CBSE 2024-25 Competency-Based Questions With Answers: Assessment is a part of learning that leads to the confirmation of knowledge gained by the learner throughout the course. The assessment can be of multiple types depending on the kind of skills it aims to analyse. For example, essay-type assessments help the tutor clarify who understands the concept well and who needs guidance. Another type of assessment is competency-based. In this, the questions are framed in such a manner that they assess the various aspects of learning from a specific chapter or topic.
The Central Board of Secondary Education (CBSE) has released the 2024-25 competency-focused practice questions for the major subjects of Class 10 and Class 12. These questions are released chapter-wise in three volumes for each subject. Here, the CBSE Class 12 Mathematics Chapter 1 Relations and Functions competency-based questions for the 2025 examination are provided. The FREE PDFs of volumes 1 and 2 are attached here that comprise MCQs and free response questions respectively.
CBSE Class 12 Maths Chapter 1 Competency-Based Questions
Q: 1 Given below is a relation R from the set X = (x,y,z) to itself.
R={(x,x), (x,y), (y,x), (y,z), (x,z)}
Which of the following is true about the relation R?
1) R is reflexive and transitive but not symmetric.
2) R is symmetric and transitive but not reflexive.
3) R is transitive but neither reflexive nor symmetric.
4) R is not reflexive, not symmetric and not transitive.
Q: 2 A and B are two sets with m elements and n elements respectively (m < n).
How many onto functions can be defined from set A to B?
1) 0
2) m!
3) n!
4) nm
Q: 3 Three students Aabha, Bhakti and Chirag were asked to define a function, f, from set X = (1, 3, 5, 7, 9) to set Y = (2, 4, 6, 8). Their responses are shown below:
Aabha: f= ((1, 2), (1, 4), (1, 6), (1, 8))
Bhakti: f= ((1, 2), (3, 4), (5, 6), (7, 8))
Chirag: f= ((1, 4), (3, 4), (5, 4), (7, 4), (9, 4))
Who defined a function correctly?
1) only Chirag
2) only Bhakti and Chirag
3) only Aabha and Bhakti
4) only Chirag and Aabha
Q: 4 Which of the following is an equivalence relation on the set P = (1, 4, 9)?
1) R₁ = ((1, 1), (4, 4), (9, 9))
2) R₂ = ((1, 1), (4, 4), (1, 4), (4, 1))
3) R₃ = ((4, 4), (9, 9), (1, 1), (9, 1), (1, 9), (1, 4), (4, 1))
4) R₄ = ((1, 4), (4, 4), (9, 4), (4, 1), (1, 1), (9.9), (9, 1))
Q: 5 The power set of a set A={a,b} is the set of all subsets of A. These subsets are given by:
P(A) = (Ф, {a}, {b}, {a,b}}
A relation R is defined on P(A) as R = ((r,s): r ⊆ s}
Which of the following is the correct representation of R in its roster form?
1) {Ф, {a}, {b}, {a,b}}
2) { (Ф, {a}), (Ф, {b}), (Ф, {a,b})}
3) { (Ф, {a}), (Ф, {b}), (Ф, {a,b}), ({a}, {a,b}), ({b}, {a,b})}
4) { (Ф, {a}), (Ф, {b}), (Ф, {a,b}), ({a}, {a,b}), ({b}, {a,b}), ({a,b}, {a,b})}
Q: 6 f: X -> X is a function on the finite set X.
Given below are two statements based on the above context one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).
Assertion (A): If f is onto, then f is one-one and if f is one-one, then f is onto.
Reason (R): Every one-one function is always onto and every onto function is always one-one.
1) Both (A) and (R) are true and (R) is the correct explanation for (A).
2) Both (A) and (R) are true but (R) is not the correct explanation for (A).
3) (A) is true but (R) is false.
4) Both (A) and (R) are false.
Q: 7 The set of non-negative integers, denoted by Z', is the set containing positive integers along with zero.
On the set Z', a function f: Z' -> Z' is defined by:
f(n) = n+1, if n is an odd integer
f(n) = 0, if n is an even integer
Which of the following is true about f?
1) f is one-one but not onto
2) f is onto but not one-one
3) f is both one-one and onto
4) f is neither one-one nor onto
Q: 8 Consider an operation * defined on the set {a,b,c} given by the following operation table.
| * | a | b | c |
| a | a | a | a |
| b | a | a | a |
| c | a | a | a |
Which of the following is true about the operation *?
1) * is not a binary operation
2) * is a binary operation that is commutative but not associative
3) * is a binary operation that is associative but not commutative
4) * is a binary operation that is both commutative and associative
Q: 9 If f(x) = x + 1 and f(g(x)) = x, then which of the following is g (1)?
1) 0
2) 1
3) 2
4) (cannot be determined without knowing what is g (x))
Q: 10 A relation R on set G (All the students in a certain mathematics class) is defined as, R={(x, y): x and y have the same mathematics teacher).
Which of the following is true about R?
1) R is reflexive and transitive but not symmetric.
2) R is transitive and symmetric but not reflexive.
3) R is reflexive and symmetric but not transitive.
4) R is an equivalence relation.
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There are two volumes of CBSE Class 12 Maths Chapter 1 Relations and Functions competency-focused practice questions for the 2024-25 session. The complete FREE PDFs are attached here. Click on the 'Download PDF' to get the PDF.
| CBSE Class 12 Maths Chapter 1 Relations and Functions Competency Focused Questions 2024-25 With Answers Volume 1 | |
| CBSE Class 12 Maths Chapter 1 Relations and Functions Competency Focused Questions 2024-25 With Answers Volume 2 |
What Are CBSE Competency-Based Questions?
CBSE competency-based questions are designed to assess students' understanding and application of concepts rather than just their ability to recall facts. These questions require students to apply their knowledge to real-world situations, think critically, and solve problems.
Why CBSE Released Different Volumes of Competency-Based Questions?
CBSE has released multiple PDFs of competency-based questions subject-wise. These PDFs comprise questions that will assess the students’ learning and various other skills. By solving these questions, the students will be able to tackle the competency-based questions in the final 2025 board exams. The PDFs are divided into volumes to provide different sets of multiple-choice questions and free-response questions subject-wise. Thus, students must solve them to prepare effectively for the final examination.
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