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CAT Masterclass: Understanding Spheres, Logical Connectives, and Some Important PYQs of Para jumbles - Day 47
Edited By Team Careers360 | Updated on Nov 06, 2024 08:57 PM IST | #CAT
Hello, CAT 2024 aspirants! As you study for the Upcoming exam on November 24, it's critical to concentrate on essential topics that will help you do better. On day 47, this article covers crucial topics including Mensuration Questions For the CAT exam, Sphere problems, Logical Deductions, and parajumbles. These topics are important on the CAT exam, therefore knowing them well can offer you an advantage.
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Mensuration, particularly sphere-related topics, is a broad subject that requires familiarity with a variety of formulae and ideas relating to areas and volumes. Logical deductions stress your thinking abilities, thus constant practice is required. Para jumbles, in which you arrange sentences to construct logical paragraphs, test your ability to integrate ideas properly.
Make sure to thoroughly practice these topics and don't forget to get the CAT Mensuration Questions and Answers PDF for more preparation. Stay focused and keep preparing to improve your chances of passing the CAT Exam!
CAT Preparation 2024 in 60 Days
Part-1: Quantitative Aptitude for CAT Exam
CAT Exam Important Topic: Strategy to Prepare “Mensuration (Sphere)” and CAT mensuration questions on sphere. Sphere questions and answers for CAT exam pdf download are available at the top of the page.
Important Concept/Formula Used in Mensuration Questions For CAT exam
Important formulae related to CAT Geometry Mensuration: Sphere and Hemisphere are given below:
A sphere is solid in the form of a ball with radius r.
Surface Area of a sphere = 4πr2
Volume of a sphere =4/3 πr3
Curved Surface Area of a Hemisphere = 2πr2
Total Surface Area of a Hemisphere = 3πr2
Volume of a Hemisphere =2/3 πr3
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowCAT Previous Year Mensuration Geometry Questions on Sphere:
Q1. Previous Year CAT Mensuration Questions are given below:
A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is 9 π cm3. Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is [TITA, CAT 2017]
Mensuration Geometry Questions with Solution are given below:
Given that the height of the cylinder is 3 cm, while its volume is 9π cm3
⟹ πr2h = 9π
⟹ r = √3 cm
See the diagram below:
x2 = 22 – (√3)2
x = 1 cm
Height of the top point of the sphere from the bottom of the cylinder = Height of cylinder + radius of sphere + x = 3+ 1+ 2 = 6 cm
Q2. Questions on CAT Geometry Mensuration are given below:
A spherical-shaped Laddoo has been placed inside an open box of the cubical shape of side 10 cm such that the sweet fit the box. A fly is sitting on one of the vertices of the cube. What is the shortest distance the fly must travel to reach the sweet? [Based on CAT PYQ]
5 cm
5(√3 – 1) cm
5(√2 – 1) cm
2.5(√3 – 1) cm
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CAT Geometry Mensuration questions with solutions are given below:
Ans: [2]
Edge of cube = diameter of sphere = 10 cm
Top view of the situation:
CD = Minimum distance required
CD = AD- BC- AB = AD – BC – CD (since AB = CD; by symmetry)
CD = (AD – BC)/2 = (10√3 – 10)/2 = 5 (√3 – 1)
[Here AD = diagonal of cube = √3 x side of cube]
Tricks and Tips for CAT Geometry Mensuration and Sphere
Tricks and tips for Sphere Questions for CAT are given below:
Imagine a ball/football as a sphere and do make the analysis
See the pattern of asked Sphere Questions for CAT
Practice Hybrid questions on the sphere with cone, a sphere with cylinder, sphere inside a cube etc.
Do not confuse curved surface area and Total Surface Area.
CAT entrance exam: Prerequisite to mensuration Problems: Sphere Questions for CAT
Geometry
Basics of trigonometry
CAT study material: References to Study Theory for Sphere (Mensuration)
NCERT Mathematics Class 9 and 10
2IIM (YouTube Channel)
References to Practice CAT mensuration questions on Sphere
Mensuration Questions For CAT exam
How to prepare quantitative Aptitude for CAT by Arun Sharma.
Concept Tree: YouTube (https://www.youtube.com/watch?v=3FRFRG_GUpw)
Practice Sample Papers and previous year mensuration questions
Part-2: CAT 2024 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation) (h2)
CAT 2024 Syllabus Topic: Strategy to prepare “Logical Connectives” for CAT
Important Rules/ Tips and Tricks to solve the questions on Logical Connectives
Rules
Logical Connectives | Given statement | Valid inference using symbol | Valid inference in words |
If | If P=>Q | ~Q=~P | Negative of the end part=> negative of starting part |
When | When P=>Q | ||
Whenever | Whenever P=>Q | ||
every time | every time P=>Q | ||
Only if | Only if P=>Q | ~P=>~Q | Negative of the start part=>negative of the end part. |
Unless | Unless P=>Q | ~Q=>P | Negative of the end part=>starting part unchanged. |
Otherwise | P otherwise Q=> rewrite as UnlessP=>Q. | ||
Either or | Either P or Q |
| Negative of any one part=> remaining part remains unchanged. |
Rewrite the given statement by putting a logical connective at the beginning of the statement if it is not already there and reverse the conditions to check the validity of the new statement.
Also check whether the negatives of both conditions still hold true.
Practice the varieties of questions based on patterns of CAT and other MBA entrance Exams.
CAT/ MBA Entrance Exam Previous Years Questions on Logical Connectives
Q1. Examine the following statements:
I. I listen to 91.9 FM only if I am in a happy mood.
II. I am never in a happy mood when I have my brother’s company.
III. Whenever I go shopping I take my brother along.
Which one of the following conclusions can be drawn from the above statements?
If I am in a happy mood, I listen to 91.9 FM.
If I am in a happy mood, I seek my brother’s company.
If I am not with my brother, then I’ll listen to the 91.9 FM.
If I am not happy I do not listen to the 91.9 FM. [Based on PYQ]
Solution: D
Only (d) can be drawn from the above statements.
If I am in a happy mood does not conclude that I will listen to 91.9 FM.
It is given that if I am in my brother’s company, I can never be in a happy mood. So, this conclusion is totally wrong.
No such relation is given
Q2. If Amit walks slower than Sumit, and Sumit walks as fast but not faster than Bhanu; then, as compared to Amit, Bhanu walks: [Based on PYQ]
slower than Amit
faster than Amit
with the same speed as Amit
Given data is not sufficient to determine
Solution: (b)
From the given information, we get the following.
Bhanu = Sumit > Amit
Bhanu walks faster than Amit.
CAT entrance exam: Prerequisite to Logical Connectives
Analytical Approach
Basics of Syllogism ism and Logical Deduction
References to CAT Study (Theory) for Logical Connectives
A new approach to Reasoning (B.S. Sijwali & S. Sijwali Arihant)
FundaMakers-CAT Preparation (YouTube link: https://www.youtube.com/watch?v=wVjpq7db4JI)
References to Practice CAT Logical Connectives
Analytical Reasoning by M. K. Pandey.
MBA Entrance Previous years Papers and Sample Papers.
PrepLadder CAT (YouTube: https://www.youtube.com/watch?v=PyJAWeMDJvg)
Part-3: CAT Exam Preparation 2024: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Para jumbles” (Part-3) for CAT-2024
Previous Years' Questions on Para Jumbles from the CAT Exam
Q1. CAT Para jumbles Questions with Solutions are given below:
The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: (CAT 2021)
But today there is an epochal challenge to rethink and reconstitute the vision and practice of development as a shared responsibility – a sharing which binds both the agent and the audience, the developed world and the developing, in a bond of shared destiny.
We are at a crossroads now in our vision and practice of development.
This calls for the cultivation of an appropriate ethical mode of being in our lives which enables us to realize this global and planetary situation of shared living and responsibility.
Half a century ago, development began as a hope for a better human possibility, but in the last fifty years, this hope has lost itself in the dreary desert of various kinds of hegemonic applications.
Ans: 2-4-1-3
Explanation: Sentence 2 indicates the main idea of the paragraph therefore it can be used as the best opening sentence. Sentence 4 describes the development process and how it has been lost his way. Sentence 1 tells the view of today’s development. Sentence 3 contains the complete idea which has been discussed in 2. So, 2413 is the correct order.
Q2. CAT Para jumbles Questions with Solutions are given below:
The five sentences (labelled 1, 2, 3, 4, 5) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: (CAT 2017)
One of the most dramatic examples in nature of ill wind that blows goodness is lightning.
In its aerial form nitrogen is insoluble, unusable and in need of transformation.
Lightning starts the series of chemical reactions that need to happen to nitrogen, ultimately helping it nourish our earth.
Nitrogen — an essential food for plants — is an abundant resource, with about 22 million tons of it floating over each square mile of earth.
Before plants can take life from the atmosphere, nitrogen must undergo transformations similar to the ones that food undergoes in our digestive machinery.
Ans: 5-3-4-2-1
Explanation: In the above passage, 5 is assigned as the best second opening statement. As it talked about the major idea of the passage. Then, 3 explains why it happens. 4 elaborate on this. So,5-3-4-2-1 is the right order.
Q3. Para jumbles CAT Questions with Solutions are given below:
The four sentences (labelled 1, 2, 3) below, when properly sequenced would yield a coherent paragraph. As the position of the opening sentence is already fixed (A), decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer: (CAT 2018)
Impartiality and objectivity are fiendishly difficult concepts that can cause all sorts of injustices even if transparently implemented.
It encourages us into bubbles of people we know and like while blinding us to different perspectives, but the deeper problem of ‘transparency’ lies in the words “and much more”.
Twitter’s website says that “tweets you are likely to care about most will show up first in your timeline based on accounts you interact with most, tweets you engage with, and much more.”
We are only told some of the basic principles, and we can’t see the algorithm itself, making it hard for citizens to analyse the system sensibly or fairly or be convinced of its impartiality and objectivity.
Ans: 3-2-4
Explanation: 324 is a clear sequence: all three sentences signify Twitter’s rules. 2 comes after 3, as the pronoun ‘it’ that starts 2 could only be pointed to the statement on Twitter’s website elaborated in 3.
Q4. The four sentences (labelled 1, 2, 3) below, when properly sequenced would yield a coherent paragraph. As the position of the closing sentence is already fixed (4), decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:
Including wearing a “hijab” or headscarf that is supposed to completely hide the hair.
Many Iranian women, especially in major cities, have long played a game of cat-and-mouse with authorities.
Iran’s Islamic Republic requires women to cover up in public.
With younger generations wearing loose scarves and outfits that push the boundaries of conservative dress.
Ans: 3-1-2
Explanation: 312 is the best sequence. 3 is the best opening statement. Then comes 1 as 1 completes the sentence that has been left unfinished in 3. 2 contains the full idea that has been discussed in 1.
CAT Pre-requisite
The basic idea of sentence structure.
Reading speed should be good and able to understand the idea of the passage.
Basics of Arranging the statements.
References to Study (Theory)para jumbles for CAT
Oxford Practice Grammar (sixth edition)
engvid.com (Web)
References to Practice CAT Para jumbles Questions
2 IIM (Web and Youtube)
Bodhee Prep CAT Preparation (Web and YouTube)
CAT Previous years Papers and Sample Papers.
Do your practice and stay focused; Day 48 will be back tomorrow.
Thank you!
All the best!
Frequently Asked Questions (FAQs)
1. What is Mensuration, and why is it significant in the CAT?
Mensuration is the calculation of areas, volumes, and surface areas of forms such as circles and squares. It's crucial since these types of problems often occur on the CAT exam, and understanding the formulae will help you score higher.
2. How can I enhance my speed on Sphere questions?
To do well on Sphere-related topics, concentrate on understanding the surface area and volume formula. Practice various problems and use the formulae properly. Regular practice will help you become quicker and more precise.
3. What are logical deductions, and how do you solve them?
Logical deductions are reasoning problems that require you to draw decisions based on the information provided. To solve them, read attentively, seek for key words, and use reasoning to arrive at the solution. Practice will allow you to improve.
4. Can I improve my ability to solve parajumbles?
In parajumbles, sentences must be arranged in the correct sequence. To improve, seek for hints such as linking words and pronouns, and practice organizing sentences so they make sense.
5. Are there any shortcuts to Mensuration questions?
While there is no simple shortcut, you may improve your speed by remembering important concepts and practicing often. Mock exams may also help you become faster and more comfortable.
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Questions related to CAT
Have a question related to CAT ?
Although, it's very unlikely that you will secure a seat in top ABM with CAT 67 percentile. Here's is a breakdown to your question:
· CAT Percentile vs. Score: A CAT score of 67 typically translates to a percentile in the range of 90-95 percentile based on the provided data from previous years. While this is a decent score overall, it falls short of the cutoffs for most top-tier ABM programs.
· Cutoffs for Top ABM Institutes:
- IIM Lucknow: For their PGP-ABM program, the qualifying CAT cutoff for the general category is around 85 percentile . However, the actual cutoff for shortlisting for the Written Ability Test (WAT) and Personal Interview (PI) stages is likely to be higher.
- IIM Ahmedabad: While they also offer an ABM program (PGP-FABM), their minimum qualifying CAT cutoff is around 80 percentile , but the final admission cutoffs are usually much higher, often in the 99+ percentile range for general candidates.
- MANAGE (National Institute of Agricultural Extension Management): Their cutoff in CAT percentile has been around 70 for the general category in recent years. With a 67 percentile, you might have a slim chance here, but it's still competitive.
- CCS NIAM (National Institute of Agricultural Marketing, Jaipur): They consider CAT scores with a significant weightage (30-51% in their selection criteria). While they don't explicitly state a cutoff, it's reasonable to assume it would be higher than 67 percentile for a good chance of admission.
· Overall Good CAT Score: Generally, a CAT percentile of 90 and above is considered a good score for securing admission to decent MBA programs in India. For top-tier institutes, a percentile of 95 and above is often preferred.
· MBA Colleges Accepting 60-70 Percentile: While there are MBA colleges that accept CAT scores in the 60-70 percentile range, these are generally not the top-ranked or most sought-after ABM programs. The focus of those lists is on general MBA programs, not specifically ABM.
While securing a seat in ABM can be tough, you can research about other colleges, consider other examinations, to improve your application profile.
You Got This !
Aman Kar 16 April,2025
Hello,
achieving a 99.99 pecentile in the CAT exam significantly enhances your prospects for admission to JBIMS, which evaluates candidates using an application rating(AR) score, which includes
-entrance exam score (CAT/MH-CET/CMAT) : 60% weightage
-Past Academic Record (PAR) : 15% weightage (https://cracku.in/colleges/jbims/admission-process/?utm_source=chatgpt.com)
-Extra-curricular Activities/Work Experience : 20% weightage (https://jbims.edu/uploads/announcement/Revised_M_Sc__Finance_Admission_Procedure_Batch_2024-26.pdf?utm_source=chatgpt.com)
-Diversity (Academic/Gender): 5% weightage
while ahigh CAT percentile is crucial, a lower academic record may impact your overall AR score. Nonetheless, exceptional performance in other areas, such as entrance exams and extracurricular activities, can help offset weaker academic credentials. it's advisable to review JBIMS's detailed admission criteria and consider strengthening other aspects of your application to enhance your chances
Riya Dhoot 10 April,2025
To find the 2024 MHT CET answer key, you'll need to check the official Maharashtra State Common Entrance Test Cell website. This is the primary source for all official announcements and documents related to the MHT CET exam. After the exam concludes, the CET Cell typically releases a provisional answer key.
Once released, the provisional answer key will likely be available as a downloadable PDF file. You'll need to navigate to the official website, look for the MHT CET section, and find the link related to the answer key. This link might be labelled "MHT CET 2024 Answer Key" or something similar.
After downloading the answer key, you can compare your responses with the official answers. If you find any discrepancies or have objections, the CET Cell usually provides a window for raising objections. You'll likely need to pay a specified fee for each objection raised. The official website will provide instructions on how to submit your objections, which may involve logging into your candidate portal and following the provided steps.
Finally, after considering all objections, the CET Cell will publish a final answer key. This final version is considered definitive, and the MHT CET results will be based on it. Keep an eye on the official website for all updates and announcements regarding the 2024 answer key.
I hope this helps.
SUKRITI GUPTA 13 April,2025
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!
SUKRITI GUPTA 05 April,2025
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.
SUKRITI GUPTA 01 April,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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