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CAT Exam- CAT Algebra question from Polynomials, LR & DI |Day 15
Edited By Team Careers360 | Updated on Sep 19, 2024 03:18 PM IST | #CAT
Based on the CAT 2024 syllabus, we previously covered strategies for Algebra (Quadratic Equations), Cube (Logical Reasoning), and Sentence Corrections with CAT algebra questions on Day 14 of our preparation series.
Now, for Day 15, we’ll focus on strategies for tackling polynomial questions in the CAT exam.
To excel in CAT 2024, follow our 60-day preparation schedule to ensure you stay organized and on track with your study plan.
Quantitative Aptitude for CAT 2024
Polynomial (Algebra), Polynomial Questions For CAT Exam & CAT algebra questions
What is polynomials?
Polynomials are mathematical expressions that consist of variables or determinants, coefficients, exponents, and constant terms combined with mathematical expressions like addition, subtraction, or multiplication.
It is generally denoted by f(x).
The general form of a polynomial equation is:
an xn + an-1 xn-1 + an-2 xn-2 + ........ + a1 x + a0
Example:
4x2 + 2x + 3 is a polynomial where x is the variable.
An example of a polynomial equation with two variables is:
3x2 + 2xy + y2 + 4x + 5y + 7, where x and y are two variables.
Degree of polynomials
The degree of a polynomial is the highest exponent of a variable in the polynomial expression with a non-zero coefficient.
Example:
7x4 + 3x3 + 9x + 1; Degree of the polynomial = 4
x3 + 3x2y4 + 3y4 + 5; Degree of the polynomial = 6
It is also to be remembered:
A polynomial with degree 0 is called a Constant or zero polynomial.
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- Quantitative Aptitude for CAT 2024
- CAT Logical Reasoning and Data Interpretation
- CAT Exam VARC
- CAT 2024 study material pdf
In other words, the degree of zero polynomial is zero.
Example: f(x) = 2
A Polynomial with degree 1 is a Linear polynomial.
Example: f(x) = 2x + 1A polynomial with degree 2 is a Quadratic polynomial.
Example: f(x) = 2x2 + x + 1A polynomial with degree 3 is a Cubic polynomial.
Example: f(x) = 2x3 + 3x2 + x + 1A polynomial with degree 4 is a Biquadratic polynomial.
Example: f(x) = 2x4 + 2y + 4z + 1
Zeros of a polynomial
A zero of a Polynomials is a value of the variable (often denoted as "x") that makes the entire polynomial equal to zero. In other words, if you substitute that value for "x" in the polynomial expression, the result will be zero. Another term for the zero of a polynomial is "root" or "solution."
In general, the number of zeroes of a polynomial is equal to its degree, and some of the zeroes may be repeated. For example, a polynomial of degree 3 will have three zeroes (counting multiplicities), and so on. Understanding the zeroes of a Polynomials is crucial in solving various mathematical problems.
There are a few ways to find the zeros of a polynomial.
The factorization method is the most commonly used.
Quadratic formula
Synthetic division
We also have to study “polynomial regression”, “Types of Polynomials ”, and “polynomial function” to learn more about this chapter.
CAT Previous Year Algebra Questions/ Polynomials CAT questions/Polynomial Questions For CAT exam
Here are some CAT previous year algebra questions shuffled up from different PYQs of the CAT exam before:
Q1. If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is:
(TITA, CAT exam 2017)
5
6
2
8
Solution:
Given that a + b + c + d = 30.
For the minimum possible value of (a – b)2 + (a – c )2+ (a – d)2,
(a – b) = (a – c) = (a – d) = 0
But this is not possible because 30 is not a multiple of 4.
We should find a as close to b, c, and d as possible.
We should take values of a, b, c and d close to 30/4 = 7.5
So, a, b, c, and d should take the values of 7 or 8.
For the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2, the difference of a taken with b, c or d should not be greater than 1.
So, Possible sets of a, b, c and d will be
a | b | c | d | (a – b)2 + (a – c)2 + (a – d)2 |
7 | 7 | 8 | 8 | 2 |
8 | 8 | 7 | 7 | 2 |
7 | 8 | 7 | 8 | 2 |
7 | 8 | 8 | 7 | 2 |
8 | 7 | 8 | 7 | 2 |
8 | 7 | 7 | 8 | 2 |
So, the minimum possible value of (a – b)2 + (a – c)2 + (a – d)2 is 2.
Hence, the correct answer is 2.
Q2. For real x, the maximum possible value of x/√(1+x4) is:
[CAT exam 2020]
A. 1
B. ½
C. 1/√2
D. 1/√3
Solution:
Dividing both numerator and denominator by x, we get,
1/√[(1/x2) + x2]
The value of (1/x2) + x2 should be the minimum to get the original fraction maximum.
For real values of x, (1/x2) + x2 has a minimum value equal to 2.
So, the maximum value of x/√(1+x4) is 1/√2.
Hence, the correct answer is 1/√2.
Tips and Tricks to Prepare Polynomials Questions for CAT
The standard form of a Linear polynomial is ax + b.
The standard form of a Quadratic polynomial is ax2 + bx + c.
The standard form of a Cubic polynomial is ax3 + bx2 + cx + d.
The standard form of a biquadratic polynomial is ax4 + bx3 + cx2 + dx + e.
The degree of a constant polynomial is 0.
For the quadratic equation ax2 + bx + c = 0 if the roots are α and β, then
Sum of the roots, α + β = –b/a
Product of the roots, α β = c/aFor the cubic equation ax3 + bx2 + cx + d = 0, if the roots are α, β, and γ, then
Sum of the roots, α + β + γ = –b/a
Product of the roots, α β γ = –d/a
Sum of the product of roots taken two at a time, α β + β γ + α γ = c/aYou have to solve different kinds of problems based on polynomials. Practice more and more problems on polynomials for CAT.
Also, learn
(x + y)2 = x2 + y2 + 2xy
(x – y)2 = x2 + y2 – 2xy
(x + y)3 = x3 + y3 + 3xy2 + 3x2y
(x – y)3 = x3 – y3 – 3x2y + 3xy2
(x – y – z)3 = x3 – y3 – z3 – 3x2y + 3xy2 – 3y2z – 3yz2 + 3xz2 – 3x2z + 6xyz
References to Study (Theory)
NCERT Class 9-10
How to Prepare Quantitative Aptitude by Arun Sharma (7th edition)
2IIM CAT Preparation (You-Tube)
References to Study (Practice) CAT Algebra Questions
Pearson (How to prepare quantitative aptitude for CAT)
https://iim-cat-questions-answers.2iim.com
Previous Year's Question Papers to practice polynomial questions for the CAT exam
CAT Logical Reasoning and Data Interpretation
Cube Part-2 (LR) And CAT Questions On Cubes
The different kinds of questions asked in the CAT Exam on Cubes are:
Type 1 Cubes questions in CAT:
Question. A cube painted on all faces is cut into 1331 cubes of the same size.
1. How many cubes are not painted on any face?
1000
729
81
270
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Download NowAnswer: (B)
Trick: Only the inner cubes
i.e., (k - 2)3, where k = dimension of larger cube/dimension of smaller cube
Here, k = 11
So, the number of cubes not painted on any face is (11 - 2)3 = 93 = 729
2. How many cubes are painted on three faces?
8
16
36
54
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Answer: (A)
Trick: Corner cubes only.
A cube has 8 corners.
Hence, the correct answer is always 8.
Type 2 Cubes questions for CAT:
Question. A cube of 4 cm is painted yellow on the pair of one opposite surface, red on the pair of another opposite surface and blue on the remaining pair of opposite surfaces. The cube is now divided into smaller cubes of equal size of 1 cm each.
3. Find the number of smaller cubes with three surfaces painted.
6
8
16
27
Answer: (B)
Trick: Corner cubes only.
A cube has 8 corners.
Hence, the correct answer is always 8.
4. Find the number of smaller cubes with two surfaces painted.
24
8
16
30
Answer: (A)
Trick: Surface cubes except for the corner cubes.
k = dimension of larger cube/ dimension of smaller cube
Cubes with two face painted = 6 × (k – 2)2 = 6 × 22 = 24
5. Find the number of cubes with two surfaces painted with yellow and red colour.
10
8
9
16
Answer: (B)
Trick: Cubes at the common edges of yellow and red surfaces, except corner cubes.
Common edges of yellow and red will be 4 and 2 cubes (except at corners) at each edge.
So, the number of cubes with two surfaces painted with yellow and red colour is 4 × 2 = 8
Type 3 Cubes questions for CAT:
Question. Here is the information given below. Based on this information, answer the questions.
A cube has six sides, each of which has a different colour: black, blue, yellow, red, pink, and white.
The red side is opposite the black.
The yellow side is between the red and the black.
The blue side is adjacent to the white.
The black side is adjacent to the white.
The red side is the bottom face.
1. What are the four colours that are adjacent to the yellow?
Black, blue, pink, red
Black, blue, red, white
Black, blue, pink, white
Black, red, pink, white
Answer: A
Trick: Except for the colour opposite to the yellow face.
So, except for white, others are adjacent to yellow.
2. Which of the information can be deduced from the information given in statements I, II, and VI?
White is on the top.
Blue is on the top.
Black is on the top.
White is opposite to black.
Answer: C
Trick: Draw an open cube diagram.
Black must be at the top according to statements I, II, and VI.
References for Study (Theory):
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
Cat preparation-iQuanta (YouTube Channel)
References to Study (Practice):
Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
Previous Year's Question Papers
CAT Exam VARC
Subject-Verb Agreement
A sentence is a group of words connected to make meaning. A sentence must use appropriate verbs, helping verbs, punctuation etc.
The Subject and Verb must agree in number and Person (Noun/ Pronoun, Singular/ Plural). Mastering subject-verb agreement rules is crucial for effective communication and writing in the English language.
Subject-verb agreement rules with examples
Person Rule:
Person | Singular | Verb | Plural | Verb |
First Person | I | Am/was/shall | We | Are/ were/ shall |
Second Person | You | Are/ were/ will | You | Are/ were/ will |
Third Person | He/She/it | It/was/will | They | Are/ were/ will |
Number Rule: The number rule is not as simple as the person's rule. There are a few exceptions too.
There are many rules such as:
Subject and Verb should be either singular or plural.
Countable nouns can take a plural, can combine with counting quantifiers (e.g., one, hundred, every, many), and can take an indefinite article such as a or an. Examples of counting nouns are table, glass, and occasion.
Uncountable nouns: they cannot take plurals or combine with number words.
Proximity Rule: Where two or more subjects are connected by: or, either…or, neither…nor. The subject that is closest to the verb decides the number of the verb.
Students can also practice on “subject-verb agreement worksheets with answers pdf”, “40 rules of subject-verb agreement pdf”, and “subject-verb agreement exercises with answers doc” to learn more about this chapter.
VARC Questions For CAT On Subject-Verb Agreement: [Based on PYQs]
The following subject-verb agreement exercises are VARC questions for CAT, based on topic subject-verb agreement based on the previous year's question papers of the CAT exam.
Correct the sentences:
Q1. The Seven Strangers, Manav included, was supposed to meet for dinner later that night after a conference.
was supposed to meet
was supposed to have met
were suppose to be meeting
were supposed to meet
they were supposed to be meeting
Answer: (D)
Here the subject is “The seven strangers”, which is plural.
So, the plural verb “were” will be used here.
The correct sentence will be:
“The Seven Strangers, Manav included, were supposed to meet for dinner later that night after a conference.”
Q2. Without proper guidance and better support, there is no chances that our candidate will win the election.
there is no chances that
there can be no chance for
there is no chance that
there are no chances for
there will be no chances for
Answer: (C)
Here the singular verb ‘is’ does not agree with the plural subject ‘chances’.
So, replace chances with a chance.
The correct sentence will be:
“Without proper guidance and better support, there is no chance that our candidate will win the election.”
Q3. After he attended the seminar, many more resources were at Philip’s disposal, including new contacts, excellent books and pamphlets to help him improve his resume.
many more resources were at Philip’s disposal
at Philip’s disposal were many more resources
there were many more resources at Philip’s disposal
Philip, at his disposal, had many more resources
Philip had many more resources at his disposal
Answer: (E)
On Comparison, we found that ‘E’ is most suitable.
The correct sentence will be:
“After he attended the seminar, Philip had many more resources at his disposal, including new contacts, excellent books, and pamphlets to help him improve his resume.”
Tips to Prepare Subject-Verb Agreement
To identify the subject, one must spot the verb and ask a question that the verb along with the predicate is supposed to answer.
A collective noun is considered as a whole and takes a singular verb.
When the plural noun denotes some specific quantity considered as a unit, the verb used is generally singular.
Words such as glasses, pliers, and scissors are regarded as plural and require plural verbs unless they’re preceded by the phrase ‘pair of ‘and this word becomes the subject.
Write rules and revise them regularly.
Attempt Mock-Test papers.
Prerequisite:
Complete Knowledge of Nouns
Complete Knowledge of Pronouns
Knowledge of Articles
Knowledge of Verbs
Basic knowledge of Tenses.
References to Study (Theory):
Advanced English grammar by Wren and Martin
CAT Edurav (Youtube Channel)
References to Study (Practice):
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
https://www.800score.com/gmat-prep/prep-guide/sample-questions/
Practice Sample Question Papers.
CAT 2024 study material pdf
CAT 2024 Quantitative Aptitude Study Material PDF - Geometry and Mensuration | CAT 2024 preparation tips with 30-day study material by Experts |
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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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