XAT- Xavier Aptitude Test 2026
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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..
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.
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.
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.
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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.
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.
Polynomials Equations of Geometrical figures.
Functions and Graph (Arihant Publication)
How to prepare Quantitative aptitude for CAT by Arun Sharma.
2IIM CAT Preparation
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
The topic covered for the day is given below: Students can refer to Linear Arrangement Part 1 for Day 16
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:
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 A
If 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)
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 |
Verbal and Non-Verbal Reasoning by R S Agrawal
Cat preparation-iQuanta (YouTube Channel)
MBAP CAT EBook (Concept Theory)
LRDI for CAT and GMAT by Nishit K Sinha. (Advance)
MBAP CAT EBook (Practice Questions).
Previous Year's Question Papers
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.
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).
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
Parts of Speech
Tenses.
Word Power Made Easy.
CAT Edurav (YouTube Channel)
Wren and Martin
Practice Sample Question Papers.
Practice and remain focused; Day 19 will be posted tomorrow.
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.
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.
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
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.
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.
Focus on domain, range, composite functions, and graph-based interpretation questions commonly asked in CAT.
Understand function behavior visually, practice previous year graphs, and interpret values with accuracy to improve graph-solving speed.
Start with definite clues, build the base structure, and eliminate options step-by-step for accurate and fast solutions.
CAT ( Common Addmission Test ) is for those students who want to study MBA or other post-graduation program in mangement field. Who have Bachelor's degree with minimum 50% recognised university can apply for CAT .final year graduation students are also eligible to apply for CAT exam .
The CAT exam for mainly those students who want to study MBA or other business related courses.This exam is an entrance exam for getting admission into top mangement colleges.the exam tests skills like English,Maths and logical thinking. CAT exam is important because scoring well in CAT it's helps to students get into best college .
If there's a slight variation in your name between your government ID and school marksheets, it's best to use the name exactly as it appears on your 10th or 12th marksheet while filling out the CAT form, since academic records are the primary documents used for verification during admission. However, ensure that the variation isn’t too major if it is, you might consider getting an affidavit or correction done in the future. For now, stay consistent with your academic records to avoid any mismatch during document verification after the exam.
With a CAT rank of 5419, your percentile is around 95 to 97. This means you may not get into the top IIMs like Ahmedabad, Bangalore, or Calcutta, because they usually take students above 98 or 99 percentile. But you still have good chances at newer IIMs and other top MBA colleges.
You can get admission into IIMs like Amritsar, Raipur, Jammu, Udaipur, and Bodh Gaya. These IIMs accept students with lower percentiles, usually between 90 and 94.
Apart from IIMs, you can also get colleges like MDI Gurugram, IMI Delhi, Great Lakes Chennai, and maybe even FMS Delhi or JBIMS Mumbai depending on your category and performance in interview rounds.
You should now start preparing for the interview, group discussions, and written tests that most colleges will conduct after shortlisting you based on your CAT rank.
Here are websites you can check for cut-off and admission details:
https://www.imsindia.com/blog/cat-cutoff/
Hello Sahitya
For FMS Delhi, your percentile should be 99%+ and it should be 99.5%+ to be on the safer side.
Now coming to the academics:
1. 10th marks: 75%+ are given 10 out of 10
2. 12th marks: 75%+ are given 10 out of 10
3. Graduation marks: FMS doesn't considers graduation marks for screening.
So if you have 75%+ in both 10th and 12th, you will get full marks in academic score.
To know more about FMS: FMS
Hope this answer helps! Thank You!!!
A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services.
A Business Development Executive identifies and pursues new business opportunities to drive company growth. They generate leads, build client relationships, develop sales strategies, and analyse market trends. Collaborating with internal teams, they aim to meet sales targets. With experience, they can advance to managerial roles, playing a key role in expanding the company’s market presence and revenue.
Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.
A Sales Manager leads a sales team to meet targets, formulates strategies, analyses performance, and monitors market trends. They typically hold a degree in management or related fields, with an MBA offering added value. The role often demands over 40 hours a week. Strong leadership, planning, and analytical skills are essential for success in this career.
A marketing manager is a person who oversees a company or product marketing. He or she can be in charge of multiple programmes or goods or can be in charge of one product. He or she is enthusiastic, organised, and very diligent in meeting financial constraints. He or she works with other team members to produce advertising campaigns and decides if a new product or service is marketable.
A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.
Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
Individuals who opt for a career as a business analyst look at how a company operates. He or she conducts research and analyses data to improve his or her knowledge about the company. This is required so that an individual can suggest the company strategies for improving their operations and processes.
In a business analyst job role a lot of analysis is done, things are learned from past mistakes and the successful strategies are enhanced further. A business analyst goes through real-world data in order to provide the most feasible solutions to an organisation. Students can pursue Business Analytics to become Business Analysts.
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