions of Mathematics – Class 11

Answer» RIGHT ANSWER is (a) {1,2,3,4,5}

For explanation I would say: We know, domain of a RELATION is the set from which relation is DEFINED i.e. set A.

So, domain = {1,2,3,4,5}.
Discussion
8.

If P X Q is an empty set then which of the following is a null set?(a) only P(b) only Q(c) either P or Q(d) both P and QThis question was posed to me during an interview.I'd like to ask this question from Cartesian Product of Sets topic in chapter Relations and Functions of Mathematics – Class 11

Answer»

Right option is (C) either P or Q

To explain: If either set P or set Q is a NULL set then P X Q is an EMPTY set.

i.e. if P is Φ or Q is Φ then P X Q = Φ.
Discussion
9.

If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find range of the relation.(a) {1,4,9}(b) {-1,1, -2,2, -3,3}(c) {1,4,8,9}(d) {-1,1, -2,2, -3,3,5}I have been asked this question in a job interview.The doubt is from Relations topic in section Relations and Functions of Mathematics – Class 11

Answer» RIGHT option is (b) {-1,1, -2,2, -3,3}

For EXPLANATION: RANGE is the set of ELEMENTS of codomain which have their PREIMAGE in domain.

Relation R = {(1,1), (1, -1), (4,2), (4, -2), (9,3), (9, -3)}.

Range = {-1,1, -2,2, -3,3}.
Discussion
10.

Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the codomain.(a) {1,2,3,4,5}(b) {2,3,4,5}(c) {1,2,3,4}(d) {1,2,3,4,5,6}This question was posed to me during an online exam.This interesting question is from Relations topic in chapter Relations and Functions of Mathematics – Class 11

Answer»

The correct option is (a) {1,2,3,4,5}

To elaborate: We KNOW, CODOMAIN of a relation is the SET to which relation is defined i.e. set A.

So, codomain = {1,2,3,4,5}.
Discussion
11.

Find range of function |x|.(a) Set of real numbers(b) Set of positive real numbers(c) Set of integers(d) Set of natural numbersThis question was posed to me in examination.This interesting question is from Functions in section Relations and Functions of Mathematics – Class 11

Answer» RIGHT OPTION is (b) Set of positive REAL numbers

The explanation is: Since the above function can have positive real value of y for all real VALUES of x. So, RANGE is set of positive real numbers.
Discussion
12.

If A={1,4,8,9} and B={1, 2, -1, -2, -3, 3,5} and R is a relation from set A to set B {(x, y): x=y^2}. Find codomain of the relation.(a) {1,4,9}(b) {-1,1, -2,2, -3,3}(c) {1,4,8,9}(d) {-1,1, -2,2, -3,3,5}The question was asked in an internship interview.The doubt is from Relations in section Relations and Functions of Mathematics – Class 11

Answer»

Correct CHOICE is (d) {-1,1, -2,2, -3,3,5}

For EXPLANATION I would say: We KNOW, codomain of a relation is the SET to which relation is defined i.e. set B.

So, codomain = {-1,1, -2,2, -3,3,5}.
Discussion
13.

If P = Q then P X Q = Q X P is true or not?(a) True(b) FalseThis question was posed to me in an internship interview.Enquiry is from Cartesian Product of Sets in division Relations and Functions of Mathematics – Class 11

Answer»

The correct option is (a) True

The BEST explanation: LET P = (x, y) and Q = (a, b)

P X Q = {(x, a), (x, b), (y, a), (y, b)}

Q X P = {(a, x), (a, y), (b, x), (b, y)}

If P = Q i.e. x=a and y=b then P X Q = {(a, a), (a, b), (b, a), (b, b)}

Q X P = {(a, a), (a, b), (b, a), (b, b)}.

Hence P X Q = Q X P.
Discussion
14.

If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set A.(a) {1}(b) {1, 2}(c) {1, a}(d) {a, b, c}The question was posed to me in semester exam.This interesting question is from Cartesian Product of Sets topic in portion Relations and Functions of Mathematics – Class 11

Answer»

The correct option is (b) {1, 2}

EASY explanation: In each ordered pair of A X B, FIRST ELEMENT belongs to set A and second element belongs to set B.

1,2 ∈ A so, A = {1, 2}.
Discussion
15.

Find domain of function |x|.(a) Set of real numbers(b) Set of positive real numbers(c) Set of integers(d) Set of natural numbersThis question was addressed to me in unit test.Question is from Functions in portion Relations and Functions of Mathematics – Class 11

Answer»

Correct answer is (a) Set of real numbers

The BEST EXPLANATION: Since the above FUNCTION can have all real VALUES of x. So, DOMAIN is set of real numbers.
Discussion
16.

f(x) = {\(\frac{|x|}{x}\) for x≠0 and 0 for x=0}. Which function is this?(a) Constant(b) Modulus(c) Identity(d) Signum functionThe question was posed to me in an online quiz.I would like to ask this question from Functions topic in portion Relations and Functions of Mathematics – Class 11

Answer»

The correct choice is (d) Signum FUNCTION

Best explanation: f(X) = {\(\FRAC{|x|}{x}\) for x≠0 and 0 for x=0}. Function is {(-3, -1), (-2, -1), (-1,1), (0,0), (1,1), (2,1), (3,1), …….}. This is signum function.
Discussion
17.

Which of the following is not a function?(a) {(1,2), (2,4), (3,6)}(b) {(-1,1), (-2,4), (2,4)}(c) {(1,2), (1,4), (2,5), (3,8)}(d) {(1,1), (2,2), (3,3)}I got this question in final exam.Origin of the question is Functions topic in portion Relations and Functions of Mathematics – Class 11

Answer» CORRECT answer is (c) {(1,2), (1,4), (2,5), (3,8)}

The explanation: A RELATION from a set A to a set B is said to be a function if every element of set A has ONE and one image in set B.

In {(1,2), (1,4), (2,5), (3,8)}, SINCE element 1 has two images 2 and 4 which is not possible in a function so, it is not a function. Rest all have one and only one image so they can be called a function.
Discussion
18.

Let A={1,2} and B={3,4}. Which of the following cannot be relation from set A to set B?(a) {(1,1), (1,2), (1,3), (1,4)}(b) {(1,3), (1,4)}(c) {(2,3), (2,4)}(d) {(1,3), (1,4), (2,3), (2,4)}The question was asked in homework.My question is taken from Relations in portion Relations and Functions of Mathematics – Class 11

Answer»

The CORRECT answer is (a) {(1,1), (1,2), (1,3), (1,4)}

EXPLANATION: A relation from set A to set B is a subset of cartesian product of A X B. In ordered PAIR, FIRST element should belong to set A and second element should belongs to set B.

In {(1,1), (1,2), (1,3), (1,4)}, 1 and 2 should also be in the set B which is not so as GIVEN in question.

Hence, {(1,1), (1,2), (1,3), (1,4)} is not a relation from set A to set B.
Discussion
19.

If A X B = {(1, a), (1, b), (1, c), (2, a), (2, b), (2, c)} then find set B.(a) {1}(b) {1, 2}(c) {1, a}(d) {a, b, c}This question was addressed to me during an interview.My question is based upon Cartesian Product of Sets topic in section Relations and Functions of Mathematics – Class 11

Answer»

The CORRECT option is (d) {a, b, C}

Explanation: In each ORDERED pair of A X B, first element belongs to SET A and SECOND element belongs to set B.

a, b, c ∈ B so, B = {a, b, c}.
Discussion
20.

Is (a, b) = (b, a)?(a) True(b) FalseI got this question in unit test.I'm obligated to ask this question of Cartesian Product of Sets in chapter Relations and Functions of Mathematics – Class 11

Answer»

Right answer is (B) False

To ELABORATE: SINCE (a, b) is an ORDERED PAIR i.e. order of first and second element matters and hence they can’t be interchanged. So, (a, b) ≠ (b, a).
Discussion
21.

If (x+2, y-3) = (5,7) then find values of x and y.(a) x=3 and y=10(b) x=3 and y=4(c) x=7 and y=4(d) x=7 and y=10I have been asked this question by my college professor while I was bunking the class.Enquiry is from Cartesian Product of Sets in chapter Relations and Functions of Mathematics – Class 11

Answer» CORRECT answer is (a) x=3 and y=10

Easy EXPLANATION: Two ordered PAIRS are SAID to be equal if and only if their corresponding ELEMENTS are equal. x+2=5 => x=3

y-3=7 => y=10

Hence, x=3 and y=10.
Discussion
22.

If set P has 4 elements and set Q has 5 elements then find the number of elements in P X Q.(a) 9(b) 4^5(c) 20(d) 5^4I got this question in a job interview.The question is from Cartesian Product of Sets topic in portion Relations and Functions of Mathematics – Class 11

Answer» RIGHT option is (C) 20

For explanation I WOULD say: If SET P has m elements and set Q has n elements then P X Q has m*n elements.

Here, m=4 and n=5 therefore P X Q has 4*5=20 elements.
Discussion
23.

If (a, b) = (x, y) then___________(a) a=x(b) a=y(c) a=y and b=x(d) a=x and b=yI had been asked this question in my homework.This interesting question is from Cartesian Product of Sets topic in section Relations and Functions of Mathematics – Class 11

Answer»

Correct option is (C) a=y and b=x

Easy explanation: Two ordered PAIRS are said to be equal if and only if their CORRESPONDING elements are equal i.e. a=x and b=y.
Discussion
24.

f(x) = \(\sqrt{9-x^2}\). Find the range of the function.(a) R(b) R^+(c) [-3,3](d) [0,3]I got this question in homework.This key question is from Functions topic in section Relations and Functions of Mathematics – Class 11

Answer»

The correct CHOICE is (d) [0,3]

EXPLANATION: We know, SQUARE root is always non-negative. So, \(\sqrt{9-x^2}\) ≥ 0. So, range of the FUNCTION is set of positive real NUMBERS.
Discussion
25.

In a function from set A to set B, image can have more than one preimage.(a) True(b) FalseThe question was asked in an interview for job.My doubt is from Functions topic in chapter Relations and Functions of Mathematics – Class 11

Answer» RIGHT option is (a) True

The best explanation: A relation from a set A to a set B is said to be a FUNCTION if EVERY element of set A has ONE and one image in set B. A preimage MUST have one image, an image can have more than one preimage.
Discussion
26.

Which function is shown in graph?(a) Constant(b) Modulus(c) Identity(d) Signum functionThe question was asked in class test.I would like to ask this question from Functions topic in division Relations and Functions of Mathematics – Class 11

Answer» RIGHT option is (a) Constant

To explain: {(1,5), (2,5), (3,5),……}. This function involves relation {(X, y): y=constant} which is INVOLVED in constant function. So, above function is constant function.
Discussion
27.

In a function from set A to set B, every element of set A has___________ image in set B.(a) one and only one(b) different(c) same(d) manyI got this question in an internship interview.My query is from Functions in section Relations and Functions of Mathematics – Class 11

Answer» CORRECT OPTION is (a) one and only one

Easiest EXPLANATION: A relation from a set A to a set B is said to be a function if every element of set A has one and one image in set B.
Discussion
28.

Let A={1,2,3,4,5} and R be a relation from A to A, R = {(x, y): y = x + 1}. Find the range.(a) {1,2,3,4,5}(b) {2,3,4,5}(c) {1,2,3,4}(d) {1,2,3,4,5,6}This question was posed to me by my college director while I was bunking the class.Question is taken from Relations in division Relations and Functions of Mathematics – Class 11

Answer»

Right CHOICE is (b) {2,3,4,5}

To elaborate: Range is the SET of ELEMENTS of CODOMAIN which have their preimage in domain.

Relation R = {(1,2), (2,3), (3,4), (4,5)}.

Range = {2,3,4,5}.
Discussion
29.

A relation is a subset of cartesian products.(a) True(b) FalseThis question was posed to me in examination.The query is from Relations in chapter Relations and Functions of Mathematics – Class 11

Answer»

The correct choice is (a) True

The explanation: A relation from a non-empty set A to a non-empty set B is a subset of cartesian product A X B. First ELEMENT is CALLED the PREIMAGE of SECOND and second element is called image of first.
Discussion
30.

Which function is shown in graph?(a) Constant(b) Modulus(c) Identity(d) Signum functionThis question was posed to me during an interview.I'd like to ask this question from Functions in portion Relations and Functions of Mathematics – Class 11

Answer»

The CORRECT option is (C) Identity

The explanation: {(1,1), (2,2), (3,3), …..}. This function INVOLVES RELATION {(x, y): y=x} which is involved in identity function. So, above function is identity function.
Discussion
31.

If set A has 2 elements and set B has 4 elements then how many relations are possible?(a) 32(b) 128(c) 256(d) 64The question was asked in an interview.Enquiry is from Relations topic in chapter Relations and Functions of Mathematics – Class 11

Answer»

Correct option is (d) 64

The EXPLANATION is: We know, A X B has 2*4 i.e. 8 elements. NUMBER of subsets of A X B is 2^8 i.e. 256.

A relation is a subset of cartesian product so, number of possible relations are 256.
Discussion
32.

If P X Q has 10 elements then which is not possible?(a) n(P)=1 and n(Q)=10(b) n(P)=10 and n(Q)=1(c) n(P)=2 and n(Q)=5(d) n(P)=5 and n(Q)=4I got this question during an internship interview.I would like to ask this question from Cartesian Product of Sets in chapter Relations and Functions of Mathematics – Class 11

Answer»

The correct choice is (d) N(P)=5 and n(Q)=4

Easiest explanation: If SET P has m elements and set Q has n elements then P X Q has m*n elements.

m*n=10 => if m=1 then n=10,

if m=2 then n=5,

if m=5 then n=2 and if m=10 then n=1.
Discussion