Great Lakes - PGPM & PGDM 2025
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Application Deadline: 10th March 2025
We're back with a strategy for the Day 19 of our preparation for the CAT 2024. In this article, we will be discussing strategies for the following topics: Maxima and Minima Questions for CAT, problem-solving questions in maths, Puzzle-solving questions, Logical Reasoning puzzles for CAT exam and questions from CAT previous year papers.
With the 60-day CAT exam preparation schedule we created for you, you can ace the CAT 2024 and get a flow, plan, and schedule for your preparation.
Maxima Minima CAT Questions are used to find the maximum or minimum possible value of a function.
Because the shape of the graph depends on these values.
Example:
In a polynomial function, the maxima is the highest point and the minima is the lowest point and the graph looks like a parabola.
Depending on the function, there are several ways to find the maximum and minimum value of a function.
Two main methods are:
Graphical method: In the graphical method, we have to plot the polynomial function on a coordinate plane and visually identify the highest and lowest points on the graph.
Algebraic method: In the algebraic method, we use calculus to find the critical points and then determine whether these points are maxima, minima, or neither.
In maxima minima aptitude questions, the function given can be:
Quadratic function
Linear function
Polynomial function etc.
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Application Deadline: 10th March 2025
250+ Companies | Highest CTC 16 LPA | Average CTC 8 LPA | Ranked as Platinum Institute by AICTE for 6 years in a row
For such functions, we need to find the maximum or minimum values.
We need to study “local Maxima and Minima ”, “maxima and minima formula”, “absolute maxima and minima”, “Maxima and Minima calculator”, and “global maxima and minima” for more details.
Here are some tips and tricks to solve maxima minima aptitude questions:
If the sum of positive numbers is constant then their product is maximum when all numbers are equal.
Example:
a + b + c = 36, find maximum value of a.b.c
The answer is (36/3)3 = 1728
Arithmetic Mean ≥ Geometric Mean
a + b + c = 11; find Maximum value of a3 × b4 × c5
a + b + c = a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5 = 11
Now, AM ≥ GM
So, (a/3 + a/3 + a/3 + b/4 + b/4 + b/4 + b/4 + c/5 + c/5 +c/5 + c/5 + c/5)/12 ≥ (a/3 .a/3 .a/3 .b/4 .b/4 .b/4 .b/4 .c/5 .c/5 .c/5 .c/5 .c/5)1/12
⇒ (11/12)12 ≥ (a/3)3 .(b/4)4 . (c/5)5
⇒ a3. b4. c5 ≤ 33 × 44 × 55 × (11/12)12
Trick: To solve Maxima and Minima Questions, we can use the following trick.
Divide 11 in the ratio 3 : 4 : 5
i.e., a = (11/12)3; b = (11/12)4; c = (11/12)5
So, a3. b4. c5 = 33 × 44 × 55 × (11/12)12 (After putting the values of a, b and c)
For a quadratic equation:
If the minimum value is to be found, convert the equation in the form of (a – b)2 + k.
(Minimum value is k)
Example: find the minimum value of a2 + 26 – 4a
a2 + 26 – 4a = (a – 2)2 + 22;
Minimum value is 22
To find the maximum value of a function f(x) can be calculated with the help of a method of derivative.
Step 1: find f’(x) i.e., the first derivative.
Step 2: Put f’(x) = 0, and find values of x for which function is either maximum or minimum.
Let the values of x be x1 and x2.
Step 3: Find f’’(x) i.e., the second derivative.
If f’’(x) > 0 at x = x1 then the function gives minimum value at x = x1.
If f’’(x) < 0 at x = x2 then the function gives the minimum value at x = x2.
These are local maxima and local minima.
Learn the above concepts well and apply them to solve questions.
Learn basic rules of differentiation.
Use the graphical method to visually identify the maxima and minima.
If the problem involves a specific interval, evaluate the polynomial at the endpoints and compare it with critical points within the interval.
Q1. If three sides of a rectangular park have a total length of 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is:
[CAT Exam 2017]
Solution:
Let one side be a and the other side be b.
So, a + 2b = 400
⇒ 2b = 400-a
⇒ b = 400-a/2
Area = ab = a (400-a)/2 = (400a – a2)/2
To find maximum value of (400a – a2); differentiate with respect to a
dA/da = 400 – 2a = 0 (For maxima)
⇒ a = 200
So, b = 100
Therefore, the longer side will be 200 ft for maximum area.
Q2. An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?
[CAT exam 2017, TITA]
Solution:
Each person must weigh 53 Kg or more.
So, remaining weight = 630 – 53 – 57 = 520
Therefore, no of remaining persons n ≤ 520/53
So, n ≤ 10 (For maximum value n = 9)
Therefore, total persons in the elevator = 9 + 2 = 11
Q3. If a and b are non-negative real numbers such that a + 2b = 6, then the average of the maximum and minimum possible values of (a + b) is:
[CAT 2022 Slot 2]
3
4
3.5
4.5
Solution:
a + 2b = 6
From the above equation, we can say that the maximum value b can take is 3 and the minimum value b can take is 0.
a + b + b = 6
a + b = 6 - b
a + b is maximum when b is minimum, i.e. b = 0
Maximum value of a + b = 6 - 0 = 6
a + b is minimum when b is maximum, i.e., b = 3
Minimum value of a + b = 6 - 3 = 3
∴ Average = (6 + 3) / 2 = 4.5
Hence, the correct answer is 4.5.
Q4. The minimum possible value of (x2 – 6x + 10) / (3 – x), for x < 3 is:
–½
2
½
–2
Solution:
(x2 – 6x + 10) / (3 – x)
= (x2 – 6x + 9 +1) / (3 – x)
= (x2 – 6x + 9)/ (3 – x) + 1 / (3 – x)
= (x – 3)2 / (3 – x) + 1/ (3 – x)
As, (x – 3)2 = (3 – x)2,
We can write,
(3 – x)2 / (3 – x) + 1/ (3 – x)
= (3 – x) + 1/ (3 – x)
Since x < 3, (3 – x) is positive.
Let k = 3 – x
Since k is positive, the minimum value of k + 1/k = 2
Hence, the correct answer is 2.
Before practising Maxima and Minima Questions for CAT, students must be well-versed with
Function and Graph
Derivatives
Basic arithmetic identities,
CAT Exam: References to Study (Theory)
NCERT Class 12 (Chapter: Functions, Derivative, Maxima and Minima)
Functions and Graph (Arihant Publication)
2IIM CAT Preparation
CAT Exam: References to Practise Maxima and Minima Questions for CAT 2024
R D Sharma
https://bodheeprep.com/maxima-minima
Previous Year's Question Papers
The topic covered for the day and Logical Reasoning puzzles for the CAT exam are given below:
Placing objects or persons in a circular table following a specific rule is a Circular arrangement.
According to a given set of rules or instructions, persons are to be arranged circularly.
Aspirants can also download the following circular arrangement questions for CAT pdf. for further references.
Puzzles Solving Questions of Circular Arrangements involves the concept of Ranking , Blood Relation , Direction Sense etc.
It carries a good weightage in the CAT exam/SNAP and other MBA entrance Exams as seen in previous years.
Problem-solving questions in maths are generally based on:
Facing towards centre
Facing outward the centre
Facing in two different directions.
Knowledge of solving problems enables you:
To identify the unique position of a person in an arrangement.
To identify respective positions of persons.
Relations among the persons/ objects.
In the CAT exam, linear and circular arrangement questions for CAT are very common.
Students can also study “circular arrangement questions pdf” and “Logical Reasoning circular arrangement questions” to know further about this topic.
Based on the information given below, answer the questions: (SNAP)
Ten friends Matt, Sam, Pat, Tom, Sid, Alex, Kat, Jim, Jane and John are having dinner on a rectangular table. Eight face each other along the length of the table while two face each other along the smaller side of the table. Pat is sitting diagonally opposite to Kat, Alex is facing Jim, John is to the right of Jane, Tom is sitting between Sam and Jim, Pat is to the extreme left of Jane who is sitting on the extreme right along the length of the table. Sid is facing Tom and Matt is on the right of Sam.
Q1. Who do you think is sitting in front of each other along the small sides of the table? (CAT exam)
Matt and John
Matt and Sam
Matt and Kat
John and Sam
Answer: A
Q2. Sid is sitting between which of the following two? (CAT exam)
Sam and Kat
Pat and Alex
Alex and Jane
Kat and Jane
Answer: B
Q3. Who is sitting diagonally opposite to each other? (CAT exam)
Sid and Tom
Sam and Jane
Alex and Jim
Jane and Kat
Answer: B
Q4. Who is sitting to the immediate right of Jim (CAT exam)
Sam
Jane
Alex
Tom
Answer: D
Q5. Who is sitting in two places left to Jane? (CAT exam)
Pat
Alex
Sid
Sam
Answer: C
Solution:
Based on the information given above; the following arrangement be formed
For this read every piece of information very carefully and place the persons.
Knowledge of Ranking , Direction Sense and Blood Relation .
Knowledge of Linear Arrangement.
Tips and Tricks for Puzzle Solving Questions of Circular Arrangement
There is no specific formula to solve CAT Circular arrangement questions.
First, find the number of persons in the arrangement. Draw a circle or rectangle (as per the given condition) and mark their positions.
If the persons are facing away from the centre, the left of the persons/ objects will be in the anticlockwise direction and the right of the persons/ objects will be in the clockwise direction.
If the persons are facing towards the centre, the right of the persons/ objects will be in the anticlockwise direction and the left of the persons/ objects will be in the clockwise direction.
Questions on rectangular arrangements are to be solved in the same way.
Remember the information by short notations.
CAT Exam: References to Study Theory (CAT circular arrangement questions)
Verbal and Non-Verbal Reasoning by R S Agrawal
Cetking (YouTube Channel)
MBAP CAT EBook (Concept Theory)
CAT Exam: References to Practise Problem-Solving Questions in Maths
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
https://cetking.com/circular/
Previous Year's Question Papers
Correct Use of Articles is one of the most significant skills one should be aware of. “The” article is commonly used with an uncountable or countable noun, indefinite or definite noun, and plural or singular noun.
Sentence improvement questions based on articles are important for both the CAT exam and real life.
It is effective in the following ways:
If you want to rack your skills up in the verbal ability domain, then practise for sentence improvement based on Articles that should be a ‘not to be missed’ topic in your life.
Correct use of articles gives precise specifications about the noun.
With the knowledge of articles, one can easily enhance the quality of a sentence.
Adding articles to your sentence can help you to speak fluently.
Students can also practice “sentence improvement questions and answers pdf”, “sentence improvement rules pdf”, and “sentence improvement mcq” to grasp more about this topic.
Direction: Write the correct form of the underlined phrase.
Q1. Union Carbide Corporation (UCC) was asked to build a plant for manufacture of Sevin, a pesticide commonly used throughout Asia.
of manufacturing the Sevin,
As to manufacture of the Sevin,
for the manufacture of Sevin,
None of these
Answer: C
‘the’ should be used before “manufacture”.
Q2. CAT exam candidates are not allowed to use calculators during their examinations, although they are permitted to do so if certain models meet the requirements.
are not allowed using calculator
do not allowed using the calculator
are not allowed to use a calculator
No correction required
Answer: C
‘a’ should be used before the “calculator”.
Q3. After Geeta fought with Seeta, she moved to a second apartment.
had moved to second apartment
moved to the second apartment
had been moved to the second apartment
No correction required
Answer: B
‘the’ should be used before ‘second’.
Q4. The prime necessity, as the Director of ICRIER said, is to neutralise the amount of imports and exports in the country in a non-discriminatory manner.
neutralising amount of the imports and the exports
neutralise the amount of the imports and exports
neutralise the amount of imports and exports
No correction required
Answer: B
‘the’ should be used before “imports and exports”.
Basic Knowledge of Sentence Structure.
Basic Knowledge of the Usage of Articles.
Make sure you pay close attention to words whose first letters are vowels, but when they are pronounced, they have the sound of a consonant or vice versa. This is the case with words like university, an honest person, etc. For more details, you can head over to the Day-6 strategy.
Practice error-based questions daily.
Read newspapers, and listen to Ted Talks so that you will get more clarity about the uses of articles.
CAT Exam: References to Study (Theory)
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
Mastering A, An, The - English Articles Solved by Douglas Porter.
A' and 'The' Explained: A learner's guide to definite and indefinite articles by Seonaid Beckwith.
CAT Exam: References to Study (Practice)
The Article Book: Practice Toward Mastering a, an, and the by Tom Cole.
Oxford Practice Grammar (sixth edition)
engvid.com (Web)
Boost your CAT preparation with a comprehensive 60-day study material by Experts | Permutation & Combination - Important Concepts, Videos, Questions for CAT & Other MBA entrance exam |
With a 65 percentile in CAT, getting admission to USMS (Guru Gobind Singh Indraprastha University) may be difficult, as its cutoff is usually 75-85 percentile or higher for the general category.
However, you can consider other good MBA colleges that accept 60-70 percentile in CAT, such as:
Christ University, Bangalore
Institute of Public Enterprise, Hyderabad
Amrita School of Business, Kochi
PES University, Bangalore
KIIT School of Management, Bhubaneswar
Rajagiri Centre for Business Studies, Kochi
Army Institute of Management, Kolkata
Research their admission criteria, placements, and faculty to choose the best fit.
Hello
With a 65 percentile in CAT , USMS (GGSIPU) admission is difficult as its cutoffs are usually higher. However, you can explore private and tier-2/tier-3 MBA colleges that accept lower CAT scores.
Options to Consider:
1. Private MBA Colleges :
Amity University, Noida
LPU (Lovely Professional University)
Alliance University, Bangalore
Christ University, Bangalore
Apeejay School of Management, Delhi
2. B-Schools Accepting Lower CAT Percentile :
BIMTECH (PGDM-Retail/IB/Insurance)
XIME Bangalore
ITM Navi Mumbai
IPE Hyderabad
Jaipuria Institute of Management
3. Other Entrance Exams :
Appear for MAT, CMAT, XAT (low percentile accepted by some colleges)
Consider state-level exams like MAH CET, KMAT or TANCET .
Hope this gives you the clarity you need.
Hello there,
With your
academic profile (General, Male, Non-Engineer)
, you should
target MBA colleges that focus more on CAT percentile than past academics.
Target Colleges & Minimum CAT Percentile:
You
can
get a good MBA college with
strategic applications
and
high CAT/XAT percentile.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
Hi,
As per your given JEE Main percentile which is 88.34 in the SC Category, Your Predicted JEE MAINS 2025 rank may range between 147086 - 170102.
Based on the previous year analysis, According to your JEE MAINS percentile and category you have less possibility of getting a seat for admission in NIT Surathkal.
Some of the other colleges in which you have chances to get admission includes:
You can predict more colleges using the JEE MAINS 2025 college predictor tool.
Hope this information will help you
With your academic background, you have a good chance of getting into some of the top IIMs. Here's a breakdown of your profile:
- Class 10:91.6% - Excellent!
- Class 12:66% - Average, but not a deal-breaker
- B.Tech Computer Science: 8.4 CGPA - Very good!
Assuming you score well in CAT , here are some IIMs you might have a good chance of getting into:
- IIM Ahmedabad: Although the qualifying CAT cut off is 85 percentile, the final cut off typically goes up to 99-100 percentile.With a good CAT score, you might be considered.
- IIM Kozhikode: The CAT cut off for IIM Kozhikode is typically around 95-98 percentile. Your academic profile and a good CAT score might make you a competitive candidate.
- IIM Indore:The CAT cut off for IIM Indore is typically around 90-95 percentile. With a good CAT score and your academic background, you might have a chance.
Keep in mind that CAT cut offs can vary from year to year, and other factors like work experience, extracurricular activities, and personal interviews also play a significant role in the admission process.
To increase your chances, focus on scoring well in CAT, and make sure you have a strong overall profile.
A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services.
A Business Development Executive (BDE) is a professional responsible for identifying growth opportunities and fostering strategic partnerships to enhance a company's market position. Typically, a BDE conducts market research, analyses industry trends, and identifies potential clients or business prospects. He or she plays a crucial role in developing and implementing sales strategies to achieve revenue targets.
A BDE often collaborates with cross-functional teams, including marketing and product development, to align business objectives. Strong communication, negotiation, and relationship-building skills are essential for success in this role. BDE strives to expand the company's customer base, drive sales, and contribute to overall organisational growth in a dynamic and competitive business environment.
Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.
A sales manager is a revenue-generating source for a company. Any organisation or company which sells a commodity or service requires sales to generate revenue. A Sales manager is a professional responsible for supervising the sales team. An Individual as a sales manager works closely with salespeople, assigns sales territories, sets quotas, mentors the members of the sales, assigns sales training, and builds a sales plan.
The Sales Manager work also includes hiring and laying off sales personnel after evaluating his or her work performance. In bigger entities, sales quotas and plans are usually set at the executive level. He or she is responsible for overseeing the set target or quotas met by salespeople or upholding any policy. He or she guides his or her fellow salespeople and allows them to sell.
Individuals who opt for a career as a business analyst look at how a company operates. He or she conducts research and analyses data to improve his or her knowledge about the company. This is required so that an individual can suggest the company strategies for improving their operations and processes.
In a business analyst job role a lot of analysis is done, things are learned from past mistakes and the successful strategies are enhanced further. A business analyst goes through real-world data in order to provide the most feasible solutions to an organisation. Students can pursue Business Analytics to become Business Analysts.
A marketing manager is a person who oversees a company or product marketing. He or she can be in charge of multiple programmes or goods or can be in charge of one product. He or she is enthusiastic, organised, and very diligent in meeting financial constraints. He or she works with other team members to produce advertising campaigns and decides if a new product or service is marketable.
A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.
Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024 | Application Deadline: 10th March 2025
Amongst top 3% universities globally (QS Rankings)
Ranked #41 amongst institutions in Management by NIRF | 100% Placement
EMBA @IIMU 2025 | Valid GMAT or GRE score
Round 03 Applications Deadline - 21st March 2025 | Average CTC 15.10 LPA
NBA Accredited | AICTE Approved