Daily Practice Problems undefined Relations and Functions

Question 1:

Let A = {a, b, c}, then the range of the relation R = {(a, b), (a, c), (b, c)} defined on A is

(a) {b, c}

(b) {c}

(d) {a, b, c}

Question 2:

Find the domain of function f(x) =

Question 3:

Draw the graph of the step function f(x) = [x].

Question 4:

Find the domain of the real function: f(x) =

Question 5:

The range of the function f(x) = |x - 1| is

(a) R

(b) (-∞, 0)

(d) [0, ∞)

Question 6:

Let A = {-2, -1, 0, 1, 2} and f : A -> Z be given by f(x) = x² - 2x – 3. Find the pre image of 6, -3 and 5.

Question 7:

If A = (1, 2, 3), B = {4}, C = {5}, then verify that A * (B - C) = (A * B) - (A * C).

Question 8:

Number of relations that can be defined on the set A = {a, b, c, d} is

(a) 24

(b) 4⁴

(d) 2¹⁶

Question 9:

Let R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b²}. Are the following true?

(i) (a, a) ∈ R for all a ∈ N

(ii) (a, b) ∈ R implies (b, a) ∈ R

(iii) (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.

Justify your answer in each case.

Question 10:

Find the range of the function f(x) =

Question 11:

Find the range of the relations: R = {(a, b) : a, b N and 2a + b = 10}.

Question 12:

Find the domain and the range of the real function: f(x) =

Question 13:

Let A = {2, 3,4, 5, 6, 7, 8, 9}. Let R be the relation on A defined by {(x, y): x, y ∈ A, x is a multiple of y and x ≠ y}.

(a) Find the relation.

(b) Find the domain of R.

(d) Find the inverse relation.

Question 14:

Which of the following is not a function?

(a) {x, y : x, y ∈ R, y = }

(b) {x, y : x, y ∈ R, }

(d) {x, y : x, y ∈ R, x = }

Question 15:

Let A = {1, 3, 5}, B = {x, y}. Represent the product B * B by arrow diagram.

Question 16:

Let R be set of points inside a rectangle of sides a and b (a, b > 1) with two sides along the positive direction of x-axis and y-axis. Then

(a) R = {(x, y) : 0 ≤ x ≤ a, 0 ≤ y ≤ b}

(b) R = {(x, y) : 0 ≤ x < a, 0 ≤ y ≤ b}

(d) R = {(x, y) : 0 ≤ x ≤ a, 0 < y < b}

Question 17:

Let A and B be two non-empty sets such that n(A) = 5, n(B) = 6 and n(A ∩ B) = 3. Find

(a) n(A × B)

(b) n(B × A)

Question 18:

Find the values of a and b, if

(a) (2a - 5, 4) = (5, b + 6)

(b) (a - 3, b + 7) = (3, 7)

Question 19:

Let A = {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by R = {(a, b): a, b ∈ A, b is exactly divisible by a}. Find the range of R.

Question 20:

The function f is defined as

Draw the graph of f(x).

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Problem-solving on Class 11 Maths Relations and Functions NCERT Chapter 2 after learning a theoretical concept is crucial for several reasons:

Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 11 Maths Relations and Functions you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 11 Maths Relations and Functions NCERT Chapter 2, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Relations and Functions Class 11 Maths in practical scenarios helps you remember them better than passive reading or memorization.
Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Relations and Functions Class 11 Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Relations and Functions. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Relations and Functions Class 11 Maths Online Tests at LearnoHub.com.
Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.

In summary, problem-solving after learning a theoretical concept on CBSE Relations and Functions Class 11 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.

You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.

Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.

All About Daily Practice Problems on Class 11 Maths Relations and Functions NCERT Chapter 2

Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 11 Maths Relations and Functions NCERT Chapter 2 useful.

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Relations and Functions Class 11 Maths NCERT Solutions
Class 11 Maths Relations and Functions Revision notes
Relations and Functions Class 11 Maths DPPs, Download PDF of solutions
Class 11 Maths Relations and Functions Online Tests
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