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Permutation and Combination Questions For CAT Exam | Day 35
Edited By Irshad Anwar | Updated on Sep 19, 2024 01:51 PM IST | #CAT
Hello CAT 2024 candidates, On November 24, the CAT exam 2024 for MBA admissions 2025–2027 will take place. In this CAT 2024 60 days preparation guide series of Careers360, we will discuss the strategies to prepare Permutation and Combination Questions For CAT Exam for day 35 that can help you prepare well and crack the CAT entrance test 2024.
This article covers the following topics i.e CAT Permutation and Combination Questions, Syllogism questions and Parallelism strategies for CAT.
CAT Preparation 2024 in 60 days
Part-1: Quantitative Aptitude for CAT exam
CAT Exam Important Topic: Strategy to Prepare “Permutations and Combinations (Principle of Counting and Arrangement)” and CAT Permutation and Combination Questions.
Permutation and combination CAT Formula and Concepts:
- Fundamental Principle of Counting
- Rule of Product: Taking 1 out of m objects and taking 1 out of n objects, the total number of ways taking 1 out of each of m and n = m x n
- Rule of Addition: Taking 1 out of m objects or taking 1 out of n objects, the total number of ways taking 1 out of each of either m or n = m + n
- Linear Arrangements: Arranging n objects at n different places = n!
- Circular Arrangements: Arranging n objects at n different places(circularly) = (n-1)!
Permutation and Combination Examples:
Permutation Examples:
Arranging Books: You have 4 different books (A, B, C, D) and you want to arrange them on a shelf. The number of ways to arrange them in a specific order would be a permutation. For example, ABCD, ACBD, BCAD, etc.
Choosing a Committee: You have 5 people and you want to choose a president, vice-president, and secretary from among them. The order in which you choose these roles matters, so this is a permutation.
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 NowCombination Examples:
Picking Fruits: You have 6 different fruits and you want to choose 3 to take with you. The order in which you choose them doesn't matter, only which fruits you select. This is a combination.
Selecting a Pizza Topping: You are ordering a pizza and can choose 4 toppings from a list of 8. The order in which the toppings are placed on the pizza doesn't matter, so this is a combination.
CAT Exam: Basic Principle of Counting: Permutation And Combination Previous Year Questions
Q1. How many four-digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, and 6, such that no digit is used more than once and 0 does not occur in the left-most position? [TITA, CAT 2017]
Solution:
This CAT Permutation and Combination questions are based on Arrangements
Some points to be noticed: permutation and combination formula -
0 does not occur in the leftmost position.
If the numbers are to be divisible by 6 it should be a multiple of 2 and 3.
So, the number should be an even number and also be divisible by 3.
Permutations and combinations Examples:
At the unit place, there can be either 0, 2, 4, 6
Permutations and combinations Case 1: Unit Place is ‘0’
Sum of the rest of three should be divisible by 3, The possible pairs are
2, 3, 4; Number of arrangements = 3! = 6.
2, 4, 6; Number of arrangements = 3! = 6.
Total Numbers in Case 1 = 12
Permutations and combinations Case 2: Unit Place is ‘2’
Sum of all four digits should be divisible by 3, The possible pairs are
0, 4, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
3, 4, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 3, 4 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 2 = 14
Permutations and combinations Case 3: Unit Place is ‘4’
Sum of all four digits should be divisible by 3, The possible pairs are
2, 3, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 2, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
0, 3, 2 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 3 = 14
Permutations and combinations Case 4: Unit Place is ‘6’
Sum of all four digits should be divisible by 3, The possible pairs are
2, 3, 4 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 2, 4 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 4 = 10
Therefore, in total we can form 12 + 14 + 14 + 10 = 50 four- digit numbers.
Hence, the answer is 50
Pre-requisite to permutations and combinations for CAT exam
Vedic Maths
Factorial
CAT study material: References to Study (Theory) permutations and combinations for CAT exam
NCERT Class 11 Maths
CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=kqTIPJQ4JAM)
References to Practice CAT Permutation and Combination Questions
Practice CAT Permutation and Combination Questions
How to prepare quantitative Aptitude for CAT by Arun Sharma.
R B Classes (YouTube, Link: https://www.youtube.com/watch?v=St4IMbF4Kh0)
Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
CAT 2024 Syllabus Topic: Strategy to prepare “Syllogism” (Part-1)
Important Concepts/ Formulas
The syllogism consists of statements and conclusions.
Some Rules:
All+ All=All
All+ No=No
All+ Some=No conclusion
Some+ All=Some
Some+ No= Some Not
Some+ Some= No Conclusion
No+ No=No Conclusion
CAT Exam: CAT Previous Year Questions on Syllogism from CAT/ MBA Entrance Exam:
Q1. The following question is given by 2 statements and 2 conclusions numbered I and II. Choose the right answer from the given options. [CMAT]
Statements:
All huts are bungalows.
All bungalows are churches.
Conclusions:
I. Some churches are huts.
II. Some churches are bungalows.
If only conclusion II follows
If either conclusion I or II follows
If only conclusion I follows
If both conclusions I and II follow
Answer: [D]
All + All = All positive conclusions will follow,
Therefore, both I and II will follow.
Q2. If all apples are red, and some apples are juicy, which of the following statements is true? [TISSNET]
All apples are juicy.
Some juicy apples are red.
Some red apples are juicy.
First statement
Second and Third Statement
Third Statement
None of the above
Syllogism questions with Answers: B
Clearly, the second and third statements will follow.
CAT entrance exam: Prerequisite to Syllogism
Set Theory
Tips and Tricks for CAT
Two types of conclusions are there:
Definite
Possible
If All A are B; Possibility: Some B is not A.
If Some B is not A; Possibility: All A are B.
If Some A are B; Possibility: All A are B; All B is A.
Consider all the possibilities.
Questions can be solved by either of the following methods:
Analytical Method
Practice Sample Papers
CAT syllabus 2024: References to Study (Theory) syllogism reasoning
Verbal and Non-Verbal Reasoning by B S Sijwali
Feel Free to Learn (YouTube link: https://www.youtube.com/watch?v=ev2SkXJVAbA&list=PLOoogDtEDyvsBG38tzlj1Zkd0PLxgZwXV)
CAT Exam: References to Practise Syllogism
Verbal and Non-Verbal Reasoning by R S Agrawal.
CAT Previous years Papers and Sample Papers.
Ck CetKing (YouTube; Link: https://www.youtube.com/watch?v=uwfrfzhBkus)
Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Parallelism”
CAT Important Basic Concept
Use of the same pattern of words for two or more ideas that have the same level of importance.
CAT Previous Years' Questions on Parallelism
Find the error and correct the sentence
Q1: Most people cope up with anxiety by reaching for food rather then deal with their feelings. {Similar to CAT PYQ]
cope up with anxiety by reaching for food rather than deal with their feelings.
cope up with anxiety by reaching for food rather than dealing with their feelings.
cope with anxiety by reaching for food rather than deal with their feelings.
cope with anxiety by reaching for food rather than dealing with their feelings.
Solution: [D]
‘Cope up with' should be replaced with 'cope with'.
'Rather then' should be 'rather than'.
Also, the parallelism error is there; change 'deal' to 'dealing'.
Q2. Ashok is not only a terrific vocalist, but also great at solving mathematics. [Sample Question]
Ashok is not only a terrific vocalist, but also great at solving mathematics.
Ashok not only is a terrific vocalist, but is also great at solving mathematics.
Not only great at solving mathematics, Ashok also is a terrific vocalist.
Ashok is not only a terrific vocalist, but also a great mathematician.
Also great at solving mathematics, Ashok is a terrific vocalist.
Ans: [D]
Grammar issue presented: Parallelism (correlative pairs)
“Not only…but also” is a correlative pair, so the elements immediately following each conjunction must be parallel.
CAT 2024: Pre-requisite
Sentence Structure
Conjunction and Prepositions
Tips and Tricks for CAT Exam
Know when the parallel structure is required.
Put structurally equivalent words or phrases in the same part of speech.
Put structurally equivalent verbs in the same form.
Use clauses or complete sentences consistently.
Avoid faulty parallelism.
CAT exam: References to Study Theory
Wren and Martin
Rodha (https://www.youtube.com/watch?v=Vnc7Y_l8Hj4)
CAT exam: References to Practice
Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.
CAT Previous years Papers and Sample Papers.
Rodha (youTube; Link: https://www.youtube.com/watch?v=IoZL7ZcuRmQ)
Keep working hard and practicing; Day 36 will be posted tomorrow.
Thank you
All the Best!
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Questions related to CAT
Have a question related to CAT ?
Hello there,
With a 53 percentile in CAT , the chances of receiving a call from XISS (Xavier Institute of Social Service) may be limited, as their typical cutoff for CAT is generally higher than this, especially for their flagship programs like MBA or PGDM .
However, admission depends on several factors such as:
-
Academic Profile
: Your
10th (67.8%)
,
12th (82.5%)
, and
graduation SGPA (7.5)
are decent, and they can contribute positively to your application.
-
Work Experience/Extra-curriculars
: If you have any relevant work experience or strong extra-curricular achievements, it might improve your chances.
- Overall Application Strength : XISS also considers your overall profile, including your statement of purpose (SOP) and interview performance .
Though the
CAT percentile
is a key factor, you might still be considered based on your overall profile if you apply to their
PGDM programs
. It's always worth checking with the college directly for the specific eligibility criteria and cutoffs for the year you're applying.
I would recommend you to use CAT College Predictor Tool by Careers360 to get the list of possible colleges you can get with your rank.
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 24 January,2025
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
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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