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This mock test of Test: Relations for JEE helps you for every JEE entrance exam.
This contains 10 Multiple Choice Questions for JEE Test: Relations (mcq) to study with solutions a complete question bank.
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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

Solution:

**Given**: 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.

Let P be the set that contains elements of A.

So, P = {1, 2, 3, 4, 5, 6, 7}

Now, we need to write one more set of elements from P.

So, square values of set P will be {1, 4, 9, 16, 25, 36, 49}

P x P = {(1,1), (1,4), (1,9), (1,16), (1,25), (1,25), (1,36), (1,49) .......}

So, Domain is {1,2,3,4,5,6,7}

Range will be {1, 4, 9, 16, 25, 36, 49}

QUESTION: 2

Which of the following statement is false?

Solution:

Number of relations from A to B is 2^{3.2}

QUESTION: 3

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

Solution:

__It's the formula__

= 2^{n(A)×n(B)}

**Given**:

n(A) = p

n(B) = q

= 2^{pq}

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,

Solution:

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

QUESTION: 5

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

Solution:

The number of relations between sets can be calculated using 2^{mn} where m and n represent the number of members in each set.

So, number of relations from A to B is 2^{6}^{.}

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 ,

Solution:

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}

QUESTION: 7

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

Solution:

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)

QUESTION: 8

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

Solution:

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

QUESTION: 9

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

Solution:

No. of relations from set A to set B =2^{n(A)n(B)} = 2^{2.2} = 16

QUESTION: 10

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

Solution:

{(x, y): x is the square of y, x ∈ P, y ∈ Q}

Option (a) is the relation written in the set builder form.

Hence, it is correct.

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