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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.
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 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 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
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 ?
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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