10th Maths Chapter 1
Relations and Functions
Exercise 1.6
10th Maths Chapter 1 Relations and Functions Exercise 1.6, 10th Maths Chapter 1 Relations and Functions Exercise 1.4, 10th Maths Chapter 1 Relations and Functions Exercise 1.5
Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Ex 1.5
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10th Maths Chapter 1 video classes
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Class 10 Chapter 1 All Exercise Sums
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Class 10 Chapter 1 Example 1.1 to 1.5
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Class 10 Chapter 1 Example 1.6 to 1.10
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Class 10 Chapter 1 Example 1.11 to 1.15
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Class 10 Chapter 1 Example 1.16 to 1.20
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10th Maths Chapter 1 Exercise 1.6, 10th Maths Exercise 1.2 | 10th Maths Ex 1.2 | 10th Maths Chapter 1 Relations and Functions Exercise 1.2 | 10th Maths Chapter 1 Relations and Functions Exercise 1.1 | 10th Maths Chapter 1 Relations and Functions Exercise 1.3 | 10th Maths Chapter 1 Relations and Functions Exercise 1.4 | 10th Maths Chapter 1 Relations and Functions Exercise 1.5 | 10th Maths Chapter 1 Relations and Functions Exercise 1.6 | Class 10 Chapter 1 Relations and Functions Example 1.11 to 1.15 | Class 10 Chapter 1 Relations and Functions Example 1.6 to 1.10 | 10th Maths Example 1.6 | 10th Maths Example 1.7 | 10th Maths Example 1.8 | 10th Maths Example 1.9 | 10th Maths Example 1.10 | Class 10 Chapter 1 Relations and Functions Example 1.1 to 1.5 TN New Syllabus 10th Maths Chapter 1 Relations And Functions Example 1.1 1 Relations and Functions | 1.1 Introduction |1.2 Ordered Pair | 1.3 Cartesian Product | 1.4 Relations | 1.5 Functions | 1.6 Representation of Functions | 1.7 Types of functions | 1.8 Special cases of Functions | 1.9 Composition of Functions 1.10 Identifying the graphs of Linear, Quadratic, | Cubic and Reciprocal functions | TN (Samacheer) 10 Maths Relations and Functions New syllabus Ex 1.1 TN (Samacheer) 10 Maths New Syllabus Relations and Functions.
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:
(3) 3
Hint: n(A × B) = 6
n(A) = 2
n(A × B) = n(A) × n(B)
6 = 2 × n(B)
n(B) = 6/2 = 3
(1) 1
(2) 2
(3) 3
(4) 6
Answer:
(3) 3
Hint: n(A × B) = 6
n(A) = 2
n(A × B) = n(A) × n(B)
6 = 2 × n(B)
n(B) = 6/2 = 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:
(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:
(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:
(2) 2
Hint:
n(A) = 5
n(B) = x
n(A × B) = 1024 = 2^10
2^5x = 2^10
⇒ 5x = 10
⇒ x =2
5. The range of the relation R = {(x, x^2) 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:
(3) {4, 9, 25, 49, 121}
Hint:
Prime number less than 13 = {2, 3, 5, 7, 11}
Range (R) = {(x, x^2)}
Range = {4, 9, 25, 49, 121} (square of x)
(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:
(3) {4, 9, 25, 49, 121}
Hint:
Prime number less than 13 = {2, 3, 5, 7, 11}
Range (R) = {(x, x^2)}
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:
(4) (3, -2)
Hint:
(a + 2, 4), (5, 2a + b)
a + 2 = 5
a = 3
2a + b = 4
6 + b = 4
b = -2
(1) (2, -2)
(2) (5, 1)
(3) (2, 3)
(4) (3, -2)
Answer:
(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) m^n
(2) n^m
(3) 2^mn – 1
(4) 2^mn
Answer:
(4) 2^mn
(1) m^n
(2) n^m
(3) 2^mn – 1
(4) 2^mn
Answer:
(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:
(1) (8, 6)
Hint:
{{a, 8), (6, b)}
a = 8
b = 6
(1) (8, 6)
(2) (8, 8)
(3) (6, 8)
(4) (6, 6)
Answer:
(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:
(3) One-to-one function
Hint:
Different elements of A has different images in B.
∴ It is one-to-one function.
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:
(3) One-to-one function
Hint:
Different elements of A has different images in B.
∴ It is one-to-one function.
10. If f (x) = 2x^2 and g(x) = 1/3x, then fog is …………..
(1) 3/2x^2
(2) 2/3x^2
(3) 2/9x^2
(4) 1/6x^2
Answer:
(3) 2/9x^2
Hint:
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:
(1) 7
Hint:
In a bijective function, n(A) = n(B)
⇒ n(A) = 7
(1) 3/2x^2
(2) 2/3x^2
(3) 2/9x^2
(4) 1/6x^2
Answer:
(3) 2/9x^2
Hint:
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:
(1) 7
Hint:
In a bijective function, n(A) = n(B)
⇒ n(A) = 7
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:
(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)}
fog = f[g(x)]
f [g(0)] = f(2) = 0
f [g(1)] = f(0) = 1
f [g(2)] = f(4) = 2
f[g(-4)] = f(2) = 0
f[g(7)] = f(0) = 1
Range of fog = {0,1,2}
13. Let f(x) = √1+x^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 these
Answer:
(3) f(xy) ≤ f(x).f(y)
Hint:
√1+x^2y^2 ≤ √(1+x2)√(1+y2)
⇒ f(xy) ≤ f(x) . f(y)
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:
(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)
Solve the two equations we get
α = 2, β = -1
15. f(x) = (x + 1)^3 – (x – 1)^3 represents a function which is
(1) linear
(2) cubic
(3) reciprocal
(4) quadratic
Answer:
(4) quadratic
Hint:
f(x) = (x + 1)^3 – (x – 1)^3
= x^3 + 3x^2 + 3x + 1 -[x^3 – 3x^2 + 3x – 1]
= x^3 + 3x^2 + 3x + 1 – x^3 + 3x^2 – 3x + 1 = 6x^2 + 2
It is a quadratic function.
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:
(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)}
fog = f[g(x)]
f [g(0)] = f(2) = 0
f [g(1)] = f(0) = 1
f [g(2)] = f(4) = 2
f[g(-4)] = f(2) = 0
f[g(7)] = f(0) = 1
Range of fog = {0,1,2}
13. Let f(x) = √1+x^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 these
Answer:
(3) f(xy) ≤ f(x).f(y)
Hint:
√1+x^2y^2 ≤ √(1+x2)√(1+y2)
⇒ f(xy) ≤ f(x) . f(y)
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:
(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)
Solve the two equations we get
α = 2, β = -1
15. f(x) = (x + 1)^3 – (x – 1)^3 represents a function which is
(1) linear
(2) cubic
(3) reciprocal
(4) quadratic
Answer:
(4) quadratic
Hint:
f(x) = (x + 1)^3 – (x – 1)^3
= x^3 + 3x^2 + 3x + 1 -[x^3 – 3x^2 + 3x – 1]
= x^3 + 3x^2 + 3x + 1 – x^3 + 3x^2 – 3x + 1 = 6x^2 + 2
It is a quadratic function.
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Class 10 Chapter 1 Relations and Functions Example 1.11 to 1.15 | Class 10 Chapter 1 Relations and Functions Example 1.6 to 1.10 | 10th Maths Example 1.6 | 10th Maths Example 1.7 | 10th Maths Example 1.8 | 10th Maths Example 1.9 | 10th Maths Example 1.10 | Class 10 Chapter 1 Relations and Functions Example 1.1 to 1.5 TN New Syllabus 10th Maths Chapter 1 Relations And Functions Example 1.1 1 Relations and Functions | 1.1 Introduction |1.2 Ordered Pair | 1.3 Cartesian Product | 1.4 Relations | 1.5 Functions | 1.6 Representation of Functions | 1.7 Types of functions | 1.8 Special cases of Functions | 1.9 Composition of Functions 1.10 Identifying the graphs of Linear, Quadratic, | Cubic and Reciprocal functions | TN (Samacheer) 10 Maths Relations and Functions New syllabus Ex 1.1 TN (Samacheer) 10 Maths New Syllabus Relations and Functions
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