The Chain Rule is a fundamental concept in calculus that plays a crucial role in various examinations. Mastering this topic not only enhances your understanding of derivatives but also boosts your confidence in solving complex problems. Practicing MCQs and objective questions on the Chain Rule is essential for effective exam preparation, helping you identify important questions and improve your problem-solving speed.
What You Will Practise Here
Understanding the definition and significance of the Chain Rule
Application of the Chain Rule in differentiation
Identifying functions suitable for the Chain Rule
Solving problems involving multiple functions
Using the Chain Rule in real-world scenarios
Common derivatives involving the Chain Rule
Diagrams illustrating the Chain Rule concept
Exam Relevance
The Chain Rule is frequently tested in various examinations, including CBSE, State Boards, NEET, and JEE. Students can expect to encounter questions that require them to apply the Chain Rule to differentiate composite functions. Common question patterns include direct application problems, as well as those that involve multiple steps and require a clear understanding of the underlying concepts.
Common Mistakes Students Make
Confusing the order of differentiation when applying the Chain Rule
Neglecting to identify all functions involved in a composite function
Overlooking the need to simplify expressions before differentiating
Misapplying the Chain Rule to functions that do not require it
FAQs
Question: What is the Chain Rule in calculus? Answer: The Chain Rule is a formula used to compute the derivative of a composite function, allowing you to differentiate functions that are nested within each other.
Question: How can I practice Chain Rule MCQ questions effectively? Answer: You can practice Chain Rule MCQ questions by solving objective questions available on educational platforms like SoulShift, which provide a variety of practice questions tailored for exam preparation.
Don't wait any longer! Start solving Chain Rule practice MCQs today to solidify your understanding and excel in your exams. Your success is just a question away!
Q. A car travels 60 km in 1 hour. If it increases its speed by 20%, how far will it travel in 1.5 hours?
A.
90 km
B.
100 km
C.
110 km
D.
120 km
Solution
New speed = 60 + (20% of 60) = 60 + 12 = 72 km/h. Distance in 1.5 hours = 72 * 1.5 = 108 km.
Q. A man sells two articles for $120 each. If he makes a profit of 20% on the first and a loss of 20% on the second, what is his overall profit or loss percentage?
A.
0%
B.
5%
C.
10%
D.
20%
Solution
Cost price of first article = 120 / 1.2 = $100. Cost price of second article = 120 / 0.8 = $150. Total cost price = 100 + 150 = $250. Total selling price = 120 + 120 = $240. Overall loss = 250 - 240 = $10. Loss percentage = (10 / 250) * 100 = 4%.
Q. A man sells two articles for $120 each. If he makes a profit of 20% on the first article and a loss of 20% on the second article, what is his overall profit or loss percentage?
A.
0%
B.
5%
C.
10%
D.
15%
Solution
Cost price of first article = 120 / 1.2 = $100. Cost price of second article = 120 / 0.8 = $150. Total cost price = 100 + 150 = $250. Total selling price = 120 + 120 = $240. Loss = 250 - 240 = $10. Loss percentage = (10 / 250) * 100 = 4%.
Q. If a man can complete a work in 10 days and another man can complete the same work in 15 days, how long will it take for both to complete the work together?
A.
6 days
B.
8 days
C.
10 days
D.
12 days
Solution
Work done by first man in one day = 1/10. Work done by second man in one day = 1/15. Together they do = 1/10 + 1/15 = 1/6. Therefore, they will complete the work in 6 days.
