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Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18
Edited By Team Careers360 | Updated on Sep 19, 2024 02:39 PM IST | #CAT
Based on the CAT syllabus 2024, we have created a study schedule to ace the CAT Exam. We discussed a plan for every day from Day 1 through Day 17 in advance.
On the basis of the CAT syllabus 2024, we discussed strategies on how to prepare for inequalities (Algebra), puzzles/problem-solving based on linear Arrangement , and vocabulary in the previous article - Day 17 of CAT preparation. We have brought you CAT problem-solving questions and answers for you to practice and learn the concepts for a better flow.
This Story also Contains
- CAT Exam Part-A: Quantitative Aptitude for CAT 2024
- Part-B: CAT Logical Reasoning and Data Interpretation:
- Part-C: CAT Exam VARC
- Free PDFs for CAT 2024 preparation
We're back with a strategy for the Day 18 of our preparation for the CAT 2024. In this article, we will be discussing strategies for the following topics and CAT problem-solving questions answers including function and graph CAT questions and CAT previous year questions on functions.
With the 60-day CAT exam preparation schedule we created for you, you can ace the CAT 2024 and get a flow, plan, and schedule for your preparation.
CAT Exam Part-A: Quantitative Aptitude for CAT 2024
Topic: Algebra (Functions and Graph) and CAT Problem-Solving Questions Answers
Definition: In a system, the output is a function of the input or, we can say function describes a relation between input and output.
For example: f(x) =x2, describes output (f(x)) varies as square of the input (x).
Functions can be well represented by graphs and with the help of graphs, solutions can be drawn effectively. The graph shows the variation of output with the inputs.
Tips and Tricks to Prepare Functions and Graphs for CAT
To solve the questions of function and graph for CAT, you have to learn some specific functions CAT questions and their graphs. A few of them are here with examples.
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 NowOdd Function: If f (– x) = – f (x)
For example: f (x) = x3 + sin x; 0 ≤ x ≤ 2π
f(–x) = (–x)3 + sin (-x) = – x3 – sin x = – f(x)
So, the given function is an odd function.
(Graph of odd functions are symmetrical about the origin)
Even function: If f (– x) = f (x)
For example: f (x) = x2 + cos x; 0 ≤ x ≤ 2π
f(–x) = (–x)2 + cos (–x) = x2 + cos x = f(x)
So, the given function is an even function.
(Graphs of even functions are symmetrical about the y-axis).
Functions can neither be odd nor even but can be expressed as the sum of even and odd functions.
Composite Functions: It is a function of some other function.
(g o f) (x) = g [f(x)]
(f o g) (x) = f [g(x)]
Understand the concept of Domain and Range:
Domain: Set of input values represented on the x-axis of the graph.
Range: Set of output values represented on the y-axis of the graph.Learn the graphs of some functions as shown and that will be very helpful.
Functions Questions For CAT From CAT Previous Year Papers
Q1. If f(x) = x2 − 7x and g(x) = x + 3, then the minimum value of f(g(x)) − 3x is: [CAT exam 2021, slot-3]
(a) – 20 (b) – 15 (c) – 12 (d) – 16
Ans: (d)
f (g(x)) – 3x
= (x + 3)2 – 7(x + 3) – 3x
= x2 + 9 + 6x – 7x – 21 – 3x
= x2– 4x – 12
= x2 – 4x + 4 – 4 – 12
= (x – 2)2 – 16
The minimum value of this function will be -16 for x =2.
Q2. If f(x + y) = f(x).f(y) and f(5) = 4, then f(10) – f(–10) is equal to [CAT exam 2024, slot-3]
(a) 3 (b) 0 (c) 14.0625 (d) 15.9375
Ans: (d)
It is given that f(x+y) = f(x) × f(y)
For y = 0, f(x) = f(x) × f(0) ⇒ f(0) = 1.
For, x = 5, f (5) = 4
Now, f(10) = f(5 + 5) = f(5) × f(5) = 4 × 4 = 16
⇒ f(10) = 16
We can write;
f(0) = f(10 - 10) = f(10 + (-10)) = f(10) × f(-10) = 1
f(-10) = 1/16
f(10) - f(-10) = 16 – 1/16 = 15.9375
Q3. For all real values of x, the range of the function f(x) = (x2 + 2x + 4)/(2x2 + 4x + 9) is:
(a) [4/9, 8/9] (b) [3/7, 8/9) (c) (3/7, 1/3) (d) [3/7, 1/2)
Ans: (d)
f(x) = (x2 + 2x + 4)/(2x2 + 4x + 9)
⇒ f(x) = (x2 + 2x + 4)/[2(x2 + 2x + 4) + 1]
Let x2 + 2x + 4 = (x + 1)2 + 3 = k
The minimum value of k is 3.
Now, f(x) = k/(2k + 1)
So, the minimum value of f(x) = 3/(2×3 + 1) = 3/7
For the maximum value of f(x), as the value of k increases, the value in the denominator also increases, which decreases the value of f(x). Thus, the fraction approaches 1/2 but never equals 1/2.
Hence, the correct answer is [3/7,1/2).
Q4. If f(x) = – 4x + 9 and g(x) = 2x – 7, then f(g(x)) = ?
(a) 6x – 16 (b) – 8x + 37 (c) 2x – 16 (d) – 2x + 2
Ans: (b)
Here f(x) = – 4x + 9 and g(x) = 2x – 7
So, f(g(x)) = f(2x – 7) = – 4(2x – 7) + 9 = – 8x + 28 + 9 = – 8x + 37
Hence, the correct answer is (b) – 8x + 37.
CAT EXAM: Prerequisite to Problem-Solving Questions For Entrance Exam based on functions and graphs for CAT
Polynomials Equations of Geometrical figures.
CAT EXAM: References to Study (Theory):
Functions and Graph (Arihant Publication)
How to prepare Quantitative aptitude for CAT by Arun Sharma.
2IIM CAT Preparation
CAT EXAM: References to Study (Practice):
The Pearson Guide to Verbal Ability and Reading Comprehension for CAT by Nishit Sinha (2020)
https://iim-cat-questions-answers.2iim.com
Previous Year's Question Papers
Part-B: CAT Logical Reasoning and Data Interpretation:
The topic covered for the day is given below: Students can refer to Linear Arrangement Part 1 for Day 16
Topic: Problem-Solving/ Puzzles (Linear Arrangement Part-2)
In this section, we will discuss the strategies to solve Puzzle questions for CAT exam based on the linear arrangement with the help of examples:
Type 1: Simple Linear Arrangement ( Puzzle questions for CAT exam)
Directions for Questions 1 to 4:
There are six friends (Andrew, Baithi, Charles, Duke, Elena, and Flora) seated in a row with numbered chairs from 1 to 6. They follow the following Seating Arrangement :
1. There are two places between Charles and Duke
2. There is one place between Andrew and Charles
3. There is one person between Flora and Elena
4. Elena is to be seated before Flora
5. Baithi is to be seated before Andrew, not necessarily immediately
6. The row does not start with Baithi
Q.1. The row would start with:
Andrew
Flora
Duke
Cannot be determined
Q.2. Elena will be seated on which seat number?
1
2
3
Cannot be determined
Q.3. Who is seated at place number 6?
Andrew
Flora
Duke
Cannot be determined
Q.4. Baithi’s position is
6
5
3
2
The solution strategy for the above problem will be:
While solving, use Initials for each Name, for example,
Write A for Andrew, B for Baithi etc.
Mark the 6 places and fill them according to the given instructions.
1 | 2 | 3 | 4 | 5 | 6 |
Given statements are
There are two places between Charles and Duke
C _____ _____ D or D ______ ______C
There is one place between Andrew and Charles
A _____ C or C _______ A
There is one person between Flora and Elena, Elena is to be seated before Flora
E _______ F
Baithi is to be seated before Andrew, not necessarily immediately
The row does not start with Baithi
Eliminate the wrong possibilities
Find the person in the first place.
From above, In the first place either A, C, D or E will come.
We cannot start with A since B should come before B. and B cannot be in the first place.
If we start with C
C ___ A D __ ___ (we cannot place E and F in this arrangement since E and F must have one person in between them)
If we start with D
D ___ ____ C __ A (we cannot place E and F in this arrangement since E and F must have one person in between them)
After placing E, F and B according to the given condition
D B E C F AIf we start with E
E ___ F ___ __ A (in this arrangement C must be just after F. So, we will not be able to place D. Therefore, this arrangement cannot be true)
The correct combination should be
1 | 2 | 3 | 4 | 5 | 6 |
D | B | E | C | F | A |
Answer: 1 (c), 2 (c), 3 (a), 4 (d)
Type 2: When two arrangements are given
Directions: Study the following information to answer the given questions:
Twelve people are sitting in two parallel rows containing six people each, in such a way that there is an equal distance between adjacent persons.
In row – 1, A, B, C, D, E and F are seated and all of them are facing south.
In row – 2, P, Q, R, S, T and V are seated and all of them are facing north.
Additional information is also given as
Each member seated in a row faces another member of the other row.
V sits third to the right of S.
S faces F and F does not sit at any of the extreme ends of the line.
D sits third to the right of C. R faces C.
The one facing E sits third to the right of P.
B and P do not sit at the extreme ends of the line.
T is not an immediate neighbour of V and A is not an immediate neighbour of F.
P sits to the left of S.
Q.1. If B and E interchange their places, who amongst the following faces B?
(a) T (b) P (c) Q (d) R (e) None of these
Ans: (c)
Q.2. Which of the following pairs must be at extreme ends but are not facing each other?
(a) R, F (b) T, A (c) D, R (d) C, Q (e) S, A
Ans: (b)
Q.3. If all the 12 persons are members of a family. Females are facing their husbands. All females are sitting at alternate places. If A is the husband of V. Then who is the husband of P?
(a) B (b) A (c) C (d) F (e) D
Ans: (a)
Solutions with Strategies:
Take two rows of six places. Consider the upper side of the paper as North and the downside as South.
Place the six people above facing downward (South) and six people in other row facing towards the North.
V sits third to the right of S.
S | V |
S faces F and F does not sit at any of the extreme ends of the line.
F | |||
S | V |
D sits third to the right of C. R faces C.
D | C | ||
R |
The one facing E sits third to the right of P, and P sits to the left of S. B and P do not sit at the extreme ends of the line, T is not an immediate neighbour of V and A is not an immediate neighbour of F.
E | |||
P | S |
Combining all the figures above
D | B | F | C | E | A |
T | P | S | R | Q | V |
CAT Exam: References to Study (Theory):
Verbal and Non-Verbal Reasoning by R S Agrawal
Cat preparation-iQuanta (YouTube Channel)
MBAP CAT EBook (Concept Theory)
CAT Exam: References to Study (Practice):
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
MBAP CAT EBook (Practice Questions).
Previous Year's Question Papers
Part-C: CAT Exam VARC
Topic: Strategies to prepare Conditionals
Conditionals and Rules, Tips to Prepare:
Conditionals are phrases used to explain the result of an event that might happen in the present or future or that could have happened in the past but didn’t.
Conditionals are divided into four parts:
Zero Conditionals: sentence formed two present simple verbs (one in the 'if clause' and one in the 'main clause'):
Rule: If + present simple, .... present simple.
Trick: Used when the result will always happen.
Examples:
If people eat too much, they get fat.
If you touch a fire, you get burned.
If babies are hungry, they cry.First Conditional:
Rule: If + Present Simple, (If Clause) ... will + infinitive (main clause)
Trick: used to talk about things which might happen in the future.
Examples:
If it rains, I won't go to the park.
If I study today, I'll go to the party tonight.
If I see her, I'll tell her.The Second Conditional: Uses the past simple after if, then 'would' and the infinitive:
Rule: if + past simple, ...would + infinitive
Tricks: We can use 'were' instead of 'was' with 'I' and 'he/she/it. This is mostly done in formal writing. We can use it to talk about things in the future that are probably not going to be true. Maybe I'm imagining some dream for example. We can use it to talk about something in the present which is impossible because it's not true.
Examples:
If I won the lottery, I would buy a big house.
If I met the Queen of England, I would say hello.
She would pass the exam if she ever studied. (She never studies, so this won't happen)
If I were you, I wouldn't go out with that man.
How is this different from the first conditional?
We can understand this with the following example:
For example (second conditional): If I had enough money, I would buy a house with twenty bedrooms and a swimming pool (I'm probably not going to have this much money, it's just a dream, not very real)
But (first conditional): If I have enough money, I'll buy some new shoes (It's much more likely that I'll have enough money to buy some shoes)The Third Conditional: Use past perfect after 'if' and then 'would have' and the past participle in the second part of the sentence:
Rule: If + past perfect, ...would + have + past participle
Trick: It represents the incidents in Past. It's used to describe a situation that didn't happen and to imagine the result of this situation.
Examples:
If she had studied, she would have passed the exam (but, really, we know she didn't study and so she didn't pass)
If I hadn't eaten so much, I wouldn't have felt sick (but I did eat a lot, and so I did feel sick).
If we had taken a taxi, we wouldn't have missed the plane.
Some Additional Tips:
Differentiate between the use of first (for particular situations) vs zero conditional (for general activities).
Differentiate between the use of first (for situations likely to happen in future) vs second conditional (for general activities that I don't think will really happen).
Practice Questions for CAT pdf on Conditionals [Based on CAT previous year papers]
Q1. What would you do differently if you _____ to do this again?
have
had
would have
None of these
Ans: (1) According to the third conditional.
Q2. The work _____ delayed if payment from the ministry don't credit on time.
is
will be
would be
None of these
Ans: (2); According to the first conditional.
Q3. When I watch TV for too long, I _____ a headache.
get
got
would get
None of these
Ans: (1); According to Zero Conditional
Prerequisite
Parts of Speech
Tenses.
CAT Exam: References to Study (Theory)
Word Power Made Easy.
CAT Edurav (YouTube Channel)
CAT Exam: References to Study (Practice)
Wren and Martin
Practice Sample Question Papers.
Practice and remain focused; Day 19 will be posted tomorrow.
Free PDFs for CAT 2024 preparation
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Questions related to CAT
Have a question related to CAT ?
Good afternoon ,
I hope you are absolutely fine. As per your mentioned query , CAT stands for Common Admission Test examination conducts once in a year. It is a national level of exam in English language. If you want to apply for this exam the application mode is online .
As per the eligibility criteria , candidate should have bachelor's degree from recognised university. Final year of college student also eligible to give this exam.
To know more , refer this:
https://bschool.careers360.com/articles/cat-eligibility-criteria
Revert for further query!
Sakshi Sharma 03 June,2025
Hi aspirant,
- In general, PUMBA (Pune University's Department of Management Sciences) requires a higher CAT percentile, usually between 94 and 96.
- Nevertheless, final selection is based on a comprehensive process that includes your CAT score (which usually carries 50% weightage), performance in the Group Discussion (GD) and Personal Interview (PI) rounds (30% weightage), academic record (10% weightage), and work experience (10% weightage).
- Even though your CAT score is strong, a strong performance in the subsequent selection rounds will be essential for admission.
- It is recommended to contact the institution directly for latest and up-to-date information.
You can refer to the link attached above for more information on the same.
All the best!
Rajeswari Dey 27 May,2025
Hi aspirant,
- Vadodara is an MHT CET exam center located outside of Maharashtra .
- This makes it easier for Gujarati applicants to take the exam.
- When completing your MHT CET application form, you will have the option of selecting your chosen exam centers , including those situated outside of Maharashtra.
You can refer to the link given above for more information on the same.
All the best!
Rajeswari Dey 25 May,2025
Hello dear,
The CAT exam requires a significant amount of time for preparation, including brushing up on basic concepts and practicing advanced problem-solving. Starting too early can feel overwhelming and may not be sustainable with other academic commitments.
The CAT exam requires a level of focus and maturity that is not always present in class 9. Starting preparation at this stage can be challenging to maintain. At class 9, you're primarily focused on learning foundational concepts. So you just need to boost your fundamentals by practicing more and more at class 9 because the Quantitative Aptitude section of CAT syllabus includes all the topics of Mathematics from Class 9 to 10 such as Arithmetic, Geometry, Algebra, Trigonometry and Mensuration.
Start Preparation 12 Months Prior:
- Begin your CAT preparation around 12 months before the exam date.
- Dedicate 5 to 6 hours daily for studying, focusing on smart work rather than just hard work.
Identify Weak Sections:
- Recognize your weak section at the start of your preparation.
- Allocate more time and attention to improving your weak areas while maintaining practice in all sections
I hope you got your answer, That's all Thank you.
Rajeswari 22 May,2025
IIFT CAT Cutoff 2024
IIFT Delhi
General: 95–98 percentile
OBC: 90+
SC: 85–95
ST/PwD: 75–93
IIFT Kolkata
General: 85–95 percentile
OBC/SC/ST: 50–95 (varies)
Note: Final selection also includes WAT, GD, PI, academics, and work experience.
harsh singh 21 May,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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