XAT- Xavier Aptitude Test 2026
75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now
Practice sets play a vital role in CAT preparation, offering real-time exam experience and improving accuracy under pressure. On Day 20, Careers360 has curated a dedicated practice test to help candidates get familiar with the actual CAT pattern. Aspirants are encouraged to use this test and continue daily practice using resources in our 60-day CAT preparation strategy. Regular practice with such tests helps tp sharpen problem-solving skills for the CAT 2025 exam.
A CAT sample paper with solutions PDF is a mock version of the actual exam, designed to simulate the CAT question pattern and difficulty level. It helps aspirants understand the exam structure, improve time management, and assess their preparation level. Practising sample papers regularly also boosts confidence and highlights weak areas that need focused revision.
This CAT Sample paper consists of three Sections:
Part- A consists of 9 questions.
Part- B consists of 7 questions.
Part- C consists of 9 questions.
75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now
Highest CTC: Rs 18.33 LPA | Average CTC: Rs 7.39 LPA | Experiential Learning | Classes by Industry Professionals | Alumni Mentorship Program
Q1. For the given pair (x, y) of positive integers, such that (-x + 3y/2) = 7 and x < 210. How many integer values of y satisfy the given conditions? (CAT previous year questions)
340
341
342
1024
Q2. A quadratic function f(x) attains a maximum of 12 at x = 1. The value of the function at x = 0 is 7. What is the value of f (x) at x = -11? (CAT previous year questions)
-805
-719
-859
-883
Q3. If the roots of the equation in y i.e. y3 – ay2 + by – c = 0 are three consecutive integers, then the smallest possible value of b (nearest to its integer value) is ______________ [TITA]
Q4. The sum of the integers in the solution set of |x2 - 7x| > 5 is: (CAT exam model paper)
10
15
20
0
Q5. The equation x2 + ax + (3-b) = 0 has real roots. What is the minimum value of a2 + b2? (CAT previous year questions)
0
2
4
8
Q6. X is p% less than Y and Z is p% more than Y. If X is 2.5p% more than Z, then find p.
(Note: p ≠ 0) - (CAT previous year questions)
20
40
60
50
Q7. The value of the base of a triangle for which area is minimum if the relation between the perpendicular distance from the vertex and the base is p = 7b2 - 84 is _______________ (where b represents base and p represents perpendicular distance) [TITA]
Q8. Let f (x) = max (2x + 1, 3 − 4x), where x is any real number. Value of f(x) at x = 7.5 is: (CAT exam model paper)
-11
- 27
16
43
Q9. Let g (x) be a function such that g (x + 1) g (x) = 12 for every real x. Then what is the value of g (11) g (0)? (CAT exam model paper)
1
12
1/12
6
Direction (Q1-Q3):
Four friends Arun, Bittu, Cirag and Dheeraj went for an excursion with their wives Priya, Renu, Sharita and Varti, not necessarily in the same order. Each couple hails from a different city, including Madurai, Cutnee, Kurnool, and Hapur, but they are not necessarily in that order. They went to Delhi to visit the Pinkfort, where they sat in a row. Each wife always sat to the immediate right of her husband.
(CAT practice questions)
(i) Bittu sat to the immediate right of Priya.
(ii) Dheeraj is from Hapur and Priya is not from Madurai.
(iii) Renu and her husband were sitting to the immediate right of the couple that hailed from Cutnee.
(iv) Chirag and his wife were sitting to the immediate left of the couple from Kurnool and Chirag was sitting to the immediate right of Sharita.
(v) Arun sat to the immediate right of Renu, who is not from Madurai.
Q1. Who is Dheeraj’s wife?
Sharita
Priya
Varti
Renu
Q2. Which couple is from Cutnee?
Varti and Bittu
Dheeraj and Renu
Chirag and Priya
Arun and Sharita
Q3. Who is the husband in the couple, who is seated second in the row from left to right?
Arun
Bittu
Chirag
Dheeraj
Direction (Q4- Q7) (CAT practice questions)
A cube is formed by joining 216 smaller and identical cubes. The bigger cube is painted black colour on all its faces. From the bigger cube, 64 smaller cubes from a corner were taken out and the cube formed by joining these 64 smaller cubes is painted pink in all its faces. Again, this cube is fitted back into its usual position in the large cube.
Q4. How many smaller cubes have no faces painted?
Q5. How many smaller cubes have three faces painted?
Q6. How many smaller cubes have only two faces painted?
Q7. How many smaller cubes have only one face painted?
In the questions below, find the phrase with an error.
Q1: If I had known, I would lend you my car.
I will lend you my car
I would lent you my car
I would have lent you my car
No improvement needed
Q2. You have no trouble at school, if you had done your homework.
You would have had no trouble at school.
You will have no trouble at school.
You would had no trouble at school
No improvement needed
Q3. If you had done better at your interview, you get that job.
You will get that job.
You would get that job.
You would have got that job.
No improvement needed
Choose appropriate sentence
Q4. While the guests danced, the thieves broke into the house.
While the guests have danced
While the guests were dancing
While the guests had danced
No improvement needed
Q5. Take a shower (a)/ you will (b)/ feel better. (c) / No error (d)
(a)
(b)
(c)
(d)
Q6. Whenever I look (a)/ at the moon, my heart (b)/ fills with the pleasure. (c)/ No error(d)
(a)
(b)
(c)
(d)
Q7. The whole block of flats (a)/ including two shops were (b)/ destroyed in fire. (c)/ No error (d)
(a)
(b)
(c)
(d)
Q8. The man who cannot (a)/ believe his senses and the man who cannot (b)/ believe anything else are insane. (c)/ No error(d)
(a)
(b)
(c)
(d)
Q9. If you go by __ train you can have quite__ comfortable journey, but make sure you get ___ express, not __ train that stops at all the stations.
a, an, a, the
an, a, the, a
No article, an, a, the
No article, a, an, a
CAT Quantitative Aptitude sample papers with detailed answers and solutions help in effective preparation. These papers resemble the actual exam pattern and include questions from all three sections, Quantitative Aptitude. Each question is accompanied by a step-by-step solution, helping aspirants understand the correct approach.
Answer 1: (B)
3y/2 = 7 + x
⇒ y = (14 + 2x)/3; for y to be integer (14 + 2x) should be divisible by 3
So, x = 2; y = 6
When x= 5, y = 8
When x = 8, y = 10
When x = 11, y = 12 and so on…
So, there is an AP in x with the first term being 2 and the common difference is 3.
nth term in x must be less than or equal to 210 i.e., 1024.
Therefore, 2 + (n-1)3 ≤ 1024
⇒ n ≤ (1022/3) +1
Therefore, n must be 341.
Hence, there can be 341 solutions.
Answer 2: (D)
If the function gets the maximum of 12 at x = 1
f(x) = a(x – 1)2 + 12
So, f (0) = a + 12 = 7 [Given]
⇒ a = –5
f(x) = –5(x – 1)2 + 12
So, f(-11) = –5(-12 – 1)2 + 12 = –845 + 12 = –833
Hence, the correct answer is –833.
Answer 3:
Let roots be (n - 1), n and (n + 1).
In a cubic equation, the coefficient of y divided by the coefficient of y3 represents the sum of the product of roots taken two at a time.
So, b = the sum of the product of roots taken two at a time
n(n - 1) + (n + 1)n + (n - 1) (n + 1) = b
⇒ n2 - n + n2 + n + n2 - 1 = b
⇒ 3n2 - 1 = b
The value of b will be minimal when the value of n2 is minimum.
i.e., n2 = 0
So, 3 × 0 - 1 = b
∴ b = -1
Hence, the correct answer is -1.
Answer 4: (D)
|x2 - 7x| > 5
⇒ x2 - 7x > 5 or x2 - 7x < -5
Case 1:
⇒ x2-7x > 5
⇒ x2 - 7x – 5 > 0
⇒ x > [(7±√69)/2], which gives two solutions x > 7 or x < 0 (for x to be integer).
Case 2:
⇒ x2 - 7x < -5
⇒ x2 - 7x + 5 < 0
⇒ x < [(7±√29)/2], which gives two solutions x < 7 or x > 0 (for x to be integer).
So, x = [1, 2, 3, 4, 5, 6]
There is no common solution in both cases.
Hence, the correct answer is 0.
Answer 5: (D)
For real roots; a2 – 4(3 – b) ≥ 0
⇒ a2 + 4b – 12 ≥ 0
⇒ a2 + 4b + b2 – b2 – 12 ≥ 0
⇒ a2 + b2 ≥ b2 – 4b + 12
⇒ a2 + b2 ≥ b2 – 4b + 4 + 8
⇒ a2 + b2 ≥ (b – 2)2 + 8
At b = 2, a2 + b2 has the minimum value. i.e., 8.
Hence, the correct answer is 8.
Answer 6: (A)
X = (100 – p) Y/100
Z = (100 + p) Y/100
X = (100 + 2.5p) Z/100
From 1st and 2nd relation, we get X = Z (100 – p) / (100 + p)
So, Z (100 – p) / (100 + p) = (100 + 2.5p) Z/100
⇒ 100(100 – p) = (100 + p) (100 + 2.5p)
⇒ – 100p = 100p – 250p + 2.5p2
⇒ 50p = 2.5p2
⇒ p = 20
Hence, the correct answer is 20.
Answer 7:
Area = ½ (base) (height) = ½ b (7b2 - 84) = 7b3/2 - 84b1/2
For Area to be minimum, find dA/db = 21/2 b2 – 42 = 0
⇒ b2 = 4
⇒ b = 2 or b = -2
Now find d2A/db2 = 21b
At b = 2; d2A/db2 = 42, which is greater than 0.
So, at b = 2, we get the minimum value of Area.
Hence, the correct answer is 2.
Answer 8: (C)
f(x) = max (2 × 7.5 + 1, 3 – 4 × 7.5) at x = 7.5
⇒ f(x) = max (16, -27) at x = 7.5
Hence, the correct answer is 16.
Answer 9: (B)
For x = 0; g(1) = 12/g(0)
Similarly g(2) = 12/g(1), which gives g(2) = g(0)
g(3) = g(1) and so on.
Therefore, g(11) = g(9) = g(7) = ……= g(1) = 12/g(0)
⇒ g (11) g (0) = 12
Hence, the correct answer is 12.
CAT Logical Reasoning sample paper solutions provide in-depth explanations for a wide range of LR questions, including puzzles, arrangements, blood relations, and logical sequences. These step-by-step solutions help candidates understand the reasoning behind each answer, improve their problem-solving techniques.
Solution 1-3:
Males: Arun, Bittu, Cirag and Dheeraj
Females: Priya, Renu, Sharita and Varti
Cities: Madurai, Cutnee, Kurnool and Hapur
Regarding the couples, the wife always sits to the immediate right of her husband.
From (i), Bittu is not the husband of Priya.
From (ii), Dheeraj is from Hapur.
From (iii), Renu is not from Cutnee.
From (iv), Cirag is not from Kurnool and is not the husband of Sharita.
From (v), Arun is not married to Renu and Renu is not from Madurai.
Possibility Table
HUSBAND | WIFE | CITY |
Bittu | Priya | Hapur |
Dheeraj | Sharita, Reno, Priya, Varita | Hapur |
Chirag | Sharita, Renu, Priya or Varita | Hapur, Kurnool, Mudrai or Cutnee |
Arun | Renu | Hapur, Cutnee, Madurai or Kurnool |
So, according to the table, there were two possibilities for Chirag's wife either Priya or Varita so we will consider these cases one by one.
Case I: If we consider Priya as Chirag’s wife and Priya can’t be from Madurai so they must be from Cutnee.
So, the arrangement could look like this:
------ Sharita Chirag --- Priya Bittu---Renu Arun-------
Now after this arrangement only one man and one woman is left so we can consider the woman as Arun’s wife and the man as Sharita’s Husband
Dheeraj ------ Sharita Chirag --- Priya Bittu---Renu Arun-------Varti
This arrangement fulfils all the conditions, so it is not required to consider any other case.
Answer 1: Dheeraj is married to Sharita. [Which is option (A)]
Answer 2: Chirag and Priya are from Cutnee. [Which is option (C)]
Answer 3: Chirag and his wife are seated second in the row. [Which is option (C)]
Solution 4 to 7:
Answer 4: By assuming a 4 × 4 × 4 cube is also not painted with pink colour, the number of cubes with no faces painted is = (6 – 2)3 = 64. Of these 64 smaller cubes now, in the second, third and fourth layers leftmost 9 cubes are painted pink, on the bottom surface four smaller cubes are painted pink and on the fourth layer back six smaller cubes are painted.
Hence, the total number of cubes with no face painted = 64 – 19 = 45
Answer 5: The number of cubes which are three faces painted before removing 64 smaller cubes = 8 and after painting with pink colour to those 64 smaller cubes seven new cubes will have three faces painted.
Hence, the total number of cubes with three faces painted = 8 + 7 = 15
Answer 6: The number of smaller cubes painted on two faces in the larger cube after removing 4 × 4 × 4 is illustrated as shown below.
9 edges with four smaller cubes with two faces painted = 9 × 4 = 36; 3 edges with one cube with two faces painted = 3 × 1 = 3
In the pink cube, there are 24 cubes on 12 edges which are painted on two faces.
Hence, the number of cubes with two faces painted = 36 + 3 + 24 = 63
Answer 7: The number of cubes with one face painted in the larger cube = 3 × 16 + 3 × 7 = 69. Number of cubes with one face painted in the 4 × 4 cube = 6 × 4 = 24
Hence, the total number of smaller cubes with one face painted = 69 + 24 = 93
CAT VARC sample paper solutions offer detailed explanations for reading passages, para jumbles, sentence completion, and odd sentence questions. These solutions guide candidates on how to approach each question type, identify key ideas, and eliminate incorrect choices.
Answer 1: (C)
if clause: had known (past perfect), Main clause: would/ could have lent.
Answer 2: (A)
if clause: had done (past perfect), the main clause: would/ could/ might have had.
Answer 3: (C)
if clause: had done (past perfect), the main clause: would/ could/ might have had.
Answer 4: (B)
The previous event is simple past, then the next event must be past continuous for continuous action.
Answer 5: D
“take a shower” is an idiomatic phrase. Hence, No error.
Answer 6: (C)
“with pleasure” is an idiomatic phrase. With pleasure replaced with “pleasure”.
Answer 7: (B)
“was” is used instead of “were”. The whole block is considered a singular subject and the singular subject takes a singular verb.
Answer 8: (D)
when two nouns get added with the use of ‘and’ and a possessive adjective article is used before both nouns then we use a plural verb but when the possessive adjective article is used with only one noun then it is considered to be one and hence singular verb is used.
Answer 9: (D)
No article is used between By and Means of transport.
Before comfortable “a” should be used.
Before “express”, “an” will be used as there is a vowel at the start.
Before “train”, “a” will be used.
CAT 2025 eBooks by Careers360 offer comprehensive preparation material covering Quant, VARC, and DILR. These digital guides include theory, shortcuts, solved examples, and practice questions, helping aspirants strengthen concepts and enhance exam strategy for a high percentile score.
eBook Title | Download Links |
3000+ Most Important Words - Vocabulary Builder | |
500+ Most Important Idioms and Phrases | |
300+ Most Important Phrasal Verbs | |
CAT 2025 Verbal Ability and Reading Comprehension (VARC) Study Material | |
Permutation & Combination - Video Lectures and Practice Questions | |
Mastering DILR Questions with Expert Solutions | |
CAT 2025 Exam's High Scoring Chapters and Topics | |
Mastering CAT Exam: VARC, DILR, and Quant MCQs & Weightages | |
CAT 2025 Mastery: Chapter-wise MCQs for Success for VARC, DILR, Quant | |
CAT 2025 Quantitative Aptitude Questions with Answers | |
CAT DILR Questions with Solution, Download LRDI Questions for CAT |
A quadratic function is a degree two polynomial function in which the variable's maximum exponent is 2.
The roots are the values of 'x' for which the quadratic equation is true, indicating where the graph intersects the x-axis.
There can be 1, 0, or 2 roots in a quadratic equation.
Real roots are real-valued equation solutions. This implies that they may be positive, negative, or zero, but not imaginary or complex. The real roots of the equation x^2-4=0 are x=2 and x=-2, which are both real values that satisfy the equation. Simply said, real roots are the values of a variable that satisfy the equation and may be found on the number line.
Yes absolutely, practices will make you better, helping in increase of speed and accuracy.
Practice sets help you apply concepts and improve problem-solving speed. They prepare you for different question types and build exam confidence.
You should attempt practice sets regularly to stay consistent. Daily or alternate-day practice helps track progress effectively.
Always review your answers carefully. Understand your mistakes and learn the correct approach. This helps avoid repeating errors in future tests.
Practice sets are great for focused learning, but cannot replace mock tests. Mock tests simulate the real exam environment and test your overall readiness.
Identify topics where you make mistakes while solving practice sets. Spend extra time revising those concepts and solving more questions from those areas.
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!!!
Hello Ayush
This is definitely a myth that with 0 work-ex you can't get IIM ABC because freshers still get into them although the competition is brutal but if you have good academics (9/9/9) and a good CAT (99.5%+), you have a chance.
These are some other good colleges except IIM ABC which you can aim for:
TIER 1:
Tier 2:
To know more about CAT: CAT by Careers360
Hope this answer helps! Thank You!!!
Hello Aspirant,
With an AIR (All India Rank) of 1,60,000 in NEET and in the OC (Open Category) there is a very slim chance of getting an MBBS seat in a government medical college, especially in General Category seats through All India Quota (AIQ), but here are some options:
You can also participate in state counselling rounds, as sometimes, seats remain vacant/unfilled, including mop-up rounds.
Hello aspirant,
The question papers for CAT MGU University can be found on their official website, or you can also visit careers360 website for the same.
The link of which, I am attaching here,
https://university.careers360.com/articles/mgu-cat-2025
Regards
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.
75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now
Amongst top 3% universities globally (QS Rankings)
NAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed
Ranked #41 amongst institutions in Management by NIRF | 100% Placement | Last Date to Apply: 30th July | Limited seats available in select program
25+ years of legacy | NAAC A+ Grade | 800+ Recruiters | 1.5 CR-Highest Package
NAAC A+ Grade | Ranked No.1 Private University in India (QS World University Rankings 2025)