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.