All Courses
Get the App Signup / Login
Sign in Open App
RPSC RAS (Rajasthan) Exam  >  RPSC RAS (Rajasthan) Notes  >  RAS RPSC Prelims Preparation - Notes, Study Material & Tests  >  3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) PDF Download

This module will teach you the basics of direct and indirect proportions. These concepts will further help you in time and work questions.

Important Formulas – chain rule

  • Direct Proportion

    Two quantities are said to be directly proportional, if on the increase or decrease of the one, the other increases or decreases the same extent.

Examples

  1. Cost of the goods is directly proportional to the number of goods. (More goods, More cost)
  2. Amount of work done is directly proportional to the number of persons who did the work. (More persons, More Work)
  • Indirect Proportion (inverse proportion)

    Two quantities are said to be indirectly proportional (inversely proportional) if on the increase of the one, the other decreases to the same extent and vice-versa.

    Examples
     
  • Number of days needed to complete a work is indirectly proportional (inversely proportional) with the number of persons who does the work (More Persons, Less Days needed)
  • The time taken to travel a distance is indirectly proportional (inversely proportional) with the speed in which one is travelling (More Speed, Less Time)

Solved Examples
 

1. If the cost of x metres of wire is d rupees, then what is the cost of y metres of wire at the same rate?

A. Rs. (xd/y)

B. Rs. x/d

C. Rs. (yd/x)

D. Rs. y/d

 

Answer : Option C

Explanation :

cost of x metres of wire = Rs. d

cost of 1 metre of wire = Rs.(d/x)

cost of y metre of wire = Rs.(y×d/x)=Rs. (yd/x)

2. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?

A. 50

B. 30

C. 40

D. 10

 

Answer : Option B

Explanation :

Meal for 200 children = Meal for 120 men

Meal for 1 child = Meal for 120/200 men

Meal for 150 children = Meal for (120×150)/200 men=Meal for 90 men

Total mean available = Meal for 120 men

Renaming meal = Meal for 120 men - Meal for 90 men = Meal for 30 men

3. 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

A. 26

B. 22

C. 12

D. 24

 

Answer : Option D

Explanation :

Let the required number of days be x

More men, less days (indirect proportion)

Hence we can write as

Men36:27}::x:18 ⇒36×18=27×x ⇒12×18=9×x

⇒12×2=x

⇒x=24


4. A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the larger wheel?

A. 15

B. 12

C. 21

D. 9

 

Answer : Option D

Explanation :

Let the number of revolutions made by the larger wheel be x

More cogs, less revolutions (Indirect proportion)

Hence we can write as

Cogs 6:14}: x: 21 ⇒6×21=14×x ⇒6×3=2×x ⇒3×3=x ⇒x=9

5. 3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day should 4 pumps work in order to empty the tank in 1 day?

A. 10

B. 12

C. 8

D. 15

 

Answer : Option B

Explanation :

Let the required hours needed be x

More pumps, less hours (Indirect proportion)
More Days, less hours (Indirect proportion)

Hence we can write as

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan)

⇒3×2×8=4×1×x

 ⇒3×2×2=x

⇒x=12

6. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

A. 9

B. 12

C. 10

D. 13

 

Answer : Option D

Explanation :
Let the required number of days be x

More hours, less days (indirect proportion)

Hence we can write as

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan)

⇒39×5×12=30×6×x ⇒39×5×2=30×x ⇒39=3×x ⇒x=13

7. A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?

A. 205

B. 200

C. 180

D. 195

 

Answer : Option D

Explanation :

Let the required number of seconds be x

More cloth, More time, (direct proportion)

Hence we can write as

Cloth         0.128:25} :: 1:x

⇒0.128x=25 ⇒x=25/0.128 ⇒25000/128=3125/16≈195

8. 21 goats eat as much as 15 cows. How many goats each as much as 35 cows?

A. 49

B. 32

C. 36

D. 41

 

Answer : Option A

Explanation :

15 cows ≡ 21 goats

1 cow ≡21/15 goats

35 cows ≡ (21×35)/15 goats≡(21×7)/3 goats≡7×7 goats ≡ 49 goats

The document 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) is a part of the RPSC RAS (Rajasthan) Course RAS RPSC Prelims Preparation - Notes, Study Material & Tests.
All you need of RPSC RAS (Rajasthan) at this link: RPSC RAS (Rajasthan)
109 docs|21 tests
Join Course for Free

Top Courses for RPSC RAS (Rajasthan)

FAQs on 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC - RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan)

1. What is the chain rule in calculus?
Ans. The chain rule is a fundamental concept in calculus that allows us to find the derivative of a composite function. It states that if we have a function composed of two or more functions, then the derivative of the composite function can be found by multiplying the derivatives of the individual functions and following a specific formula.
2. How is the chain rule applied in solving mathematical problems?
Ans. The chain rule is applied by first identifying the composite function and breaking it down into its individual functions. Then, we find the derivative of each individual function. Finally, we multiply the derivatives together according to the chain rule formula to obtain the derivative of the composite function.
3. What is the importance of the chain rule in real-world applications?
Ans. The chain rule is essential in real-world applications involving rates of change. It allows us to analyze complex systems by breaking them down into simpler functions and understanding how changes in one variable affect the overall system. For example, in physics, the chain rule is used to calculate velocities, accelerations, and other derivatives in motion problems.
4. Can you provide an example of how to use the chain rule in solving a problem?
Ans. Sure! Let's say we have a function f(x) = sin(3x^2 + 2x). To find the derivative of this function, we can apply the chain rule. First, we identify the inner function as g(x) = 3x^2 + 2x and the outer function as h(x) = sin(x). Taking the derivatives, we get g'(x) = 6x + 2 and h'(x) = cos(x). Finally, we apply the chain rule formula: f'(x) = g'(x) * h'(g(x)). Therefore, f'(x) = (6x + 2) * cos(3x^2 + 2x).
5. Are there any common mistakes to avoid when using the chain rule?
Ans. Yes, there are a few common mistakes to avoid when using the chain rule. One mistake is forgetting to multiply the derivatives of the individual functions together. Another mistake is mixing up the order of the functions when applying the chain rule formula. It's important to correctly identify the inner and outer functions to ensure the correct application of the chain rule. Additionally, being cautious about simplifying expressions too early or incorrectly can also lead to mistakes.
Related Exams
About this Document
4.78/5 Rating
Dec 18, 2024 Last updated
Document Description: 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC for RPSC RAS (Rajasthan) 2024 is part of RAS RPSC Prelims Preparation - Notes, Study Material & Tests preparation. The notes and questions for 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC have been prepared according to the RPSC RAS (Rajasthan) exam syllabus. Information about 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC covers topics like and 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC Example, for RPSC RAS (Rajasthan) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC.
Introduction of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC in English is available as part of our RAS RPSC Prelims Preparation - Notes, Study Material & Tests for RPSC RAS (Rajasthan) & 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC in Hindi for RAS RPSC Prelims Preparation - Notes, Study Material & Tests course. Download more important topics related with notes, lectures and mock test series for RPSC RAS (Rajasthan) Exam by signing up for free. RPSC RAS (Rajasthan): 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan)
Description
Full syllabus notes, lecture & questions for 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes, Study Material & Tests - RPSC RAS (Rajasthan) - RPSC RAS (Rajasthan) | Plus excerises question with solution to help you revise complete syllabus for RAS RPSC Prelims Preparation - Notes, Study Material & Tests | Best notes, free PDF download
Information about 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC
In this doc you can find the meaning of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC defined & explained in the simplest way possible. Besides explaining types of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC theory, EduRev gives you an ample number of questions to practice 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC tests, examples and also practice RPSC RAS (Rajasthan) tests
109 docs|21 tests
Join Course for Free
Download as PDF
Explore Courses for RPSC RAS (Rajasthan) exam

Top Courses for RPSC RAS (Rajasthan)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes

,

past year papers

,

practice quizzes

,

mock tests for examination

,

study material

,

Study Material & Tests - RPSC RAS (Rajasthan)

,

ppt

,

Semester Notes

,

Sample Paper

,

shortcuts and tricks

,

Important questions

,

Study Material & Tests - RPSC RAS (Rajasthan)

,

Free

,

pdf

,

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes

,

MCQs

,

Exam

,

Previous Year Questions with Solutions

,

Viva Questions

,

Study Material & Tests - RPSC RAS (Rajasthan)

,

video lectures

,

Summary

,

Objective type Questions

,

Extra Questions

,

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC | RAS RPSC Prelims Preparation - Notes

;
Additional Information about 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC for RPSC RAS (Rajasthan) Preparation

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC Free PDF Download

The 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC is an invaluable resource that delves deep into the core of the RPSC RAS (Rajasthan) exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC now and kickstart your journey towards success in the RPSC RAS (Rajasthan) exam.

Importance of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC

The importance of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC cannot be overstated, especially for RPSC RAS (Rajasthan) aspirants. This document holds the key to success in the RPSC RAS (Rajasthan) exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC Notes

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC. It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC Notes on EduRev are your ultimate resource for success.

3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC RPSC RAS (Rajasthan) Questions

The "3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC RPSC RAS (Rajasthan) Questions" guide is a valuable resource for all aspiring students preparing for the RPSC RAS (Rajasthan) exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC on the App

Students of RPSC RAS (Rajasthan) can study 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC, students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of 3. Chain Rule; Quantitative Aptitude; Civil Service Examination; RPSC is prepared as per the latest RPSC RAS (Rajasthan) syllabus.
© EduRev
Education Revolution
Follow Us
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup