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..
IIM Kozhikode will retain its three-stage admission process for the MBA (PGP) 2026–28 batch, with CAT 2025 scores carrying a final weightage of 35 percent. The minimum overall CAT cut-off for general category candidates remains at 85 percentile, with sectional qualifying scores required in VARC, DILR, and QA. Shortlisting of candidates will be based on CAT performance, academic record, and personal interview rounds.
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
Day 18: Preparation Strategy for CAT Exam
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.
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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.
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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)) = ?
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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 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)
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.
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.
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: 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’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.
The results for the CAT 2025 entrance, which is conducted on November 30, 2025, were declared on December 22, 2025. Candidates can download and see their results on the official IIM CAT website. On the website, click on the "CAT 2025 Result/Scorecard" link to download the result by entering the required details.
The link to the website where you can check the published result is attached herewith. The result will be out soon. You can also check the cutoffs on the website of Careers360.
CAT does not restrict eligibility based on stream. Candidates from commerce, arts, science, engineering or any other background can appear for CAT and apply to MBA programmes offered by IIMs and other top B-schools.
The basic eligibility criteria for CAT are:
You must hold a bachelor’s degree in any discipline from a recognised university with at least 50 percent marks (45 percent for SC, ST and PwD categories). Final-year graduation students are also eligible to apply.
Being a commerce graduate can actually be an advantage in areas such as accounting, finance, economics and business studies, especially during MBA coursework in finance, marketing and operations.
After qualifying CAT, admission depends on multiple factors including CAT percentile, academic background, work experience (if any), performance in GD, WAT and personal interview rounds. Many IIMs and B-schools follow a diverse academic background policy, which means non-engineering candidates, including commerce graduates, often receive additional weightage.
Apart from IIMs, several reputed institutes such as FMS Delhi, SPJIMR Mumbai, MDI Gurgaon, IMT Ghaziabad, and many state and private universities also accept CAT scores for MBA admissions.
So, as a commerce graduate, you are fully eligible to appear for CAT and pursue an MBA, provided you meet the minimum academic requirements and perform well in the selection process.
If you want, I can also help you with realistic CAT percentile targets based on your academic profile or suggest suitable MBA colleges.
With a CAT 2025 raw score of 84 and strong sectionals, your expected percentile may fail in the high 98 range , depending on scaling. Your excellent academics and 2 years of work experience strengthen your profile .IIM Lucknow calls are possible but competitive for EWS engineers , while FMS Delhi looks mainly at CAT score and VARC , so you have a reasonable chance there . Final calls depend on cutoffs and composite score.
For a raw score of 56 in CAT 2025 Slot 3, your expected overall percentile is likely to be in the range of the 90th-95th percentile. The exact percentile can vary slightly on the final normalization process and the process and performance of all test-takers. In this
article
you'll find more about the CAT result.
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