10th Maths - Book Back Answers - Chapter 1 Exercise 1.6 - English Medium Guides

 

SSLC / 10th - Maths - Book Back Answers - Chapter 1 Exercise 1.6 - English Medium

Tamil Nadu Board 10th Standard Maths - Chapter 1 Exercise 1.6: Book Back Answers and Solutions

    This post covers the book back answers and solutions for Chapter 1 Exercise 1.6 – Maths from the Tamil Nadu State Board 10th Standard Maths textbook. These detailed answers have been carefully prepared by our expert teachers at KalviTips.com.

    We have explained each answer in a simple, easy-to-understand format, highlighting important points step by step under the relevant subtopics. Students are advised to read and memorize these subtopics thoroughly. Once you understand the main concepts, you’ll be able to connect other related points with real-life examples and confidently present them in your tests and exams.

    By going through this material, you’ll gain a strong understanding of Chapter 1 Exercise 1.6 along with the corresponding book back questions and answers (PDF format).

Question Types Covered:

• 1 Mark Questions: Choose the correct answer, Fill in the blanks, Identify the correct statement, Match the following 
• 2 Mark Questions: Answer briefly 
• 3, 4, and 5 Mark Questions: Answer in detail

All answers are presented in a clear and student-friendly manner, focusing on key points to help you score full marks.

All the best, Class 10 students! Prepare well and aim for top scores. Thank you!

Chapter 1 Relations and functions Ex 1.6

I. Multiple Choice Questions

1. If n(A × B) = 6 and A= {1, 3} then n (B) is _________.

 (1) 1

(2) 2

(3) 3

(4) 6

Answer Key:

(3) 3

Hint: 

n(A × B) = 6

n(A) = 2

n(A × B) = n(A) × n(B)

6 = 2 × n(B)

n(B) = 62 = 3

2. A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A ∪ C) × B] is

(1) 8

(2) 20

(3) 12

(4) 16

Answer Key:

(3) 12
Hint:
A = {a, b, p}, B = {2, 3}, C = {p, q, r, s}
n (A ∪ C) × B
A ∪ C = {a, b, p, q, r, s}
(A ∪ C) × B = {{a, 2), (a, 3), (b, 2), (b, 3), (p, 2), (p, 3), (q, 2), (q, 3), (r, 2), (r, 3), (s, 2), (s, 3)
n [(A ∪ C) × B] = 12

 

3. If A = {1,2}, B = {1,2, 3, 4}, C = {5,6} and D = {5, 6, 7, 8} then state which of the following statement is true _________.  

(1) (A × C) ⊂ (B × D)
(2) (B × D) ⊂ (A × C)
(3) (A × B) ⊂ (A × D)
(4) (D × A) ⊂ (B × A)
Answer Key:
(1) (A × C) ⊂ (B × D)

Hint:

n(A × B) = 2 × 4 = 8
(A × C) = 2 × 2 = 4
n(B × C) = 4 × 2 = 8
n(C × D) = 2 × 4 = 8
n(A × C) = 2 × 2 = 4
n(A × D) = 2 × 4 = 8
n(B × D) = 4 × 4 = 16

∴ (A × C) ⊂ (B × D)

 

4. If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is
(1) 3
(2) 2
(3) 4
(4) 6
Answer Key:
(2) 2
Hint:
n(A) = 5
n(B) = x
n(A × B) = 1024 = 2¹⁰
2^5x = 2¹⁰
⇒ 5x = 10
⇒ x =2

5. The range of the relation R = {(x, x²) a prime number less than 13} is _________.

(1) {2, 3, 5, 7}
(2) {2, 3, 5, 7, 11}
(3) {4, 9, 25, 49, 121}
(4) {1, 4, 9, 25, 49, 121}
Answer Key:
(3) {4, 9, 25, 49, 121}
Hint:
Prime number less than 13 = {2, 3, 5, 7, 11}
Range (R) = {(x, x²)}
Range = {4, 9, 25, 49, 121} (square of x)

 

6. If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a, b) is
(1) (2, -2)
(2) (5, 1)
(3) (2, 3)
(4) (3, -2)
Answer Key:
(4) (3, -2)
Hint:
(a + 2, 4), (5, 2a + b)
a + 2 = 5
a = 3
2a + b = 4
6 + b = 4
b = -2

 

7. Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is _________.
(1) mⁿ
(2) n^m
(3) 2^mn – 1
(4) 2^mn
Answer Key:
(4) 2^mn

 

8. If {(a, 8),(6, b)}represents an identity function, then the value of a and b are respectively

(1) (8, 6)
(2) (8, 8)
(3) (6, 8)
(4) (6, 6)
Answer Key:
(1) (8, 6)
Hint:
{{a, 8), (6, b)}
a = 8
b = 6

 

9. Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}.
A function f: A → B given by f = {(1, 4), (2, 8),(3,9),(4,10)} is a _________.

(1) Many-one function

(2) Identity function

(3) One-to-one function

(4) Into function

Answer Key:

(3) One-to-one function

Hint:

Different elements of A has different images in B.

∴ It is one-to-one function.

Question 10.
If f (x) = 2x² and g(x) =$\frac{\mathbf{1}}{\mathbf{3}\mathbf{x}}$, then fog is _________.

(1) $\frac{\mathbf{3}}{\mathbf{2}{\mathbf{x}}^{\mathbf{2}}}$
(2) $\frac{\mathbf{2}}{\mathbf{3}{\mathbf{x}}^{\mathbf{2}}}$

(3) $\frac{\mathbf{2}}{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}$

(4) $\frac{\mathbf{1}}{\mathbf{6}{\mathbf{x}}^{\mathbf{2}}}$

Answer Key:

(3) $\frac{\mathbf{2}}{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}$

Hint: 

f(x)=2x²; g(x)=$\frac{\mathbf{1}}{\mathbf{3}\mathbf{x}}$

$\frac{\mathbf{fog=f[g(x)]}}{}$

$\frac{\mathbf{=f(}}{}$$\frac{\mathbf{1}}{\mathbf{3}\mathbf{x}}$$\frac{\mathbf{)}}{}$

$\frac{\mathbf{=}}{}$2($\frac{\mathbf{1}}{\mathbf{3}\mathbf{x}}$)²$\frac{\mathbf{ }}{}$

$\frac{\mathbf{fog=}}{}$$\frac{\mathbf{2}}{\mathbf{9}{\mathbf{x}}^{\mathbf{2}}}$$\frac{\mathbf{ }}{}$

$\frac{\mathbf{ }}{}$

Question 11.

If f: A → B is a bijective function and if n(B) = 7, then n(A) is equal to

(1) 7

(2) 49

(3) 1

(4) 14

Answer Key:

(1) 7

Hint:

In a bijective function, n(A) = n(B)

⇒ n(A) = 7

 

Question 12.
Let f and g be two functions given by f = {(0,1),(2, 0),(3-4),(4,2),(5,7)} g = {(0,2),(1,0),(2, 4),(-4,2),(7,0)} then the range of f o g is _________.
(1) {0,2,3,4,5}
(2) {-4,1,0,2,7}
(3) {1,2,3,4,5}
(4) {0,1,2}
Answer Key:
(4) {0,1,2}
Hint: f = {(0, 1)(2, 0)(3, -4) (4, 2) (5, 7)}
g = {(0,2)(l,0)(2,4)(-4,2)(7,0)}

 

Question 13.

Let f(x)=$\sqrt{\mathbf{1}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}}$ then

(1) f(xy) = f(x),f(y)

(2) f(xy) ≥ f(x),f(y)
(3) f(xy) ≤ f(x).f(y)
(4) None of thes3

Answer Key:

(3) f(xy) ≤ f(x).f(y)

Hint

$\sqrt{\mathbf{1}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}{\mathbf{y}}^{\mathbf{2}}}\mathbf{\le }\sqrt{\mathbf{(}\mathbf{1}\mathbf{+}{\mathbf{x}}^{\mathbf{2}}\mathbf{)}}\sqrt{\mathbf{(}\mathbf{1}\mathbf{+}{\mathbf{y}}^{\mathbf{2}}\mathbf{)}}$ 

⇒ f(xy) ≤ f(x) . f(y)

 

Question 14.
If g= {(1,1),(2,3),(3,5),(4,7)} is a function given by g(x) = αx + β then the values of α and β are

(1) (-1,2)
(2) (2,-1)
(3) (-1,-2)
(4) (1,2)
Answer Key:
(2) (2, -1)

Hint:

g (x) = αx + β
g(1) = α(1) + β
1 = α + β ….(1)
g (2) = α (2) + β
3 = 2α + β ….(2)

Question 15.
f(x) = (x + 1)³ – (x – 1)³ represents a function which is _________.

(1) linear

(2) cubic

(3) reciprocal

(4) quadratic

Answer Key:

(4) quadratic

Hint:

f(x) = (x + 1)³ – (x – 1)³

 = x³ + 3x² + 3x + 1 -[x³ – 3x² + 3x – 1]

= x³ + 3x² + 3x + 1 – x³ + 3x² – 3x + 1 = 6x² + 2

It is a quadratic function.