Mathematics Sets Functions and Groups MCQS Online Preparation Sample Paper Questions with Answer
This is the basis of discrete mathematics, for the ECAT (Engineering College Admission Test), the mathematics sets functions and groups is an important part. So, they are important and fundamental for understanding the structures and relations of the numerical quantities in problem-solving algebra and higher-level mathematics.
Logical reasoning is a life skill that can be improved by Mastering sets of functions and groups which is essential for excelling in ECAT and other competitive examinations. This test preparation guide provides basic & important concepts, properties, numbers & solution MCQs for students according to their preparation.
Understanding Mathematics Sets Functions and Groups
1. Sets in Mathematics
A set is a well-defined collection of distinct objects, numbers, or elements. Sets are widely used in mathematics for grouping related elements.
- Types of Sets:
- Empty Set (Null Set): A set with no elements, denoted as or {}.
- Singleton Set: A set with only one element, e.g., {3}.
- Finite Set: A set with a countable number of elements, e.g., {1, 2, 3, 4}.
- Infinite Set: A set with an uncountable number of elements, e.g., the set of natural numbers.
- Subset & Superset: If every element of set A is also in set B, then A is a subset of B, denoted as.
- Power Set: The set of all subsets of a given set.
- Operations on Sets: Union (), Intersection (), and Complement ().
2. Functions in Mathematics
A function is a rule that assigns each element in one set to exactly one element in another set.
- Types of Functions:
- One-to-One (Injective): Each input has a unique output.
- Onto (Surjective): Every element in the output set is mapped by at least one input.
- Bijective: A function that is both one-to-one and onto.
- Domain & Range: The domain is the set of input values, and the range is the set of output values.
3. Groups in Mathematics
A group is a set with a binary operation that follows four key properties:
- Closure: The operation on any two elements results in another element within the set.
- Associativity: for all elements in the set.
- Identity Element: There exists an element (e) such that.
- Inverse Element: For every element, there exists an element such that.
MCQs Preparation Strategy
To excel in mathematics sets, functions, and groups MCQs, follow these strategies:
- Concept Clarity: Understand the fundamental definitions and properties.
- Practice Regularly: Solve past ECAT papers and sample MCQs.
- Memorize Key Properties: Review rules for sets, function mappings, and group operations.
- Time Management: Improve speed by practicing under timed conditions.
- Use Diagrams: Venn diagrams can help in solving set-related questions efficiently.
Sample MCQs for Practice
1. If B⊆A, then the complement of A in B is Ac =
- A∩B
- A∪B
- B – A correct
- A – B
2. {x | x ε N ^ x < 1} is
- Empty set correct
- A set with two points
- A set with three points
- Singleton set
3. A⊆B means
- A is a subset of B correct
- A is a superset of B
- A is equal to B
- A is equivalent to B
4. The set {(a, b)} is
- Singleton set correct
- Empty set
- Infinite set
- Two point set
5. {x : x ε Z⁺ and x < – 1 } is
- Empty set correct
- Singleton set
- A set with two points
- A set with three points
6. A subset A of B which is different from the set B itself, is
- Not a subset of B
- Superset of B
- Improper subset of B
- Proper subset of B correct
7. The number of subsets of a set of 4 elements:
- 16 correct
- 4
- 8
- 6
8. The set of rational numbers Q is a subset of
- The set of complex numbers C correct
- The set of natural numbers N
- The set of integers Z
- The set even integers E
9. A set containing only one element is called the
- Empty set
- Null set
- Solution set
- Singleton set correct
10. If every element of a set A is also element of set B, then
- A ∩ B = φ
- B⊆A
- None of these
- A⊆B correct
11. If A⊆B and B⊆A, then
- A = φ
- A∩B = φ
- B = φ
- A = B correct
12. A ⊇B means
- A is equal to B
- A is a superset of B correct
- A is equivalent to B
- A is a subset of B
13. The set {{1, 2, 3}, {4, 5}} has
- Two elements correct
- Five elements
- One element
- Infinite elements
14. If B⊆A, then the complement of B in A is Bc =
- A∪B
- A – B correct
- B – A
- A∩B
15. {x|x ε N, x ≤ 10} is the
- Set builder method correct
- Descriptive method
- Non-descriptive method
- Tabular method
16. The union of two sets A and B is
- A = B
- A ≠ B
- A ∩B
- A ∪ B correct
17. The set A is
- Improper subset of A correct
- Not a subset of A
- Proper subset of A
- Not a superset of A
18. {x|x = p/q , p, q ε Z ^ q ≠ 0} is set of all
- Integers
- Irrational numbers
- Natural numbers
- Rational numbers correct
19. The set of real numbers R is a subset of
- The set of even integers E
- The set of natural numbers N
- The set of complex numbers C correct
- The set if integers Z
20. The intersection of two sets A and B is
- A = B
- A ∪B
- A ≠ B
- A∩B correct
21. If n(A) = m, then nP(A)=
- 2n
- 3m
- 2m correct
- 2²m
22. The set of students of your class is
- Infinite set
- Empty set
- Finite set correct
- Null set
23. If A = { }, then P(A) =
- Empty set
- { 0 }
- None of these
- { φ } correct
24. φ is
- Singleton set
- A set with three points
- A set with two points
- Empty set correct
25. If there is at least one element of B which is not in A, then
- A = B
- B = φ
- A ≠ B correct
- A∪B = φ
Conclusion
A strong grasp of mathematics sets functions and groups is crucial for excelling in the ECAT mathematics section. Understanding set operations, function properties, and group theory principles will help students solve complex mathematical problems efficiently.
Conceptual understanding, regular practice, and problem-solving techniques make one perfect in this topic. With the help of structured preparation and MCQ solving, candidates will be able to improve their test performance and score high on the ECAT. These topics are crucial not only for ECAT but also as a foundation to further her studies in engineering and mathematics.