Great Lakes - PGDM & PGPM Admissions 2026
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
Conquering Functions & Graphs, Puzzle Questions for Linear Arrangement, and Conditionals- Day 18
Ongoing Event
CAT Application Date:01 Aug' 25 - 13 Sep' 25
The CAT syllabus 2025 forms the foundation of our 60-day CAT exam preparation schedule, carefully structured to help you cover all key areas with clarity and consistency. After tackling topics like inequalities in algebra, linear arrangement-based puzzles, and vocabulary in Day 17, we now bring you Day 18. In this article, we focus on function and graph questions based on the CAT syllabus 2025. Also, learn about CAT previous year questions on functions, Arrangement, paired with step-by-step solutions to strengthen your problem-solving skills and boost your CAT 2025 performance..
LiveCAT 2025 Registration LIVE: IIM Kozhikode to close registration tomorrow; IIM admission criteriaSep 12, 2025 | 7:12 AM ISTRead More
IIM Kozhikode will close the Common Admission Test (CAT 2025) registration tomorrow. Aspirants can fill the CAT application form 2025 on the official website, iimcat.ac.in.
This Story also Contains
- CAT Exam Part-A: Quantitative Aptitude for CAT 2025
- Part-B: CAT Logical Reasoning and Data Interpretation:
- Part-C: CAT Exam VARC
- Free PDFs for CAT 2025 preparation
CAT Exam Part-A: Quantitative Aptitude for CAT 2025
CAT Exam Part-A: Quantitative Aptitude for CAT 2025 tests your mathematical skills, logical reasoning, and problem-solving ability. Mastering key topics like algebra, arithmetic, geometry, and number systems is essential to score well and boost your overall percentile.
Topic: Algebra (Functions and Graph) and CAT Problem-Solving Questions and 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.
Odd 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.
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 Now
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 2025, 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 for 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.
Frequently Asked Questions (FAQs)
Q: What’s the best way to solve linear arrangement puzzle questions?
A:
Start with definite clues, build the base structure, and eliminate options step-by-step for accurate and fast solutions.
Q: How should I approach graph-based CAT questions effectively?
A:
Understand function behavior visually, practice previous year graphs, and interpret values with accuracy to improve graph-solving speed.
Q: What is the domain and co-domain of a function?
A:
Domain is a set of input values represented on the x-axis of the graph.
Co-domain or range is a set of output values represented on the y-axis of the graph.
Q: What are the types of puzzles in logical reasoning?
A:
The main four types of puzzles are
Linear and circular arrangement
Floor-based Puzzles
Tabular Puzzles
Miscellaneous Puzzles which may include three or more categories
Q: What are conditional statements in grammar?
A:
Conditional statements in grammar are those sentences which give us a condition and its probable outcome. They often use conjunctions like ‘if’ or ‘unless’ to act as a linker between the condition and the result.
Q: What are the two parts of conditional sentences?
A:
The two parts of conditional sentences are
The if clause or the condition part describes the condition or the situation.
The main clause or the result part describes the outcome when the condition is met.
Q: What are the key concepts to cover in functions for CAT 2025?
A:
Focus on domain, range, composite functions, and graph-based interpretation questions commonly asked in CAT.
Q: What is a function in maths?
A:
A function can be defined as a relation between a set of inputs where each input has exactly one output. In other words, it maps one element of the input set to one element of the output set.
Articles
Related Stories
|
Upcoming Bschool Exams
Certifications By Top Providers
Explore Top Universities Across Globe
Popular Courses and Specializations
List of colleges accepting CAT
Browse Bschool Colleges by State
Questions related to CAT
On Question asked by student community
Have a question related to CAT ?
Yes, you can pursue an MBA at Babasaheb Bhimrao Ambedkar University (BBAU), Lucknow, through the CAT exam.
Eligibility Criteria:
-
Educational Qualification: A bachelor's degree with at least 50% marks (45% for SC/ST/PwD candidates) from a recognized university.
-
Entrance Exam: A valid CAT score is required for admission.
Admission Process:
-
Application: Register online through the BBAU admission portal.
-
Entrance Exam: Appear for the CAT exam and obtain a valid score.
-
Counseling: Shortlisted candidates will be called for counseling based on their CAT scores.
-
Document Verification: Submit necessary documents for verification.
-
Fee Payment: Complete the fee payment to confirm admission.
Course Details:
-
Duration: 2 years (full-time).
-
Specializations: Finance, Marketing, Human Resource Management, among others.
Placement Opportunities:
BBAU has a strong placement record, with top companies recruiting MBA graduates.
For more details and to apply, visit the official BBAU MBA admission page
Hello Amgothu
With 305 marks in ICAR PG and being from ST category, your chances of getting an AIEEA (CAT) seat is good, especially in plant sciences and less competitive subjects
Hello
As you said you by mistakenly done that, you don't need to get worry regarding that ,
Just inform the help desk and carry the correct certifications , the state certificate will not disqualify you .
The steps you can follow is -
1. You can check if the correction window is available or not
2. Contact the CAT desk immediately.
Hope this helps
In CAT registration, you cannot create a new user ID with the same mobile number, even if you use a different email ID. Each mobile number and email can be linked to only one account. If you already registered once, the system will not accept a duplicate with that number. To register again, you must use a new mobile number and new email ID. If you lost your old login, you can recover it through the forgot password/user ID option on the CAT portal.
Yes, you can fill the CAT form even if you currently have a backlog. CAT eligibility requires you to be in your final year of graduation or already graduated backlogs don’t stop you from applying.
While filling the form:
-
Enter the aggregate percentage/CGPA of marks you have obtained up to the latest semester for which results are declared (in your case till 4th semester).
-
There will be an option to mention that you have a backlog.
-
If you clear the backlog later, you’ll just need to show the updated marks during admission.
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
MBA/PGDM Admissions OPEN
Great Lakes PGPM & PGDM Admissions 2026
ApplyAdmissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
IBSAT 2025-ICFAI Business School MBA/PGPM 2026
ApplyIBSAT 2025-Your gateway to MBA/PGPM @ IBS Hyderabad and 8 other IBS campuses | Scholarships worth 10 CR
XAT- Xavier Aptitude Test 2026
Apply75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now
SDMIMD-PGDM Admissions 2026
ApplyAverage CTC 10 LPA | International Collaborations | Avail Merit Scholarships
Great Lakes - PGDM & PGPM Admissions 2026
ApplyAdmissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
Symbiosis MBA - SNAP 2025
Apply1 Exam accepted by 17 Top Symbiosis Institutes for 29 MBA programmes.
CAT Notifications
Never miss an CAT update
Get timely CAT updates directly to your inbox. Stay informed!