Explore Exams
Login Signup
Sign in Open App
CAT Exam  >  CAT Notes  >  100 DILR Questions for CAT Preparation  >  Practice Question - 72 (Maxima Minima)

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation PDF Download

A new game show on TV has 100 boxes numbered 1, 2, . . . , 100 in a row, each containing a mystery prize. The prizes are items of different types, a, b, c, . . . , in decreasing order of value. The most expensive item is of type a, a diamond ring, and there is exactly one of these. You are told that the number of items at least doubles as you move to the next type. For example, there would be at least twice as many items of type b as of type a, at least twice as many items of type c as of type b and so on. There is no particular order in which the prizes are placed in the boxes.

Q1: What is the minimum possible number of different types of prizes?

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

Ans: 2
It is given that the most expensive item is a diamond ring of type a and there is exactly one of these. Since the item b should be at least twice. The minimum number of items will be obtained when a = 1 and b = 99, which means there are only two different types of items.

Q2: What is the maximum possible number of different types of prizes?

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

Ans: 6
It is given that the most expensive item is a diamond ring of type a and there is exactly one of these. Since the number of items of type b should be at least twice of that of a and the number of items of type c should be at least twice of that of b and so on. So the maximum number of different types of items of a, b, and c will be obtained when a = 1, b = 2, c = 4, d = 8, e = 16, f = 69. Hence the maximum number of different types of items will be 6.
If the number of items is 7, then the minimum number of prizes should be 1 + 2 + 4 + 8 + 16 + 32 + 64 = 127 which is more than 100.
Hence 6 is the answer.

Q3: Which of the following is not possible?
(a) There are exactly 75 items of type e.
(b) There are exactly 30 items of type b.
(c) There are exactly 45 items of type c.
(d) There are exactly 60 items of type d.

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

Ans: (c)
Option (a): There are exactly 75 items of type e.
a = 1, b = 2, c = 4, d = 8, e = 85. Here the maximum value of e = 85. Hence it can take the value 75.
An example of such case is a = 1, b = 2, c = 4, d = 18, e = 75
Option (b): There are exactly 30 items of type b.
a = 1 b = 30 and c = 69. Hence this case is also possible.
Option (c): There are exactly 45 items of type c.
Since the value of d should be at least 90, it means that d is not present because 45 + 90 will be more than 100 (maximum number of items). Only a, b and c are present.
The maximum value of b = 22 and a =1, but 45 + 22 + 1 = 68, which is less than 100. So this case is not possible.
Option (d): There are exactly 60 items of type d.
d = 60, c = 30, b = 9 and a = 1. a + b + c + d = 100. Hence this case is possible.
C is the answer.

Q4:  You ask for the type of item in box 45. Instead of being given a direct answer, you are told that there are 31 items of the same type as box 45 in boxes 1 to 44 and 43 items of the same type as box 45 in boxes 46 to 100.
What is the maximum possible number of different types of items?
(a) 5
(b) 6
(c) 4
(d) 3

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT PreparationView Answer  Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

Ans: (a)
The total number of items from 1 to 100, which are of same type as in box 45 = 31 + 1 + 43 = 75
Now to maximize the number of items, a = 1, b = 2, c = 4, d = 18 and e = 75(given)
There can be maximum 5 types of items.
If we consider number of items to be 6, then minimum number of items of 5th type will be 16, 1 + 2 + 4 + 8 + 16 + 75 = 106 which is more than 100.

The document Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation is a part of the CAT Course 100 DILR Questions for CAT Preparation.
All you need of CAT at this link: CAT
102 videos|123 docs|121 tests
Join Course for Free

FAQs on Practice Question - 72 (Maxima Minima) - 100 DILR Questions for CAT Preparation

1. What are maxima and minima in calculus?
Ans. Maxima and minima refer to the highest and lowest points on a function, respectively. A maximum point is a point where the function value is greater than the values at nearby points, while a minimum point is where the function value is less than those nearby points. These concepts are essential in optimization problems, where one seeks to find the best solution under given constraints.
2. How do you determine if a critical point is a maximum or minimum?
Ans. To determine whether a critical point is a maximum or minimum, you can use the second derivative test. If the second derivative of the function at that point is positive, the function is concave up, indicating a local minimum. If the second derivative is negative, the function is concave down, indicating a local maximum. If the second derivative is zero, the test is inconclusive, and you may need to use other methods.
3. What is the importance of the first derivative in finding maxima and minima?
Ans. The first derivative of a function provides information about the slope of the function. By finding where the first derivative is equal to zero, you can identify critical points, which are potential locations for maxima and minima. Analyzing the sign of the first derivative before and after these critical points helps determine whether the function is increasing or decreasing, thus identifying whether the critical point is a maximum or minimum.
4. Can you explain the concept of global maxima and minima?
Ans. Global maxima and minima refer to the absolute highest and lowest points of a function over its entire domain. A function may have multiple local maxima and minima, but the global maximum is the highest value of the function across all points, while the global minimum is the lowest. Finding global extrema can be more complex, especially for functions defined over a closed interval or those involving constraints.
5. What role do constraints play in optimization problems involving maxima and minima?
Ans. Constraints limit the possible solutions in optimization problems. When a function is maximized or minimized subject to constraints, methods such as Lagrange multipliers can be used. This technique allows you to find the extrema of a function while satisfying the given constraints, ensuring that the solution is feasible within the defined boundaries of the problem.
About this Document
Sep 04, 2025 Last updated
Related Exams
CAT
Document Description: Practice Question - 72 (Maxima Minima) for CAT 2025 is part of 100 DILR Questions for CAT Preparation preparation. The notes and questions for Practice Question - 72 (Maxima Minima) have been prepared according to the CAT exam syllabus. Information about Practice Question - 72 (Maxima Minima) covers topics like and Practice Question - 72 (Maxima Minima) Example, for CAT 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Practice Question - 72 (Maxima Minima).
Introduction of Practice Question - 72 (Maxima Minima) in English is available as part of our 100 DILR Questions for CAT Preparation for CAT & Practice Question - 72 (Maxima Minima) in Hindi for 100 DILR Questions for CAT Preparation course. Download more important topics related with notes, lectures and mock test series for CAT Exam by signing up for free. CAT: Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation
Description
Full syllabus notes, lecture & questions for Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation - CAT | Plus excerises question with solution to help you revise complete syllabus for 100 DILR Questions for CAT Preparation | Best notes, free PDF download
Information about Practice Question - 72 (Maxima Minima)
In this doc you can find the meaning of Practice Question - 72 (Maxima Minima) defined & explained in the simplest way possible. Besides explaining types of Practice Question - 72 (Maxima Minima) theory, EduRev gives you an ample number of questions to practice Practice Question - 72 (Maxima Minima) tests, examples and also practice CAT tests
102 videos|123 docs|121 tests
Join Course for Free
Download as PDF
Explore Courses for CAT exam
Related Searches

practice quizzes

,

Semester Notes

,

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

,

Extra Questions

,

Sample Paper

,

Free

,

ppt

,

shortcuts and tricks

,

study material

,

Objective type Questions

,

MCQs

,

Exam

,

Summary

,

Viva Questions

,

video lectures

,

mock tests for examination

,

Previous Year Questions with Solutions

,

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

,

Practice Question - 72 (Maxima Minima) | 100 DILR Questions for CAT Preparation

,

Important questions

,

pdf

,

past year papers

;
Additional Information about Practice Question - 72 (Maxima Minima) for CAT Preparation

Practice Question - 72 (Maxima Minima) Free PDF Download

The Practice Question - 72 (Maxima Minima) is an invaluable resource that delves deep into the core of the CAT 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 Practice Question - 72 (Maxima Minima) now and kickstart your journey towards success in the CAT exam.

Importance of Practice Question - 72 (Maxima Minima)

The importance of Practice Question - 72 (Maxima Minima) cannot be overstated, especially for CAT aspirants. This document holds the key to success in the CAT 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.

Practice Question - 72 (Maxima Minima) Notes

Practice Question - 72 (Maxima Minima) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to Practice Question - 72 (Maxima Minima). 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, Practice Question - 72 (Maxima Minima) Notes on EduRev are your ultimate resource for success.

Practice Question - 72 (Maxima Minima) CAT Questions

The "Practice Question - 72 (Maxima Minima) CAT Questions" guide is a valuable resource for all aspiring students preparing for the CAT 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 Practice Question - 72 (Maxima Minima) on the App

Students of CAT can study Practice Question - 72 (Maxima Minima) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the Practice Question - 72 (Maxima Minima), 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 Practice Question - 72 (Maxima Minima) is prepared as per the latest CAT syllabus.
© EduRev
Education Revolution
Signup to see your scores go up
within 7 days!
Takes less than 10 seconds to signup