Daily Practice Problems undefined Continuity and Differentiability

Question1:

The derivative of at is [Level: Easy]

(a)

(b)

(d) none of these.

Question2:

A function satisfies the equation and . If is differentiable at and , then is equal to [Level: Difficult]

(a)

(b)

(c)

(d) none of these.

Question3:

If , then is equal to [Level: Difficult]

(a)

(b)

(d) 0, .

Question4:

Let and , then [Level: Moderate]

(a) and are continuous at

(b) and are differentiable at

(d) and are not differentiable at .

Question5:

The and is continuous at , then is equal to [Level: Moderate]

(a)

(b)

(c)

(d) none of these.

Question6:

If is continuous function and discontinuous, then [Level: Moderate]

(a) must be continuous

(b) must be discontinuous

(d) none of these.

Question7:

If , then is [Level: Easy]

(a) continuous but not differentiable for all x

(b) continuous and differentiable for all x

(d) continuous but not differentiable at .

Question8:

The function is defined as Then the value of to be assigned at so that the function is continuous, is [Level: Easy]

(a)

(b)

(c)

(d) .

Question9:

Let be the inverse of an invertible function which is differentiable at , then is equal to [Level: Easy]

(a)

(b)

(c)

(d) none of these.

Question10:

If and . Then is [Level: Easy]

(a) continuous at

(b) not continuous at

(d) not defined at .

Question11:

If , then derivative of at [Level: Moderate]

(a) is equal to

(b) is equal to

(d) does not exist.

Question12.

If is continuous at , then [Level: Moderate]

(a)

(b)

(c)

(d) .

Question13.

Let a function satisfies the equation , If is continuous at , then [Level: Moderate]

(a) is discontinuous

(b) is continuous

(d) none of these.

Question14.

Let . If is continuous in , then is equal to [Level: Moderate]

(a)

(b)

(c)

(d) .

Question15.

The function , where denotes the greatest integer function, then is discontinuous at [Level: Moderate]

(a) all integer points

(b) all x

(d) all non-integer points.

Question16.

The function is [Level: Moderate]

(a) Continuous at

(b) not continuous at

(d) none of these.

Question17.

Let and , where and , then is equal to [Level: Difficult]

(a)

(b)

(c)

(d) .

Question18.

If the derivative of the function is everywhere continuous and is given by

, then [Level: Moderate]

(a)

(b)

(c)

(d) .

Question19.

Let be defined for all and be continuous. Let satisfy and . Then [Level: Difficult]

(a) is bounded

(b) as x→0

(d) .

Question20.

If a function is defined as, then [Level: Difficult]

(a) is continuous at but not differentiable at

(b) is continuous as well as differentiable at

(d) none of these.

**********

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Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic JEE Maths Continuity and Differentiability 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.
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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 Continuity and Differentiability JEE Maths Notes on LearnoHub.com
Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Continuity and Differentiability. 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 Continuity and Differentiability JEE Maths Online Tests at LearnoHub.com.
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In summary, problem-solving after learning a theoretical concept on CBSE Continuity and Differentiability JEE 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 JEE Maths Continuity and Differentiability NCERT Chapter 5

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 JEE Maths Continuity and Differentiability NCERT Chapter 5 useful.

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