Tamil Nadu Board of Secondary EducationHSC Science Class 11

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 1 - Sets, Relations and Functions [Latest edition]

Solutions for Chapter 1: Sets, Relations and Functions

Below listed, you can find solutions for Chapter 1 of Tamil Nadu Board of Secondary Education Tamil Nadu Board Samacheer Kalvi for Class 11th Mathematics Volume 1 and 2 Answers Guide.

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5
Exercise 1.1 [Pages 7 - 9]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 1 Sets, Relations and Functions Exercise 1.1 [Pages 7 - 9]

Exercise 1.1 | Q 1. (i) | Page 7

Write the following in roaster form.

{x ∈ N : x2 < 121 and x is a prime}

Exercise 1.1 | Q 1. (ii) | Page 7

Write the following in roster form.

The set of all positive roots of the equation (x − 1)(x + 1)(x2 − 1) = 0

Exercise 1.1 | Q 1. (iii) | Page 7

Write the following in roster form

{x ∈ N : 4x + 9 < 52}

Exercise 1.1 | Q 1. (iv) | Page 7

Write the following in roster form.

{x : (x − 4)/(x + 2) = 3, x ∈ R – {– 2}}

Exercise 1.1 | Q 2 | Page 7

Write the set {−1, 1} in set builder form

Exercise 1.1 | Q 3. (i) | Page 7

State whether the following set are finite or infinite.

{x ∈ N : x is an even prime number}

Exercise 1.1 | Q 3. (ii) | Page 7

State whether the following set are finite or infinite.

{x ∈ N : x is an odd prime number}

Exercise 1.1 | Q 3. (iii) | Page 7

State whether the following set are finite or infinite.

{x ∈ Z : x is even and less than 10}

Exercise 1.1 | Q 3. (iv) | Page 7

State whether the following set are finite or infinite.

{x ∈ R : x is a rational number}

Exercise 1.1 | Q 3. (v) | Page 7

State whether the following set are finite or infinite.

{x ∈ N : x is a rational number}

Exercise 1.1 | Q 4. (i) | Page 7

By taking suitable sets A, B, C, verify the following results:

A × (B ∩ C) = (A × B) ∩ (A × C)

Exercise 1.1 | Q 4. (ii) | Page 7

By taking suitable sets A, B, C, verify the following results:

A × (B ∪ C) = (A × B) ∪ (A × C)

Exercise 1.1 | Q 4. (iii) | Page 7

By taking suitable sets A, B, C, verify the following results:

(A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A)

Exercise 1.1 | Q 4. (iv) | Page 7

By taking suitable sets A, B, C, verify the following results:

C − (B − A) = (C ∩ A) ∪ (C ∩ B')

Exercise 1.1 | Q 4. (v) | Page 7

By taking suitable sets A, B, C, verify the following results:

(B − A) ∩ C = (B ∩ C) − A = B ∩ (C − A)

Exercise 1.1 | Q 4. (vi) | Page 7

By taking suitable sets A, B, C, verify the following results:

(B − A) ∪ C = (B ∪ C) − (A − C)

Exercise 1.1 | Q 5 | Page 7

Justify the trueness of the statement:
“An element of a set can never be a subset of itself.”

Exercise 1.1 | Q 6 | Page 7

If n(P(A)) = 1024, n(A ∪ B) = 15 and n(P(B)) = 32, then find n(A ∩ B)

Exercise 1.1 | Q 7 | Page 7

If n (A ∩ B) = 3 and n(A ∪ B) = 10, then find n(P(A ∆ B))

Exercise 1.1 | Q 8 | Page 7

For a set A, A × A contains 16 elements and two of its elements are (1, 3) and (0, 2). Find the elements of A

Exercise 1.1 | Q 9 | Page 8

Let A and B be two sets such that n (A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y, z are distinct elements

Exercise 1.1 | Q 10 | Page 9

If A × A has 16 elements, S = {(a, b) ∈ A × A : a < b} ; (−1, 2) and (0, 1) are two elements of S, then find the remaining elements of S

Exercise 1.2 [Pages 18 - 19]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 1 Sets, Relations and Functions Exercise 1.2 [Pages 18 - 19]

Exercise 1.2 | Q 1. (i) | Page 18

Discuss the following relation for reflexivity, symmetricity and transitivity:

The relation R defined on the set of all positive integers by “mRn if m divides n”

Exercise 1.2 | Q 1. (ii) | Page 18

Discuss the following relation for reflexivity, symmetricity and transitivity:

Let P denote the set of all straight lines in a plane. The relation R defined by “lRm if l is perpendicular to m”

Exercise 1.2 | Q 1. (iii) | Page 18

Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”

Exercise 1.2 | Q 1. (iv) | Page 18

Discuss the following relation for reflexivity, symmetricity and transitivity:

Let A be the set consisting of all the female members of a family. The relation R defined by “aRb if a is not a sister of b”

Exercise 1.2 | Q 1. (v) | Page 18

Discuss the following relation for reflexivity, symmetricity and transitivity:

On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”

Exercise 1.2 | Q 2. (i) | Page 18

Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it reflexive

Exercise 1.2 | Q 2. (ii) | Page 18

Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it symmetric

Exercise 1.2 | Q 2. (iii) | Page 18

Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it transitive

Exercise 1.2 | Q 2. (iv) | Page 18

Let X = {a, b, c, d} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence

Exercise 1.2 | Q 3. (i) | Page 18

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it reflexive

Exercise 1.2 | Q 3. (ii) | Page 18

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it symmetric

Exercise 1.2 | Q 3. (iii) | Page 18

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it transitive

Exercise 1.2 | Q 3. (iv) | Page 18

Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it equivalence

Exercise 1.2 | Q 4 | Page 18

Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation

Exercise 1.2 | Q 5. (i) | Page 18

On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it  is reflexive

Exercise 1.2 | Q 5. (ii) | Page 18

On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is symmetric

Exercise 1.2 | Q 5. (iii) | Page 18

On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is transitive

Exercise 1.2 | Q 5. (iv) | Page 18

On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is equivalence

Exercise 1.2 | Q 6 | Page 18

Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai

Exercise 1.2 | Q 7. (i) | Page 18

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is reflexive

Exercise 1.2 | Q 7. (ii) | Page 18

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is symmetric

Exercise 1.2 | Q 7. (iii) | Page 18

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is transitive

Exercise 1.2 | Q 7. (iv) | Page 18

On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is equivalence

Exercise 1.2 | Q 8 | Page 19

Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?

Exercise 1.2 | Q 9 | Page 19

In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation

Exercise 1.3 [Pages 37 - 38]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 1 Sets, Relations and Functions Exercise 1.3 [Pages 37 - 38]

Exercise 1.3 | Q 1 | Page 37

Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as “x related to y if the student x belongs to the section y”. Is this relation a function? What can you say about the inverse relation? Explain your answer

Exercise 1.3 | Q 2 | Page 37

Write the values of f at − 4, 1, −2, 7, 0 if

f(x) = {{:(- x + 4,  "if" - ∞ < x ≤ - 3),(x + 4,  "if" - 3 < x < -2),(x^2 - x,  "if" - 2 ≤ x < 1),(x - x^2,  "if"  1 ≤ x < 7),(0,  "otherwise"):}

Exercise 1.3 | Q 3 | Page 37

Write the values of f at −3, 5, 2, −1, 0 if

f(x) = {{:(x^2 + x - 5,  "if"  x ∈ (−∞, 0)),(x^2 + 3x - 2,  "if"  x ∈ (3, ∞)),(x^2,  "if"  x ∈ (0",", 2)),(x^2 - 3,  "otherwise"):}

Exercise 1.3 | Q 4. (i) | Page 37

State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?

If A = {a, b, c} and f = {(a, c), (b, c), (c, b)}; (f : A → A)

Exercise 1.3 | Q 4. (ii) | Page 37

State whether the following relations are functions or not. If it is a function check for one-to-oneness and ontoness. If it is not a function, state why?

If X = {x, y, z} and f = {(x, y), (x, z), (z, x)}; (f : X → X)

Exercise 1.3 | Q 5. (i) | Page 37

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

neither one-to-one nor onto

Exercise 1.3 | Q 5. (ii) | Page 37

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

not one-to-one but onto

Exercise 1.3 | Q 5. (iii) | Page 37

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

one-to-one but not onto

Exercise 1.3 | Q 5. (iv) | Page 37

Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

one-to-one and onto

Exercise 1.3 | Q 6 | Page 37

Find the domain of 1/(1 - 2sinx)

Exercise 1.3 | Q 7 | Page 37

Find the largest possible domain of the real valued function f(x) = sqrt(4 - x^2)/sqrt(x^2 - 9)

Exercise 1.3 | Q 8 | Page 37

Find the range of the function 1/(2 cos x - 1)

Exercise 1.3 | Q 9 | Page 37

Show that the relation xy = −2 is a function for a suitable domain. Find the domain and the range of the function

Exercise 1.3 | Q 10 | Page 37

If f, g : R → R are defined by f(x) = |x| + x and g(x) = |x| – x find g o f and f o g

Exercise 1.3 | Q 11 | Page 38

If f, g, h are real valued functions defined on R, then prove that (f + g) o h = f o h + g o h. What can you say about f o (g + h)? Justify your answer

Exercise 1.3 | Q 12 | Page 38

If f : R → R is defined by f(x) = 3x − 5, prove that f is a bijection and find its inverse

Exercise 1.3 | Q 13 | Page 38

The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x) = 0.35x. Determine the domain of this function

Exercise 1.3 | Q 14 | Page 38

The distance of an object falling is a function of time t and can be expressed as s(t) = −16t2. Graph the function and determine if it is one-to-one

Exercise 1.3 | Q 15 | Page 38

The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S are functions of the mileage m; C(m) = 0.4 m + 50 and S(m) = 0.03 m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles

Exercise 1.3 | Q 16 | Page 38

A salesperson whose annual earnings can be represented by the function A(x) = 30,000 + 0.04x, where x is the rupee value of the merchandise he sells. His son is also in sales and his earnings are represented by the function S(x) = 25,000 + 0.05x. Find (A + S)(x) and determine the total family income if they each sell Rupees 1,50,00,000 worth of merchandise

Exercise 1.3 | Q 17 | Page 38

The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. On the same day the function for exchanging Singapore Dollar to Indian Rupee is g(y) = 50.50y, where y represents the number of Singapore dollars. Write a function which will give the exchange rate of American dollars in terms of Indian rupee

Exercise 1.3 | Q 18 | Page 38

The owner of a small restaurant can prepare a particular meal at a cost of Rupees 100. He estimates that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is given by the function D(x) = 200 − x. Express his day revenue, total cost and profit on this meal as functions of x

Exercise 1.3 | Q 19 | Page 38

The formula for converting from Fahrenheit to Celsius temperatures is y = (5x)/9 - 160/9. Find the inverse of this function and determine whether the inverse is also a function

Exercise 1.3 | Q 20 | Page 38

A simple cipher takes a number and codes it, using the function f(x) = 3x − 4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x(by drawing the lines)

Exercise 1.4 [Page 44]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 1 Sets, Relations and Functions Exercise 1.4 [Page 44]

Exercise 1.4 | Q 1. (i) | Page 44

For the curve y = x3 given in Figure 1.67, draw
y = −x

Exercise 1.4 | Q 1. (ii) | Page 44

For the curve y = x3 given in Figure 1.67, draw
y = x3 + 1

Exercise 1.4 | Q 1. (iii) | Page 44

For the curve y = x3 given in Figure 1.67, draw
y = x3 − 1

Exercise 1.4 | Q 1. (iv) | Page 44

For the curve y = x3 given in Figure 1.67, draw
y = (x + 1)3 with the same scale

Exercise 1.4 | Q 2. (i) | Page 44

For the curve y = x^((1/3)) given in Figure 1.68, draw

y = - x^((1/3))

Exercise 1.4 | Q 2. (ii) | Page 44

For the curve y = x^((1/3)) given in Figure 1.68, draw

y = x^((1/3)) + 1

Exercise 1.4 | Q 2. (iii) | Page 44

For the curve y = x^((1/3)) given in Figure 1.68, draw

y = x^((1/3)) - 1

Exercise 1.4 | Q 2. (iv) | Page 44

For the curve y = x^((1/3)) given in Figure 1.68, draw

y = (x + 1)^((1/3))

Exercise 1.4 | Q 3 | Page 44

Graph the functions f(x) = x3 and g(x) = root(3)(x) on the same coordinate plane. Find f o g and graph it on the plane as well. Explain your results

Exercise 1.4 | Q 4 | Page 44

Write the steps to obtain the graph of the function y = 3(x − 1)2 + 5 from the graph y = x2

Exercise 1.4 | Q 5. (i) | Page 44

From the curve y = sin x, graph the function.
y = sin(− x)

Exercise 1.4 | Q 5. (ii) | Page 44

From the curve y = sin x, graph the function
y = − sin(−x)

Exercise 1.4 | Q 5. (iii) | Page 44

From the curve y = sin x, graph the function
y = sin(pi/2 + x) which is cos x

Exercise 1.4 | Q 5. (iv) | Page 44

From the curve y = sin x, graph the function
y = sin (pi/2 - x) which is also cos x (refer trigonometry)

Exercise 1.4 | Q 6. (i) | Page 44

From the curve y = x, draw y = − x

Exercise 1.4 | Q 6. (ii) | Page 44

From the curve y = x, draw y = 2x

Exercise 1.4 | Q 6. (iii) | Page 44

From the curve y = x, draw y = x + 1

Exercise 1.4 | Q 6. (iv) | Page 44

From the curve y = x, draw y = 1/2 x +  1

Exercise 1.4 | Q 6. (v) | Page 44

From the curve y = x, draw 2x + y + 3 = 0

Exercise 1.4 | Q 7. (i) | Page 44

From the curve y = |x|, draw y = |x − 1| + 1

Exercise 1.4 | Q 7. (ii) | Page 44

From the curve y = |x|, draw y = |x + 1| − 1

Exercise 1.4 | Q 7. (iii) | Page 44

From the curve y = |x|, draw y = |x + 2| − 3

Exercise 1.4 | Q 8 | Page 44

From the curve y = sin x, draw y = sin |x| (Hint: sin(−x) = − sin x)

Exercise 1.5 [Pages 46 - 48]

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 1 Sets, Relations and Functions Exercise 1.5 [Pages 46 - 48]

MCQ

Exercise 1.5 | Q 1 | Page 46

Choose the correct alternative:

If A = {(x, y) : y = e x , x ∈ R} and B = {(x, y) : y = e−x, x ∈ R} then n(A ∩ B) is

• Infinity

• 0

• 1

• 2

Exercise 1.5 | Q 2 | Page 46

Choose the correct alternative:

If A = {(x, y) : y = sin x, x ∈ R} and B = {(x, y) : y = cos x, x ∈ R} then A ∩ B contains

• no element

• infinitely many elements

• only one element

• cannot be determined

Exercise 1.5 | Q 3 | Page 46

Choose the correct alternative:

The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one of the following is true?

• R = {(0, 0), (0, −1), (0, 1), (−1, 0), (−1, 1), (1, 2), (1, 0)}

• R−1 = {(0, 0), (0, −1), (0, 1), (−1, 0), (1, 0)}

• Domain of R is {0, −1, 1, 2}

• Range of R is {0, −1, 1}

Exercise 1.5 | Q 4 | Page 46

Choose the correct alternative:

If f(x) = |x − 2| + |x + 2|, x ∈ R, then

• f(x) = {{:(- 2x,  "if"  x ∈ (- ∞, - 2]),(4,  "if"  x ∈ (- 2, 2]),(2x,  "if"  x ∈ (2, ∞)):}

• f(x) = {{:(2x,  "if"  x ∈ (- ∞, - 2]),(4x,  "if"  x ∈ (- 2, 2]),(- 2x,  "if"  x ∈ (2, ∞)):}

• f(x) = {{:(- 2x,  "if"  x ∈ (- ∞, - 2]),(- 4x,  "if"  x ∈ (- 2, 2]),(2x,  "if"  x ∈ (2, ∞)):}

• f(x) = {{:(- 2x,  "if"  x ∈ (- ∞, - 2]),(2x,  "if"  x ∈ (- 2, 2]),(2x,  "if"  x ∈ (2, ∞)):}

Exercise 1.5 | Q 5 | Page 46

Choose the correct alternative:

Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?

• T is an equivalence relation but S is not an equivalence relation

• Neither S nor T is an equivalence relation

• Both S and T are equivalence relation

• S is an equivalence relation but T is not an equivalence relation.

Exercise 1.5 | Q 6 | Page 46

Choose the correct alternative:

Let A and B be subsets of the universal set N, the set of natural numbers. Then A' ∪ [(A ∩ B) ∪ B'] is

• A

• A'

• B

• N

Exercise 1.5 | Q 7 | Page 46

Choose the correct alternative:

The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

• 1120

• 1130

• 1100

• insufficient data

Exercise 1.5 | Q 8 | Page 47

Choose the correct alternative:

If n((A × B) ∩ (A × C)) = 8 and n(B ∩ C) = 2, then n(A) is

• 6

• 4

• 8

• 16

Exercise 1.5 | Q 9 | Page 47

Choose the correct alternative:

If n(A) = 2 and n(B ∪ C) = 3, then n[(A × B) ∪ (A × C)] is

• 23

• 32

• 6

• 5

Exercise 1.5 | Q 10 | Page 47

Choose the correct alternative:

If two sets A and B have 17 elements in common, then the number of elements common to the set A × B and B × A is

• 217

• 172

• 34

• insufficient data

Exercise 1.5 | Q 11 | Page 47

Choose the correct alternative:

For non-empty sets A and B, if A ⊂ B then (A × B) ∩ (B × A) is equal to

• A ∩ B

• A × A

• B × B

• none of these

Exercise 1.5 | Q 12 | Page 47

Choose the correct alternative:

The number of relations on a set containing 3 elements is

• 9

• 81

• 512

• 1024

Exercise 1.5 | Q 13 | Page 47

Choose the correct alternative:

Let R be the universal relation on a set X with more than one element. Then R is

• not reflexive

• not symmetric

• transitive

• none of the above

Exercise 1.5 | Q 14 | Page 47

Choose the correct alternative:

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is

• reflexive

• symmetric

• transitive

• equivalence

Exercise 1.5 | Q 15 | Page 47

Choose the correct alternative:

The range of the function  1/(1 - 2 sin x) is

• (- ∞, – 1) ∪ (1/3, ∞)

• (- 1, 1/3)

• [- 1, 1/3]

• (- ∞, – 1] ∪ [1/3, ∞)

Exercise 1.5 | Q 16 | Page 47

Choose the correct alternative:

The range of the function f(x) = |[x] − x|, x ∈ R is

• [0, 1]

• [0, ∞)

• [0, 1)

• (0, 1)

Exercise 1.5 | Q 17 | Page 47

Choose the correct alternative:

The rule f(x) = x2 is a bijection if the domain and the co-domain are given by

• R, R

• R,(0, ∞)

• (0, ∞), R

• [0, ∞), [0, ∞)

Exercise 1.5 | Q 18 | Page 47

Choose the correct alternative:

The number of constant functions from a set containing m elements to a set containing n elements is

• mn

• m

• n

• m + n

Exercise 1.5 | Q 19 | Page 47

Choose the correct alternative:

The function f : [0, 2π] → [−1, 1] defined by f(x) = sin x is

• one-to-one

• onto

• bijection

• cannot be defined

Exercise 1.5 | Q 20 | Page 47

Choose the correct alternative:

If the function f : [−3, 3] → S defined by f(x) = x2 is onto, then S is

• [−9, 9]

• R

• [−3, 3]

• [0, 9]

Exercise 1.5 | Q 21 | Page 47

Choose the correct alternative:

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

• an one-to-one function

• an onto function

• a function which is not one-to-one

• not a function

Exercise 1.5 | Q 22 | Page 48

Choose the correct alternative:

The inverse of f(x) = {{:(x,  "if"  x < 1),(x^2,  "if"  1 ≤ x ≤ 4),(8sqrt(x),  "if"  x > 4):} is

• f–1(x) = {{:(x,  "if"  x < 1),(sqrt(x),  "if"  1 ≤ x ≤ 16),(x^2/64,  "if"  x > 16):}

• f–1(x) = {{:(- x,  "if"  x < 1),(sqrt(x),  "if"  1 ≤ x ≤ 16),(x^2/64,  "if"  x > 16):}

• f–1(x) = {{:(x^2,  "if"  x < 1),(sqrt(x),  "if"  1 ≤ x ≤ 16),(x^2/64,  "if"  x > 16):}

• f–1(x) = {{:(2x,  "if"  x < 1),(sqrt(x),  "if"  1 ≤ x ≤ 16),(x^2/64,  "if"  x > 16):}

Exercise 1.5 | Q 23 | Page 48

Choose the correct alternative:

Let f : R → R be defined by f(x) = 1 − |x|. Then the range of f is

• R

• (1, ∞)

• (−1, ∞)

• (−∞, 1]

Exercise 1.5 | Q 24 | Page 48

Choose the correct alternative:

The function f : R → R is defined by f(x) = sin x + cos x is

• an odd function

• neither an odd function nor an even function

• an even function

• both odd function and even function

Exercise 1.5 | Q 25 | Page 48

Choose the correct alternative:

The function f : R → R is defined by f(x) = ((x^2 + cos x)(1 + x^4))/((x - sin x)(2x - x^3)) + "e"^(-|x|) is

• an odd function

• neither an odd function nor an even function

• an even function

• both odd function and even function

Solutions for Chapter 1: Sets, Relations and Functions

Exercise 1.1Exercise 1.2Exercise 1.3Exercise 1.4Exercise 1.5

Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 1 - Sets, Relations and Functions

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Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 1 Sets, Relations and Functions are Introduction to Sets, Relations and Functions, Sets, Cartesian Product, Constants and Variables, Intervals and Neighbourhoods, Functions, Graphing Functions Using Transformations, Concept of Relation.

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