Test: Relations - JEE MCQ

# Test: Relations - JEE MCQ

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## 10 Questions MCQ Test Mathematics (Maths) for JEE Main & Advanced - Test: Relations

Test: Relations for JEE 2024 is part of Mathematics (Maths) for JEE Main & Advanced preparation. The Test: Relations questions and answers have been prepared according to the JEE exam syllabus.The Test: Relations MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Relations below.
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Test: Relations - Question 1

### Let A = {1, 2, 3, …, 50} and R be the relation “is square of” on A. Then R as a subset of A x A is written as:

Detailed Solution for Test: Relations - Question 1

Since x is the square of y in relation R.
i.e. option D is correct.

Test: Relations - Question 2

### Which of the following statement is false?

Detailed Solution for Test: Relations - Question 2

Option D: The number of relations from A to B is 23*2= 26

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Test: Relations - Question 3

### If n(A) = p and n(B) = q, then how many relations are there from A to B?

Detailed Solution for Test: Relations - Question 3

Number of relation from A to B = 2n(A)×n(B)

n(A) = p, n(B) = q
⇒ Number of relation from A to B  = 2pq

Test: Relations - Question 4

Let R be a relation defined on the set of N natural numbers as R = {(x, y): y is a factor of x, x, y∈ N} then,

Detailed Solution for Test: Relations - Question 4

R = {(x, y): y is a factor of x, x, y∈ N}
As we know that 2 is a factor of 4
So, according to the options (4, 2) ϵ R

Test: Relations - Question 5

If A = {1, 2, 3}, and B = {3, 6} then the number of relations from A to B is

Detailed Solution for Test: Relations - Question 5

The number of relations between sets can be calculated using 2mn where m and n represent the number of members in each set.
So, number of relations from A to B is 26.

Test: Relations - Question 6

Let R be a relation defined as R = {(x, y): y = 2x, x is natural number < 5} then Range of R is given as ,

Detailed Solution for Test: Relations - Question 6

X is a natural number and x < 5, the number is 1, 2, 3, 4
y = 2x

► x(1), y = 2 × 1 = 2
► x(2), y = 2 × 2 = 4
► x(3), y = 2 × 3 = 6
► x(4), y = 2 × 4 = 8

Range = {2, 4, 6, 8}

Test: Relations - Question 7

A relation R defined on the set A = {1, 2, 3, 5} as {(x, y): x + y >10 : x, y ∈ A} is:

Detailed Solution for Test: Relations - Question 7

A = {1, 2, 3, 5}
R = {(x, y): x + y >10: x, y ∈ A}
For any value of x, y ∈ A, the condition does not hold.
Therefore, R = Φ (Empty set)

Test: Relations - Question 8

If A = {1, 2, 3}, B = {4, 5, 6}, which of the following is not a relation from A to B

Detailed Solution for Test: Relations - Question 8

A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}

Test: Relations - Question 9

If n(A) = 2, n(B) = 2. What is the total number of relations from A to B?

Detailed Solution for Test: Relations - Question 9

Hint: To solve this problem you don’t need to count the number of relations by assuming it on your own. Use the formula of the number of relations from set A to set B.

It is given that A = {1, 2} and B = {3, 4}
The number of elements in A is n(A)=2 and that of B is n(B) = 2.
The formula for the number of relations from one set to another is:
2(number of elements in the first set) x (number of elements of the second set)
Therefore, we can write it as follows.
No. of relations from set A to set B = 2n(A)n(B) =  2(2*2) = 16
Hence, the number of relations from A to B is 16.

Test: Relations - Question 10

The relation shown in the arrow diagram in set builder form is

Detailed Solution for Test: Relations - Question 10

Set P is square of the element of set Q.
{(x, y): x is the square of y, x ∈ P, y ∈ Q}

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