Decoding CAT 2025 Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison - Day 37

Decoding CAT 2025 Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison - Day 37

Ongoing Event

CAT Application Date:01 Aug' 25 - 13 Sep' 25

Team Careers360Updated on 03 Apr 2025, 10:38 AM IST

The CAT exam for MBA admissions 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.

Decoding CAT 2025 Preparation: Exploring PnC, Selections, Syllogism Important PYQs, and Comparison - Day 37
CAT 2025 Permutation and Combination Problems, Syllogism Tricks With Solutions

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

  1. The number of permutations of n distinct items taking r items at a time is

nPr = n!/n-r!

  1. nPn = n!

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  1. nCr = nCn-r

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  1. Out of n given things, the number of ways of selecting any number = 2n -1.

  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

  1. The number of diagonals in an n-sided regular polygon = nC2 – n

  1. 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

  1. Learn all the formulas and understand their applications.

  1. 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]

  1. 16

  2. 20

  3. 14

  4. 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

  1. Vedic Maths

  2. Factorial

  3. Fundamental Principle of counting

CAT study material: References to Study (Theory)

Permutation and Combination problems:

  1. NCERT Class 11 Maths

  2. CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=509qwiX-3qY)

  3. https://www.youtube.com/watch?v=QsKl5GbBcHU

Study material: References to Practice CAT Permutation and Combination Questions (Syllogism)

  1. How to prepare quantitative Aptitude for CAT by Arun Sharma.

  2. 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.

  1. If only conclusion I follows

  2. If only conclusion II follows

  3. If either I or II follows

  4. If neither I nor II follows

  5. 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.

  1. All follows

  2. I, II and III follow

  3. I, IV and III follow

  4. II, IV and III follow

  5. 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

  1. Set Theory

  2. Venn Diagram

  3. Concept of Syllogism

References to Study (Theory syllogism questions for CAT

  1. Verbal and Non-Verbal Reasoning by B S Sijwali

  2. CAT Handa (YouTube link: https://www.youtube.com/watch?v=4N8qsbClYpA)

References to Practice syllogism questions for CAT

  1. Verbal and Non-Verbal Reasoning by R S Agrawal.

  2. 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

  1. more taller

  2. more tall

  3. taller

  4. tall

Ans: [C]

Here is a comparison between two persons.

Q2. This is the ____________chocolate I have ever had.

  1. best

  2. better

  3. good

  4. well

Ans: [A]

‘best’ is best suited because comparison is with all time.

CAT 2025:Prerequisite

  1. Sentence Structure

  2. Adjectives and Adverbs

  3. Comparative and Superlative Degrees

Tips and Tricks for CAT Exam

  1. Learn comparative and superlative adjectives.

  2. 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.

  1. 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

  1. 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

  1. Comparative adjectives: using much, a lot, far, etc.

  1. Comparative adjectives: using than

  1. Comparative adjectives: -er and -er, more and more

  1. Comparative adjectives: the -er, the -er and the more …, the more …

  1. Use than, not that or as to introduce a clause after a comparative adjective or adverb

CAT exam: References to Study (Theory)

  1. Wren and Martin

  2. (https://www.youtube.com/watch?v=cpQbmdKkNFs)

CAT exam: References to Study (Practice)

  1. Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.

  2. CAT Previous years Papers and Sample Papers.

  3. (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)

Click here to download

CAT 2023 Official Question Paper and Answer Key (Slot 3)

Click here to download




Frequently Asked Questions (FAQs)

Q: Does CAT repeat questions from previous years?
A:

CAT does not directly repeat questions, but the same type of questions and ideas are asked annually. Number Systems, Algebra, Logical Puzzles, and Reading Comprehension topics often crop up in other forms. Working on previous year papers makes it easier for aspirants to realize the pattern of the exam and come up with improved strategies.

Q: Are mock tests important for CAT 2025 preparation?
A:

Yes, mock tests are crucial for CAT 2025 preparation since it helps the candidate, to carefully analyse their weakness and strength.

Q: What is the duration of CAT 2025 paper?
A:

The time duration for the CAT 2025 exam paper is two hours i.e. 120 minutes. The exam is conducted in different slots for the exam day.

Q: How to register for the CAT Exam 2025?
A:

To register for the CAT exam 2025, the candidate must visit the official website of the CAT. Create a login profile using e-mail ID, mobile number, and other necessary details and upload the documents required. Then finally submit the registration fees and the process is completed.

Q: When will the CAT 2025 registration start?
A:

CAT registration will start around August 2025. Candidates can start registering for the CAT exam on the official website of the CAT. 

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Questions related to CAT

On Question asked by student community

Have a question related to CAT ?

Yes, you can fill the CAT form even if you currently have a backlog. CAT eligibility requires you to be in your final year of graduation or already graduated backlogs don’t stop you from applying.

While filling the form:

  • Enter the aggregate percentage/CGPA of marks you have obtained up to the latest semester for which results are declared (in your case till 4th semester).

  • There will be an option to mention that you have a backlog.

  • If you clear the backlog later, you’ll just need to show the updated marks during admission.

Hello Aspirant,

Yes, you can apply for the CAT exam as a final-year student. You must declare your backlog on the online application form. You do not write about it on the final-year student certificate; that document is to certify your enrollment status. You must clear all backlogs before the final admission process to any MBA college.

Hello,

Thank you for your question!

KL- MAT syllabus: Quantitative Aptitude, Reasoning, English/Verbal Ability, and General Awareness (similar to MAT/CMAT pattern).

CAT scores are valid in many private universities including KL University, but always check the year’s admission notification.

CAT vs other exams: CAT is toughest (IIMs + top B-schools), while MAT/CMAT/ATMA are relatively easier and accepted by many mid-level private universities.

Hello it will clear your doubt!

Hello Aspirant,

  1. I saw a cat. The cat found an old map inside a drawer of the king's palace.

Here's why:

  • "a cat": It's the first time we mention the cat, so it's indefinite.

  • "The cat": Now we're talking about that specific cat we just mentioned, so it's definite.

  • "an old map": It's the first time we mention a map, and "old" starts with a vowel sound, so "an."

  • "a drawer": It's one of possibly many drawers, not a specific one known to us yet.

  • "the king's palace": This is a specific, unique place, so "the."

Hello Kapish

You can find the last 5 year questions of DILR for CAT at Careers360 website. Moreover, you can find the previous year papers of all the subjects i.e. DILR, Quants and VARC. I am attaching the link through which you would be able to access the same.

Here's the link: CAT Previous Year Papers by CAREERS360
Sample paper of DILR: CAT Sample Paper (DILR) by CAREERS360

Thank You!!!