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Class 12 Jac Board 2024

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Questions and Answers

In set theory, if A = {1, 2, 3} and B = {2, 3, 4}, what is A ∩ B?

{2, 3, 4}

{1, 2, 3, 4}

{2, 3} (correct)

{1, 4}

In a function f(x) = 2x + 3, what is the value of f(4)?

11 (correct)

What is the range of the function g(x) = x^2 + 1?

y ≥ 1

y ≥ 0 (correct)

y > 1

y > 0

Explain the concept of relations in the context of mathematics.

Relations in mathematics refer to the connections or associations between two or more sets of elements. These connections can be represented by ordered pairs, where the first element is related to the second element in some way. Relations can be classified as reflexive, symmetric, transitive, or equivalence relations, and are fundamental in understanding functions and mappings. Signup and view all the answers

What is the difference between a function and a relation?

A relation is a set of ordered pairs, while a function is a specific type of relation where each input value (domain) is associated with exactly one output value (range). In other words, a function is a special kind of relation in which each input is related to exactly one output. Signup and view all the answers

Discuss the significance of studying relations and functions in the context of class 12 mathematics.

Studying relations and functions is crucial in mathematics as it provides a foundation for understanding various mathematical concepts and applications. Relations and functions help in modeling real-world situations, analyzing data, and solving problems in fields such as science, engineering, economics, and computer science. Additionally, they form the basis for advanced topics in calculus, algebra, and discrete mathematics, making them essential for further studies in these areas. Signup and view all the answers

Study Notes

Set Theory and Intersection

A = {1, 2, 3}
B = {2, 3, 4}
Intersection A ∩ B = {2, 3}, containing elements common to both sets.

Function Evaluation

Given function f(x) = 2x + 3
For f(4), substitute x with 4: f(4) = 2(4) + 3 = 8 + 3 = 11.

Function Range

g(x) = x² + 1, a quadratic function.
The minimum value occurs at x = 0: g(0) = 1.
Therefore, the range of g(x) is [1, ∞).

Concept of Relations in Mathematics

A relation is a set of ordered pairs, representing a connection between two sets.
Can be defined over various domains and codomains, showcasing how elements relate to one another.

Difference Between Function and Relation

A function is a specific type of relation where each input has exactly one output.
In contrast, a general relation may associate a single input with multiple outputs.

Importance of Studying Relations and Functions

Vital in understanding mathematical concepts and real-world applications in class 12 mathematics.
Forms the foundation for advanced topics like calculus and algebra, aiding in problem-solving and analytical skills.

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Description

Test your knowledge of relations and functions in Class 12 Jac board 2024 with this quiz. Explore set theory by finding the intersection of sets A and B, calculate the value of a function at a specific point, and determine the range of a given function. Strengthen your grasp of these fundamental concepts with this quiz.