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Decoding CAT 2024 Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison - Day 37
Edited By Team Careers360 | Updated on Jan 08, 2025 07:14 AM IST | #CAT
The CAT exam for MBA admissions 2026-2028 is expected to take place in November 2025. In this 60-day CAT 2025 preparation guide series by Careers360, we’ll discuss strategies for tackling Permutation and Combination problems on Day 37, helping you prepare effectively and succeed in the CAT entrance test.
This article covers permutation and combination problems, syllogism questions with answers, and tips for understanding comparison in VARC. Permutation and combination problems are often considered challenging, and many aspirants struggle with them. To aid your preparation, we've included Permutation and Combination examples with answers, as well as previous years' questions (PYQs) for practice.
CAT Preparation 2025 in 60 days
Part-1: Quantitative Aptitude for CAT exam (Permutation and Combination Aptitude)
CAT Exam Important Topic: Strategy to Prepare Permutation and Combination (Selection, Grouping and Distribution) and permutation and combination problems.
Permutation and combination problems
The number of permutations of n distinct items taking r items at a time is
nPr = n!/n-r!
nPn = n!
CAT 2024 College Predictor
Know Your Chances for getting Calls from IIMs & other Top MBA Colleges through CAT Percentile, based on your category, academic profile, work-ex & CAT result.
Use NownCr = nCn-r
Out of n given things, the number of ways of selecting any number = 2n -1.
Dividing n items into two groups of p and q items
= n!/q! p!
If p =q and two groups are not identical; a number of groups will be n! /(p!)2
If p =q and two groups are identical; a number of groups will be n!/2! (p!)2
The number of diagonals in an n-sided regular polygon = nC2 – n
Divide questions of distributions into the following categories while solving:
Identical Objects Identical Places
Identical Objects Distinct Places
Distinct Objects Identical Places
Distinct Objects Distinct Places
Learn all the formulas and understand their applications.
Practice all kinds of Permutation and Combination problems.
CAT Exam:
Previous Year CAT Questions on Permutations and Combinations (Selections and Groupings, Distributions):
Q1. The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is [TITA, CAT 2021 Slot-2]
Permutation and Combination examples with answers: 1000 ways
Given that, there are 15 identical balloons, 6 identical pencils, and 3 identical erasers.
We need to distribute these items among 3 children, such that each child gets at least four balloons and one pencil.
First, distribute 4 balloons and 1 pencil to each child. Now, we have 3 balloons, 3 pencils, and 3 erasers left with us after distribution.
Remaining balloons can be distributed in following possible combination;
(3, 0, 0), (2, 1, 0), (1, 1, 1)
(3, 0, 0) can be arranged in three ways.
(2, 1, 0) can be arranged in six ways.
(1, 1, 1) can be arranged in only one way.
The total ways of distributing the remaining balloons are 6+ 3+ 1= 10 ways.
Similarly, we can arrange 3 pencils in 10 ways and 3 erasers in 10 ways.
Therefore, the total number of ways is 10 x 10 x 10 = 1000 ways
Permutation and Combination Aptitude
Q2. In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser. Still, nobody gets more than 3 erasers? [CAT 2017]
16
20
14
15
Permutation and combination examples with answers
Ans: A
We have to find by how many numbers of ways the erasers are distributed such that each kid gets at least one eraser but nobody gets more than 3 erasers.
4 kids are getting a, b, c, d erasers such that a + b + c + d = 7.
a = p+1
b = q+ 1
c = x+ 1
d = z+1 since each should have at least 1 eraser.
So, p + q+ x+ y = 3
number of ways of distribution = n+rCr-1; here n =3, r = 4(number of variables)
So, the number of ways of distribution = 6C3 = 20 ways
If one kid a, gets 4 erasers the other kids b, c, and d can get each one respectively such that 4, 1, 1, 1 or 1, 1, 1, 4 or 1, 4, 1, 1 or 1, 1, 4, 1 so there are chances of 4 ways.
So, required ways = 20 – 4 = 16 ways
CAT entrance exam: Pre-requisite to permutation and combination problems
CAT permutation and combination questions
Vedic Maths
Factorial
Fundamental Principle of counting
CAT study material: References to Study (Theory)
Permutation and Combination problems:
NCERT Class 11 Maths
CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=509qwiX-3qY)
https://www.youtube.com/watch?v=QsKl5GbBcHU
Study material: References to Practice CAT Permutation and Combination Questions (Syllogism)
How to prepare quantitative Aptitude for CAT by Arun Sharma.
CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=RAOTFT1_Ynk)
Part-2: CAT 2025 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
CAT 2025 Syllabus Topic: Strategy to prepare “Syllogism through PYQs” (Part-2) and syllogism reasoning questions and Syllogism examples with answers
CAT Exam:
Previous Year CAT Questions on Syllogism from CAT/ MBA Entrance Exam:
Q1. The following question is given by 3 statements and 2 conclusions numbered I and II. Choose the right answer from the given options. [MAHCET MBA 2024]
Statements:
I. No Box is a Book.
II. Few cups are books.
III. Only a few knives are Boxes.
Conclusions:
I. Some Knives being a book is a possibility.
II. All Cups being a Book is a possibility.
If only conclusion I follows
If only conclusion II follows
If either I or II follows
If neither I nor II follows
If both conclusions follow
Solution: [E]
Cat Tips for syllogism 1: Draw Venn Diagram first
Cat Tips for syllogism 2: ‘A few’ means ‘some’
Cat Tips for syllogism 3: Go through Conclusions.
Conclusion 1: Some Knives being a book is a possibility.
Some Knives are there which are not certain to be either Boxes or Books. Therefore, Some knives can be book. So, first will follow.
Conclusion 2: All Cups being a Book is a possibility.
All cups can be inside Book. So, this is a possibility. Therefore, II will follow.
Syllogism examples with answers
Q2.
Statements
i) Some Cubes are Circles.
ii) No Circle is a Triangle.
iii) No line is a Cube.
Conclusions:
i) All Cubes can never be triangles.
ii) Some lines are Circles.
iii) No triangle is a cube.
iv) No line is a circle.
All follows
I, II and III follow
I, IV and III follow
II, IV and III follow
None of these
Solution: (E)
Cat Tips for syllogism 1: Draw Venn Diagram first
Cat Tips for syllogism 2: Go through Conclusions.
i) All Cubes can never be triangles: Some cubes are Circles. So, definitely, some cubes are there which can never be Triangle.
Therefore, (i) will follow.
ii) Some lines are Circles: Not a definite conclusion; it will not follow.
iii) No triangle is a cube: Not a definite conclusion; it will not follow.
iv) No line is a circle: Not a definite conclusion; it will not follow.
Clearly, the third statement will follow.
CAT entrance exam: Prerequisite to syllogism reasoning questions
Set Theory
Concept of Syllogism
References to Study (Theory syllogism questions for CAT
Verbal and Non-Verbal Reasoning by B S Sijwali
CAT Handa (YouTube link: https://www.youtube.com/watch?v=4N8qsbClYpA)
References to Practice syllogism questions for CAT
Verbal and Non-Verbal Reasoning by R S Agrawal.
MBA Entrance Exams Previous years Papers.3. ELITES GRID (YouTube; Link: https://www.youtube.com/watch?v=sn_k4q6BHxk)
Part-3: CAT Exam Preparation 2025: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Comparison (Comparatives and Superlatives)” for CAT-2025.
CAT Important Concepts
Comparative Adjectives and Superlative Adjectives Fast?Faster (Comparative)?Faster (Superlative)
Comparative Adverbs and Superlative Adverbs
Negative Comparatives
CAT Previous Years' Questions on Comparison (Comparatives and Superlatives).
Q1: My daughter is__________ than my wife
more taller
more tall
taller
tall
Ans: [C]
Here is a comparison between two persons.
Q2. This is the ____________chocolate I have ever had.
best
better
good
well
Ans: [A]
‘best’ is best suited because comparison is with all time.
CAT 2025:Prerequisite
Sentence Structure
Adjectives and Adverbs
Comparative and Superlative Degrees
Tips and Tricks for CAT Exam
Learn comparative and superlative adjectives.
Learn the pronunciation of these comparatives and superlatives:
long /lɒŋ/ longer /lɒŋgə(r)/ longest /lɒŋgəst/
strong /strɒŋ/ stronger /strɒŋgə(r)/ strongest /strɒŋ gəst/
young /jʌŋ/ younger /jʌŋgə(r)/ youngest /jʌŋgəst/Put structurally equivalent verbs in the same form.
Some one-syllable adjectives have irregular comparative and superlative forms:
bad, worse, worst far, farther/further, farthest/furthest
good, better, best old, older/elder, oldest/eldest
Two-syllable adjectives
Two-syllable adjectives ending in -y change y to i and take the -er and -est endings:
busy, busier, busiest
happy, happier, happiest
easy, easier, easiest
funny, funnier, funniest
Comparative adjectives: using much, a lot, far, etc.
Comparative adjectives: using than
Comparative adjectives: -er and -er, more and more
Comparative adjectives: the -er, the -er and the more …, the more …
Use than, not that or as to introduce a clause after a comparative adjective or adverb
CAT exam: References to Study (Theory)
Wren and Martin
(https://www.youtube.com/watch?v=cpQbmdKkNFs)
CAT exam: References to Study (Practice)
Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.
CAT Previous years Papers and Sample Papers.
(youTube; Link: https://www.youtube.com/watch?v=pm9fq1MbR_I)
Day 37 will be posted tomorrow, so practice and stay focused.
Thank you!
All the Best!
Free PDFs for CAT Preparation 2025
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
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Questions related to CAT
Have a question related to CAT ?
The Common Admission Test (CAT) is a highly competitive entrance exam in India for admission to prestigious management programs like the MBA, primarily at the Indian Institutes of Management (IIMs) and other top business schools. It tests a candidate's aptitude in areas such as quantitative ability, verbal ability, logical reasoning, and data interpretation. CAT is valuable for students aspiring to build a career in business, management, or entrepreneurship, as it opens doors to world-class education, exceptional networking opportunities, and lucrative career prospects. Excelling in CAT demonstrates analytical thinking, problem-solving skills, and leadership potential, essential qualities for success in the corporate world.
Tanya Gupta 23 January,2025
Hello there,
With a 77.38 percentile in CAT and sectionals of 61/89/67 , it may be challenging to secure admission to NIT Tiruchirappalli for an MBA, as their cutoff tends to be higher. However, there are still some possibilities, and you could consider these steps:
-
NIT Tiruchirappalli (MBA): Generally, the cutoff for NIT Trichy’s MBA program is around 85-90 percentile, depending on the year and category. Your chances might be slim, but it’s always good to check with the college directly for their specific cutoff.
-
Other Colleges to Consider:
-
IMT Ghaziabad (Consider their sectional cutoffs):
Known for its management programs, IMT could be a good option with your profile.
-
XIME Bangalore:
This college has a more accessible cutoff and offers a good ROI.
-
UPES Dehradun:
If you're looking at newer or specialized MBA programs, UPES could be another option.
-
KIIT School of Management, Bhubaneswar:
They accept CAT scores and have reasonable cutoffs.
-
IIMs (if in lower percentiles in the category, check IIMs like IIM Jammu, IIM Bodh Gaya, or IIM Kashipur).
-
Symbiosis Pune (SIBM):
They have slightly more flexible cutoffs, depending on their intake.
-
IMT Ghaziabad (Consider their sectional cutoffs):
Known for its management programs, IMT could be a good option with your profile.
-
Other Entrance Exams: You could also look at other entrance exams like XAT, NMAT, or SNAP to apply to colleges like XLRI Jamshedpur, NMIMS Mumbai, or Symbiosis Institutes.
Additionally, considering your strong sectional score in DILR (89), you could focus on colleges with a more flexible approach to sectionals and percentile aggregation.
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.
kumardurgesh1802 23 January,2025
Hello there,
With a 65 percentile in CAT and belonging to the General category , getting admission to USMS (University School of Management Studies) can be challenging, as their cutoffs are generally higher, typically around 85-90 percentile or more. However, admission can depend on factors like:
-
Category-wise cutoff : Sometimes, the cutoff for the General category can be higher, but you may still apply as there might be specific reservation relaxations or fluctuations based on the number of applicants.
-
Interviews and GD : Even if you meet the minimum cutoff, interviews and group discussions are a mandatory part of the selection process. They assess your communication skills, leadership qualities, and overall fit for the program.
Recommendations:
-
Check the official cutoff
for USMS for your specific year.
-
Prepare for interviews
: It is likely that you will have to appear for the next rounds if you qualify. Preparing well for the interview is important, as it can make a difference in your selection.
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.
kumardurgesh1802 21 January,2025
Top MBA colleges based on CAT, XAT, SNAP, and NMAT scores include some of India’s best institutions. For CAT, the IIMs (Ahmedabad, Bangalore, Calcutta) and FMS Delhi are highly regarded. XAT results in prestigious colleges like XLRI Jamshedpur and XIMB. SNAP is known for Symbiosis Institutes, such as SIBM Pune and SCMHRD. NMAT scores open doors to NMIMS Mumbai, SPJIMR Mumbai, and ISB Hyderabad. Each exam has unique eligibility requirements, and their cutoffs vary, so it's important to research the specific criteria and select based on your preferences and strengths.
Ankit 17 January,2025
Hello,
Here are important points regarding your query :-
- Opportunity for candidates: IIM Kashipur might be inviting candidates for further consideration, regardless of initial CAT scores.
- Broadening applicant pool: They may aim to review diverse profiles beyond just percentile.
- Different criteria: Other factors like academic performance, work experience, and diversity may contribute to the decision.
- Possibility of screening: The email could be a formality, and actual shortlisting will depend on various selection criteria.
- No guarantee of shortlist: The invitation doesn’t ensure selection; many institutes offer preliminary applications before filtering through comprehensive evaluations.
Hope it helps !
Prachi Kumari 13 January,2025
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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