RD Sharma Class 11 Solutions Chapter 2 Relations Exercise 2.1 (Updated for 2024)

RD Sharma Solutions Class 11 Maths Chapter 2 Exercise 2.1: Is here to help you with preparing the Relation chapter with ease. To make it a much better exam session, here are exercises RD Sharma Solutions Class 11 Maths Chapter 2 Exercise 2.1. Here students will get a better look at the RD Sharma Solutions Class 11 Maths Chapter 2 Exercise 2.1 which concentrates on sums on ordered pairs along with cartesian products of the set.

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Chapter 2 Exercise 2.1 RD Sharma Class 11 PDF Solutions

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(1) (i) If (a/3 + 1, b – 2/3) = (5/3, 1/3), find the values of a and b.

(ii) If (x + 1, 1) = (3y, y – 1), find the values of x and y.

Solution:

Given: 

(a/3 + 1, b – 2/3) = (5/3, 1/3)

By the definition of equality of ordered pairs,

Let us solve for a and b

a/3 + 1 = 5/3 and b – 2/3 = 1/3

a/3 = 5/3 – 1 and b = 1/3 + 2/3

a/3 = (5-3)/3 and b = (1+2)/3

a/3 = 2/3 and b = 3/3

a = 2(3)/3 and b = 1

a = 2 and b = 1

∴ Values of a and b are, a = 2 and b = 1

(ii) If (x + 1, 1) = (3y, y – 1), find the values of x and y.

Given:

(x + 1, 1) = (3y, y – 1)

By the definition of equality of ordered pairs,

Let us solve for x and y

x + 1 = 3y and 1 = y – 1

x = 3y – 1 and y = 1 + 1

x = 3y – 1 and y = 2

Since, y = 2 we can substitute in

x = 3y – 1

= 3(2) – 1

= 6 – 1

= 5

∴ Values of x and y are, x = 5 and y = 2

2. If the ordered pairs (x, – 1) and (5, y) belong to the set {(a, b): b = 2a – 3}, find the values of x and y.

Solution:

Given:

The ordered pairs (x, – 1) and (5, y) belong to the set {(a, b): b = 2a – 3}

Solving for first-order pair

(x, – 1) = {(a, b): b = 2a – 3}

x = a and -1 = b

By taking b = 2a – 3

If b = – 1 then 2a = – 1 + 3

= 2

a = 2/2

= 1

So, a = 1

Since x = a, x = 1

Similarly, solving for second-order pair

(5, y) = {(a, b): b = 2a – 3}

5 = a and y = b

By taking b = 2a – 3

If a = 5 then b = 2×5 – 3

= 10 – 3

= 7

So, b = 7

Since y = b, y = 7

∴ Values of x and y are, x = 1 and y = 7

3. If a ∈ {- 1, 2, 3, 4, 5} and b ∈ {0, 3, 6}, write the set of all ordered pairs (a, b) such that a + b = 5.

Solution:

Given: a ∈ {- 1, 2, 3, 4, 5} and b ∈ {0, 3, 6},

To find: the ordered pair (a, b) such that a + b = 5

Then the ordered pair (a, b) such that a + b = 5 are as follows

(a, b) ∈ {(- 1, 6), (2, 3), (5, 0)}

4. If a ∈ {2, 4, 6, 9} and b ∈ {4, 6, 18, 27}, then form the set of all ordered pairs (a, b) such that a divides b and a<b.

Solution:

Given:

a ∈ {2, 4, 6, 9} and b ∈{4, 6, 18, 27}

Here,

2 divides 4, 6, 18 and is also less than all of them

4 divides 4 and is also less than none of them

6 divides 6, 18 and is less than 18 only

9 divides 18, 27 and is less than all of them

∴ Ordered pairs (a, b) are (2, 4), (2, 6), (2, 18), (6, 18), (9, 18) and (9, 27)

5. If A = {1, 2} and B = {1, 3}, find A x B and B x A.

Solution:

Given:

A = {1, 2} and B = {1, 3}

A × B = {1, 2} × {1, 3}

= {(1, 1), (1, 3), (2, 1), (2, 3)}

B × A = {1, 3} × {1, 2}

= {(1, 1), (1, 2), (3, 1), (3, 2)}

6. Let A = {1, 2, 3} and B = {3, 4}. Find A x B and show it graphically

Solution:

Given:

A = {1, 2, 3} and B = {3, 4}

A x B = {1, 2, 3} × {3, 4}

= {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

Steps to follow to represent A × B graphically,

Step 1: One horizontal and one vertical axis should be drawn

Step 2: Element of set A should be represented in a horizontal axis and on vertical axis elements of set B should be represented

Step 3: Draw dotted lines perpendicular to horizontal and vertical axes through the elements of set A and B

Step 4: Point of intersection of these perpendicular represents A × B

7. If A = {1, 2, 3} and B = {2, 4}, what are A x B, B x A, A x A, B x B, and (A x B) ∩ (B x A)?

Solution:

Given:

A = {1, 2, 3} and B = {2, 4}

Now let us find: A × B, B × A, A × A, (A × B) ∩ (B × A)

A × B = {1, 2, 3} × {2, 4}

= {(1, 2), (1, 4), (2, 2), (2, 4), (3, 2), (3, 4)}

B × A = {2, 4} × {1, 2, 3}

= {(2, 1), (2, 2), (2, 3), (4, 1), (4, 2), (4, 3)}

A × A = {1, 2, 3} × {1, 2, 3}

= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}

B × B = {2, 4} × {2, 4}

= {(2, 2), (2, 4), (4, 2), (4, 4)}

The intersection of two sets represents common elements of both the sets

So,

(A × B) ∩ (B × A) = {(2, 2)}

Well, everything from EX 2.1 RD Sharma Solutions CBSE Class 11 Maths Chapter 2 is chalked down here. Take advantage of the situation and start with a fresh mind for a thorough look at the exercise-wise solutions. Hope you find our study material effective for your maths exam. 

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