Welcome to Class 12 Maths MCQ – Relations and Functions chapter, Here, we provide 20 multiple-choice questions related to “Relations and Functions” from Class 12 Mathematics. Dive in and see how well you understand these Maths concepts.

## 1. Which of the following is not a function?

### Answer:

### Explanation:

For x = 1, y can be both 1 and -1. Thus, it does not pass the vertical line test, making it not a function.

## 2. The domain of the function f(x) = √x is:

### Answer:

### Explanation:

The square root is defined for non-negative values of x.

## 3. A relation that is reflexive, symmetric, and transitive is called:

### Answer:

### Explanation:

An equivalence relation satisfies the reflexive, symmetric, and transitive properties.

## 4. The range of the function f(x) = x^2 is:

### Answer:

### Explanation:

The square of any real number is non-negative.

## 5. The function f: R → R defined by f(x) = 2x + 3 is:

### Answer:

### Explanation:

The function is injective (one-one) and surjective (onto) as it covers all real values.

## 6. The number of relations from a set with 3 elements to a set with 2 elements is:

### Answer:

### Explanation:

The number of relations from a set with m elements to a set with n elements is 2^(mn). So, 2^(3*2) = 8.

## 7. Which of the following relations is not symmetric?

### Answer:

### Explanation:

For symmetry, if (a,b) is in relation then (b,a) must also be in the relation. This is not true for the given set.

## 8. The inverse of the function y = 3x – 7 is:

### Answer:

### Explanation:

Swap x and y and solve for y to find the inverse function.

## 9. A function which is both one-one and onto is called:

### Answer:

### Explanation:

A bijective function is both injective (one-one) and surjective (onto).

## 10. The relation R in the set {1,2,3} defined as R = {(1,1), (2,2)} is:

### Answer:

### Explanation:

The relation is symmetric as (a,b) and (b,a) both are present for all a and b in the relation.

## 11. The domain of the function f(x) = 1/x is:

### Answer:

### Explanation:

The function is undefined when x = 0.

## 12. The relation R on the set of real numbers given by R = {(a,b): a ≤ b} is:

### Answer:

### Explanation:

For all real numbers a, a ≤ a (reflexive) and if a ≤ b and b ≤ c, then a ≤ c (transitive).

## 13. If f: A → B and g: B → C are functions, then the composition of f and g is a function from:

### Answer:

### Explanation:

The composition g∘f is defined from A to C.

## 14. A function which is one-one but not onto is called:

### Answer:

### Explanation:

An injective function is one-one but not necessarily onto.

## 15. If f and g are inverse functions, then:

### Answer:

### Explanation:

For two functions to be inverses, the compositions in both orders should return the input.

## 16. If the relation R is transitive, and (a,b) ∈ R and (b,c) ∈ R then:

### Answer:

### Explanation:

By transitive property, if (a,b) and (b,c) are in R, then (a,c) must also be in R.

## 17. Which of the following functions have the entire real line as their range?

### Answer:

### Explanation:

The cube of any real number can be any real number.

## 18. The number of reflexive relations on a set with 5 elements is:

### Answer:

### Explanation:

The number of reflexive relations on a set with n elements is 2^(n^2-n).

## 19. A function is said to be onto if:

### Answer:

### Explanation:

An onto (or surjective) function is one where every element of the codomain is the image of at least one element of the domain.

## 20. Which of the following is true for a function f(x) = x^2 – 4x + 4?

### Answer:

### Explanation:

The function represents a parabola with vertex (2,0) and is not one-one. Also, it is not onto as its range does not cover all real values.