Samacheer Kalvi solutions for Mathematics [English] Class 10 SSLC TN Board chapter 1 - Relations and Functions [Latest edition]

Find A × B, A × A and B × A :

A = {2, −2, 3} and B = {1, −4}

Find A × B, A × A and B × A :

A = B = {p, q}

Find A × B, A × A and B × A:

A = {m, n}; B = Φ

Let A = {1, 2, 3} and B = {x | x is a prime number less than 10}. Find A × B and B × A

If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)} find A and B

If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that A × A = (B × B) ∩ (C × C)

Given A = {1, 2, 3}, B = {2, 3, 5}, C = {3, 4} and D = {1, 3, 5}, check if (A ∩ C) × (B ∩ D) = (A × B) ∩ (C × D) is true?

Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that A × (B ∪ C) = (A × B) ∪ (A × C)

Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that  A × (B ∩ C) = (A × B) ∩ (A × C)

Let A = {x ∈ W | x < 2}, B = {x ∈ N | 1 < x < 4} and C = {3, 5}. Verify that (A ∪ B) × C = (A × C) ∪ (B × C)

Let A = The set of all natural number less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that (A ∩ B) × C = (A × C) ∩ (B × C)

Let A = The set of all natural number less than 8, B = The set of all prime numbers less than 8, C = The set of even prime number. Verify that A × (B – C) = (A × B) – (A × C)

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₁ = {(2, 1), (7, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₂ = {(–1, 1)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₃ = {(2, –1), (7, 7), (1, 3)}

Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?

R₄ = {(7, –1), (0, 3), (3, 3), (0, 7)}

Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R

A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range

Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}

Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible

{(x, y) | y = x + 3, x, y are natural numbers < 10}

A company has four categories of employees given by Assistants (A), Clerks (C), Managers (M), and an Executive Officer (E). The company provides ₹ 10,000, ₹ 25,000, ₹ 50,000, and ₹ 1,00,000 as salaries to the people who work in the categories A, C, M, and E respectively. If A₁, A₂, A₃, A_4, and A₅ were Assistants; C₁, C₂, C₃, C₄ were Clerks; M₁, M₂, M₃ were managers and E₁, E₂ was Executive officers and if the relation R is defined by xRy, where x is the salary given to person y, express the relation R through an ordered pair and an arrow diagram

Let f = {(x, y) | x, y ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?

Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x ∈ X, f(x) = x² + 1} is a function from X to N?

Given the function f: x → x² – 5x + 6, evaluate f(– 1)

Given the function f: x → x² – 5x + 6, evaluate f(2a)

Given the function f: x → x² – 5x + 6, evaluate f(2)

Given the function f: x → x² – 5x + 6, evaluate f(x – 1)

A graph representing the function f(x) is given in it is clear that f(9) = 2

Find the following values of the function 

(a) f(0)

(b) f(7)

(c) f(2)

(d) f(10)

A graph representing the function f(x) is given in it is clear that f(9) = 2

For what value of x is f(x) = 1?

A graph representing the function f(x) is given in it is clear that f(9) = 2

 Describe the following Domain

A graph representing the function f(x) is given in it is clear that f(9) = 2

Describe the following Range

A graph representing the function f(x) is given in it is clear that f(9) = 2

What is the image of 6 under f?

Let f(x) = 2x + 5. If x ≠ 0 then find `(f(x + 2) -"f"(2))/x`

A function f is defined by f(x) = 2x – 3 find `("f"(0) + "f"(1))/2`

A function f is defined by f(x) = 2x – 3 find x such that f(x) = 0

A function f is defined by f(x) = 2x – 3 find x such that f(x) = x

A function f is defined by f(x) = 2x – 3 find x such that f(x) = f(1 – x)

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal square from the corner and turning up the side as shown. Express the volume V of the box as a function of x

A function f is defined by f(x) = 3 – 2x. Find x such that f(x²) = (f(x))²

A plane is flying at a speed of 500 km per hour. Express the distance ‘d’ travelled by the plane as function of time t in hour

The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Check if this relation is a function

The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Find a and b

The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Find the height of a person whose forehand length is 40 cm

The data in the adjacent table depicts the length of a person's forehand and their corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b, where a, b are constant.

Find the length of forehand of a person if the height is 53.3 inches

Determine whether the graph given below represent function. Give reason for your answer concerning graph

Determine whether the graph given below represent function. Give reason for your answer concerning graph

Determine whether the graph given below represent function. Give reason for your answer concerning graph

Determine whether the graph given below represent function. Give reason for your answer concerning graph

Let f: A → B be a function defined by f(x) = `x/2` – 1, where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by set of ordered pairs

Let f: A → B be a function defined by f(x) = `x/2` – 1, where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by a table

Let f: A → B be a function defined by f(x) = `x/2` – 1, where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by an arrow diagram

Let f: A → B be a function defined by f(x) = `x/2` – 1, where A = {2, 4, 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}. Represent f by a graph

Represent the function f = {(1, 2), (2, 2), (3, 2), (4, 3), (5, 4)} through an arrow diagram

Represent the function f = {(1, 2), (2, 2), (3, 2), (4, 3), (5, 4)} through a table form

Represent the function f = {(1, 2), (2, 2), (3, 2), (4, 3), (5, 4)} through a graph

Show that the function f : N → N defined by f(x) = 2x – 1 is one-one but not onto

Show that the function f : N → N defined by f(m) = m² + m + 3 is one-one function

Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x³ then, find the range of f

Let A = {1, 2, 3, 4} and B = N. Let f : A → B be defined by f(x) = x³ then, identify the type of function

In the following case state whether the function is bijective or not. Justify your answer

f: R → R defined by f(x) = 2x + 1

In the following case state whether the function is bijective or not. Justify your answer

f: R → R defined by f(x) = 3 – 4x²

Let A = {–1, 1} and B = {0, 2}. If the function f: A → B defined by f(x) = ax + b is an onto function? Find a and b

If the function f is defined by f(x) = `{{:(x + 2";", x > 1),(2";", -1 ≤ x ≤ 1),(x - 1";", -3 < x < -1):}` find the value of f(3)

If the function f is defined by f(x) = `{{:(x + 2";", x > 1),(2";", -1 ≤ x ≤ 1),(x - 1";", -3 < x < -1):}` find the value of f(0)

If the function f is defined by f(x) = `{{:(x + 2";", x > 1),(2";", -1 ≤ x ≤ 1),(x - 1";", -3 < x < -1):}` find the value of f(− 1.5)

If the function f is defined by f(x) = `{{:(x + 2";", x > 1),(2";", -1 ≤ x ≤ 1),(x - 1";", -3 < x < -1):}` find the value of f(2) + f(– 2)

A function f: [– 5, 9] → R is defined as follow :

f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find f(– 3) + f(2)

A function f: [– 5, 9] → R is defined as follow :

f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find f(7) – f(1)

A function f: [– 5, 9] → R is defined as follow :

f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find 2f(4) + f(8)

A function f: [– 5, 9] → R is defined as follow :

f(x) = `{{:(6x + 1";", -5 ≤ x < 2),(5x^2 - 1";", 2 ≤ x < 6),(3x - 4";", 6 ≤ x ≤ 9):}` Find `(2"f"(- 2) - "f"(6))/("f"(4) + "f"( -2))`

The distance S object travel under the influence of gravity in time t seconds is given by S(t) = `1/2` gt² + at + b where, (g is the acceleration due to gravity), a, b are constant. Verify whether the function S(t) is one-one or not.

The function ‘t’ which map temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = `9/5` C + 32. Find, t(0)

The function ‘t’ which map temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = `9/5` C + 32. Find, t(28)

The function ‘t’ which map temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = `9/5` C + 32. Find, t(– 10)

The function ‘t’ which map temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = `9/5` C + 32. Find, the value of C when t(C) = 212

The function ‘t’ which map temperature in Celsius (C) into temperature in Fahrenheit (F) is defined by t(C) = F where F = `9/5` C + 32. Find, the temperature when the Celsius value is equal to the Fahrenheit value

Using the function f and g given below, find fog and gof. Check whether fog = gof

 f(x) = x – 6, g(x) = x² 

Using the function f and g given below, find fog and gof. Check whether fog = gof

f(x) = `(2)/x`, g(x) = 2x² – 1

Using the function f and g given below, find fog and gof. Check whether fog = gof

f(x) = `(x + 6)/3`, g(x) = 3 – x

Using the function f and g given below, find fog and gof. Check whether fog = gof

f(x) = 3 + x, g(x) = x – 4

Using the function f and g given below, find fog and gof. Check whether fog = gof

f(x) = 4x² – 1, g(x) = 1 + x

Find the value of k, such that fog = gof

f(x) = 3x + 2, g(x) = 6x – k

Find the value of k, such that fog = gof

f(x) = 2x – k, g(x) = 4x + 5

If f(x) = 2x – 1, g(x) = `(x + 1)/(2)`, show that fog = gof = x

If f(x) = x² – 1, g(x) = x – 2 find a, if gof(a) = 1

Find k, if f(k) = 2k – 1 and fof(k) = 5

Let A, B, C ⊆ N and a function f: A → B be defined by f(x) = 2x + 1 and g: B → C be defined by g(x) = x². Find the range of fog and gof.

If f(x) = x² – 1. Find fof

If f(x) = x² – 1. Find fofof

If f : R → R and g : R → R are defined by f(x) = x⁵ and g(x) = x⁴ then check if f, g are one-one and fog is one-one?

Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)

f(x) = x – 1, g(x) = 3x + 1 and h(x) = x² 

Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)

f(x) = x², g(x) = 2x and h(x) = x + 4

Consider the function f(x), g(x), h(x) as given below. Show that (fog)oh = fo(goh)

f(x) = x – 4, g(x) = x² and h(x) = 3x – 5

Let f = {(–1, 3), (0, –1), (2, –9)} be a linear function from Z into Z. Find f(x)

In electrical circuit theory, a circuit C(t) is called a linear circuit if it satisfies the superposition principle given by C(at₁ + bt₂) = aC(t₁) + bC(t₂), where a, b are constants. Show that the circuit C(t) = 3t is linear.

Multiple Choice Question :

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

Multiple Choice Question :

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

Multiple Choice Question :

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 ______

Multiple Choice Question :

If there are 1024 relation from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

Multiple Choice Question :

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

Multiple Choice Question :

If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a, b) is

Multiple Choice Question :

Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.

Multiple Choice Question :

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

Multiple choice question :

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

Multiple choice question : 

If f(x) = 2x² and g(x) = `1/(3x)`, then fog is

Multiple choice question : 

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

Multiple choice question : 

Let f and g be two function 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 fog is

Multiple choice question : 

Let f(x) = `sqrt(1 + x^2)` then

Multiple choice question : 

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

Multiple choice question : 

f(x) = (x + 1)³ – (x – 1)³ represent a function which is

If the ordered pairs (x² – 3x, y² + 4y) and (– 2, 5) are equal, then find x and y

The Cartesian product A × A has 9 elements among which (– 1, 0) and (0, 1) are found. Find the set A and the remaining elements of A × A

Given that f(x) = `{{:(sqrt(x - 1), x ≥ 1),(4, x < 1):}` Find f(0)

Given that f(x) = `{{:(sqrt(x - 1), x ≥ 1),(4, x < 1):}` Find f(3)

Given that f(x) = `{{:(sqrt(x - 1), x ≥ 1),(4, x < 1):}` Find f(a + 1) in terms of a. (Given that a ≥ 0)

Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f : A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f

Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`

If f(x)= x², g(x) = 3x and h(x) = x – 2 Prove that (fog)oh = fo(goh)

Let A = {1, 2} and B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify whether A × C is a subset of B × D?

If f(x) = `(x - 1)/(x + 1), x ≠ - 1` Show that f(f(x)) = `- 1/x`, Provided x ≠ 0

The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`

 Calculate the value of `"gg" (1/2)`

The function f and g are defined by f(x) = 6x + 8; g(x) = `(x - 2)/3`

Write an expression for gf(x) in its simplest form

Write the domain of the following real function:

f(x) = `(2x + 1)/(x - 9)`

Write the domain of the following real function:

p(x) = `(-5)/(4x^2 + 1)`

Write the domain of the following real function:

g(x) = `sqrt(x - 2)`

Write the domain of the following real function:

h(x) = x + 6