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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.
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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.
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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.
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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)
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Greetings! Here's a detailed response to your query
Okay, so you're a bit confused about what to put in those CAT, FMS, DSE, and IIFT forms regarding your 12th scores. Since you did CBSE, they usually only consider your final 12th standard marks.
Even though you did great in 11th, scoring 495 out of 500, for these entrance exam forms, they're specifically asking about your 12th board exam marks .You mentioned you got 400 out of 500 in 12th, which comes out to 80%.
Therefore, when filling out the forms for CAT, FMS, DSE, and IIFT, you should enter 80% as your 12th percentage. The aggregate of 11th and 12th isn't typically what they're looking for in these sections. They want to know how you performed in your final board exams. So, stick with the 80% from your 12th results. Good luck with your applications!
Greetings! Here's a detailed response to your query:-
Determination of the best time to start the journey of CAT examination is based on individual factors like your current skill level, knowledge ,potential, learning pace and availability. To give yourself the best chance of success on the CAT exam , which usually takes place in November, it's advisable to begin studying between January and March of that same year. This 8 to 12-month preparation window is widely recommended by experts. But if you're managing your college along with the CAT preparations make sure you start from 2nd year onwards. It will hep you manage stress and you'll have ample amount of time to get along with the syllabus , pattern and various practice and mocks .
You'll be able to build a strong foundation in each sections and be able to know your strengths and weaknesses in different topics. The CAT syllabus is extensive, and early preparation allows for thorough coverage. Assess your learning speed and adjust your preparation timeline accordingly.
Essentially, while the ideal start time is subjective, beginning your CAT preparation well in advance is generally considered the most effective strategy for achieving optimal results.
The CUSAT CAT previous year question papers are available on the Careers360 website. You can find question papers from 2012 to 2023, which can be downloaded in PDF format HERE
Additionally, the official website of Cochin University of Science and Technology (CUSAT) also provides previous year question papers. To access them, you can follow these steps:
- Visit the CUSAT official website - admissions.cusat.ac.in.
- Click on the resources tab from the homepage.
- Select the previous year's question papers from the drop-down menu.
- Select the Common Admission Test (CAT) question papers link.
- Now click on the B.Tech course.
By practicing with these previous year question papers, you can get familiar with the exam pattern, identify important topics, and improve your time management skills.
Hey Shathvika, that's a great question! So, you're wondering about MBA entrance exams besides the CAT , right? Absolutely, there are quite a few others you can consider in India. Here's a rundown: Xavier Aptitude Test (XAT) : XLRI Jamshedpur runs this one, and over 150 B-schools across India accept it. You'll usually find it in January. What's cool about the XAT is that it often includes sections on Decision Making and sometimes even an Essay Writing part. Management Aptitude Test (MAT) : This is conducted by the All India Management Association (AIMA). A lot of schools – over 600 in India – take MAT scores. The best part? You can take it four times a year: February, May, September, and December. Plus, you can choose between Paper-Based (PBT), Computer-Based (CBT), and even Internet-Based (IBT) options. Symbiosis National Aptitude Test (SNAP) : If you're eyeing a Symbiosis institute for your MBA, this is the one. Symbiosis International (Deemed University) conducts it, and it's usually in December. SNAP's also known for having a somewhat unique way of scoring. Common Management Admission Test (CMAT) : The National Testing Agency (NTA) conducts the CMAT. AICTE-approved institutions all over India will accept it. This one's also typically held in January. It checks you on things like quantitative skills, logical thinking, how well you understand language, and your general knowledge. NMAT by GMAC : The Graduate Management Admission Council (GMAC) is behind this exam. NMIMS and quite a few other management schools accept it. What’s interesting is that you have a 75-day window, usually from October to December, to take it. And, you can even retake it up to three times if you want to improve your score! Indian Institute of Foreign Trade (IIFT) Exam : NTA also conducts this one. If you are keen on IIFT Delhi and Kolkata, this is your ticket. Expect to take it in December. This exam puts a little more weight on questions about international business and trade. MICA Admission Test (MICAT) : MICA Ahmedabad uses this for its PGDM-C program. They hold it twice a year, generally in December and January. MICAT looks at how creative you are, how well you write, and your general abilities. Graduate Management Admission Test (GMAT) : GMAC runs the GMAT as well. Many B-schools in India, and even more worldwide, accept GMAT scores. You can take it pretty much any time of the year. People often go for the GMAT if they're thinking about executive MBA programs or schools with a focus on international business. Lovely Professional University National Entrance and Scholarship Test (LPUNEST) : LPU conducts it for admissions into its undergraduate and postgraduate programs. It's held multiple times throughout the year. It also works as a scholarship test, so doing well can get you some financial aid. So, there you have it! Each of these exams has its own quirks when it comes to structure, who can take it, and the scores you need. It’s worth digging into each one a bit to see which one fits best with what you've studied and where you want to take your career. Good luck!
Hello Ayush,
K.R. Mangalam University utilizes a blend of MCQs, descriptive formats, and practical assessments to evaluate student performance. The continuous evaluation system ensures that students are assessed regularly throughout the semester, contributing to a more comprehensive understanding of their academic progress.
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