For students diving into Class 11 Maths, mastering these foundational topics can open doors to more advanced areas of study. We’ve curated a set of 20 multiple-choice questions (MCQs) covering Relations and Functions. Let’s dive in and test your knowledge!

## 1. Which of the following is a relation from set A = {1, 2} to set B = {3, 4}?

### Answer:

### Explanation:

A relation consists of ordered pairs where the first element is from set A and the second element is from set B.

## 2. How many relations can be defined from a set containing 'n' elements to itself?

### Answer:

### Explanation:

A relation is a subset of the Cartesian product of a set with itself, so there are 2^(n^2) possible relations.

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

### Answer:

### Explanation:

A function has only one output for each input, and in this case, there are two inputs.

## 4. The domain of the function f(x) = √(x – 3) is:

### Answer:

### Explanation:

The value under the square root must be non-negative for real values.

## 5. If f and g are two functions defined by f(x) = 2x + 3 and g(x) = x – 5, then (f◦g)(x) is:

### Answer:

### Explanation:

(f◦g)(x) = f(g(x)) = f(x – 5) = 2(x – 5) + 3.

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

### Answer:

### Explanation:

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

## 7. The range of the function f(x) = x^3 is:

### Answer:

### Explanation:

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

## 8. The horizontal line test is used to determine:

### Answer:

### Explanation:

If any horizontal line intersects the graph of a function at most once, the function is one-to-one.

## 9. Which of the following is the identity function?

### Answer:

### Explanation:

The identity function returns the input value as the output.

## 10. The relation R on the set A of all books in a library such that 'aRb' if a and b are written by the same author, is:

### Answer:

### Explanation:

Since every book is written by the same author as itself, the relation is reflexive. If book a and book b are written by the same author, then book b and book a are also written by the same author, making it symmetric. If book a is written by the same author as book b and book b is written by the same author as book c, then book a is written by the same author as book c, making it transitive. Hence, it is an equivalence relation.

## 11. If the composition of two functions f and g (f◦g) is the identity function, then g is the:

### Answer:

### Explanation:

The composition of a function and its inverse will give the identity function.

## 12. The number of relations from a set A containing 3 elements to a set B containing 2 elements is:

### Answer:

### Explanation:

The number of relations from set A to set B is 2^(number of elements in A × number of elements in B) = 2^(3×2) = 16.

## 13. Which of the following relations is not reflexive on the set of natural numbers?

### Answer:

### Explanation:

For the relation to be reflexive, every element must be related to itself. In the relation "a > b", no natural number is greater than itself.

## 14. The function defined by f(x) = 2x + 1 is:

### Answer:

### Explanation:

For every distinct x, f(x) produces a distinct value, making it one-to-one. And for every real number y, there exists an x such that f(x) = y, making it onto.

## 15. If the domain of a function is all real numbers, and its codomain is also all real numbers, and it is given that the function is onto, then:

### Answer:

### Explanation:

Since the function is onto and its codomain is all real numbers, the range must also be all real numbers.

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

### Answer:

### Explanation:

A relation that satisfies all three properties (reflexive, symmetric, and transitive) is termed an equivalence relation.

## 17. The vertical line test is used to determine:

### Answer:

### Explanation:

If any vertical line intersects the graph of a relation more than once, then the relation is not a function.

## 18. Which of the following functions has the greatest domain?

### Answer:

### Explanation:

The function f(x) = x^2 is defined for all real numbers.

## 19. A relation R on a set A is said to be symmetric if:

### Answer:

### Explanation:

Symmetry in relations implies that if a is related to b, then b is also related to a.

## 20. Which of the following is not a function from set A = {1, 2, 3} to set B = {4, 5, 6}?

### Answer:

### Explanation:

For a relation to be a function, every element in set A must be related to exactly one element in set B. In this case, 3 is not related to any element in set B.