# NCERT Class 12-Mathematics: Chapter –1 Relations and Functions Part 4

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## Objective Type Questions

### Choose the Correct Answer from the Given Four Options in Each of the Examples 17 to 25

**Question 17:**

Let R be a relation on the set **N** of natural numbers defined by if divides . Then R is

(A) Reflexive and symmetric

(B) Transitive and symmetric

(C) Equivalence

(D) Reflexive, transitive but not symmetric

**Answer:**

The correct choice is (D).

Since *n* divides , R is reflexive. R is not symmetric since is transitive since for whenever and , i.e., divides and divides , then will divide .

**Question 18:**

Let L denote the set of all straight lines in a plane. Let a relation R be defined by if and only if is perpendicular to . Then R is

(A) Reflexive

(B) Symmetric

(C) Transitive

(D) None of these

**Answer:**

The correct choice is (B).

**Question 19:**

Let be the set of natural numbers and the function be defined by . Then is

(A) Surjective

(B) Injective

(C) Bijective

(D) None of these

**Answer:**

(B) Is the correct option.

**Question 20:**

Set A has elements and the set B has elements. Then the number of injective mappings that can be defined from A to B is

(A)

(B)

(C) 24

(D) 64

**Answer:**

The correct choice is (C).

The total number of injective mappings from the set containing elements into the set containing elements is .

**Question 21:**

Let be defined by and be defined by , then *f* is

(A)

(B)

(C)

(D)

**Answer:**

(C) is the correct choice.

**Question 22:**

Let be defined by . Then is given by

(A)

(B)

(C)

(D) None of these

**Answer:**

(A) Is the correct choice.

**Question 23:**

Let be defined by . Then, pre-images of and , respectively, are

(A)

(B)

(C)

(D)

**Answer:**

(C) Is the correct choice since for or and for and hence .