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The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20
Edited By Team Careers360 | Updated on Nov 07, 2024 09:18 AM IST | #CAT
Practice sets are very crucial from an exam point of view. On day 20 Career’s 360 has prepared this practice test to give the candidates exposure to the actual exam pattern. Students may refer to it and practice more papers in the following days using our articles. You may prepare for the CAT test in an organized way by following our 60-day CAT exam preparation strategy. Make sure to improve your test-taking skills by practising with these CAT practice questions every day.
This Story also Contains
- CAT Sample Paper with solutions PDF
- CAT Exam: Sample Papers: Answers and Solutions
- CAT Exam: Sample Papers: Answers and Solutions
- CAT Exam: Sample Papers: Answers and Solutions
- Free Ebooks for CAT Preparation 2024
CAT Sample Paper with solutions PDF
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.
Quantitative Aptitude
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
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Use NowQ3. 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
Logical Reasoning
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?
VARC (CAT solved papers)
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
Error detection - (CAT exam paper sample)
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)
Fill the blank with the correct Article:
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 Exam: Sample Papers: Answers and Solutions
Part-A: Quantitative Aptitude
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 Exam: Sample Papers: Answers and Solutions
Part B - Logical Reasoning
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 Exam: Sample Papers: Answers and Solutions
Part-C: VARC
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.
Free Ebooks for CAT Preparation 2024
300+ Phrasal Verbs List for CAT Exam, Types With Examples & Practice Questions | CAT Quantitative Aptitude Questions with Answers PDF |
Frequently Asked Questions (FAQs)
1. What is a quadratic function?
A quadratic function is a degree two polynomial function in which the variable's maximum exponent is 2.
2. What are the roots of a quadratic equation?
The roots are the values of 'x' for which the quadratic equation is true, indicating where the graph intersects the x-axis.
3. How many roots can a quadratic equation have?
There can be 1, 0, or 2 roots in a quadratic equation.
4. What are real roots?
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.
5. Do these practice tests help me to score well?
Yes absolutely, practices will make you better, helping in increase of speed and accuracy.
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Questions related to CAT
Have a question related to CAT ?
With a 65 percentile in CAT, getting admission to USMS (Guru Gobind Singh Indraprastha University) may be difficult, as its cutoff is usually 75-85 percentile or higher for the general category.
However, you can consider other good MBA colleges that accept 60-70 percentile in CAT, such as:
Christ University, Bangalore
Institute of Public Enterprise, Hyderabad
Amrita School of Business, Kochi
PES University, Bangalore
KIIT School of Management, Bhubaneswar
Rajagiri Centre for Business Studies, Kochi
Army Institute of Management, Kolkata
Research their admission criteria, placements, and faculty to choose the best fit.
Poral Siddartha (siddu) 02 March,2025
Hello
With a 65 percentile in CAT , USMS (GGSIPU) admission is difficult as its cutoffs are usually higher. However, you can explore private and tier-2/tier-3 MBA colleges that accept lower CAT scores.
Options to Consider:
1. Private MBA Colleges :
Amity University, Noida
LPU (Lovely Professional University)
Alliance University, Bangalore
Christ University, Bangalore
Apeejay School of Management, Delhi
2. B-Schools Accepting Lower CAT Percentile :
BIMTECH (PGDM-Retail/IB/Insurance)
XIME Bangalore
ITM Navi Mumbai
IPE Hyderabad
Jaipuria Institute of Management
3. Other Entrance Exams :
Appear for MAT, CMAT, XAT (low percentile accepted by some colleges)
Consider state-level exams like MAH CET, KMAT or TANCET .
Hope this gives you the clarity you need.
Mitali Sharma 02 March,2025
Hello there,
With your
academic profile (General, Male, Non-Engineer)
, you should
target MBA colleges that focus more on CAT percentile than past academics.
Target Colleges & Minimum CAT Percentile:
- Top IIMs (A, B, C, L, K, I, FMS, XLRI, SPJIMR, MDI, etc.) – 90-99+ percentile (Tough due to low 12th marks)
- New & Baby IIMs (IIM Trichy, Udaipur, Rohtak, etc.) – 85+ percentile
- Tier-2 Colleges (IMT, TAPMI, GIM, KJ Somaiya, etc.) – 75-85 percentile
-
Tier-3 Colleges (BIMTECH, NDIM, ITM, etc.) – 60-75 percentile
What to Focus On?
- Score high in CAT (85+ percentile recommended)
- Apply to non-CAT colleges (XAT, NMAT, SNAP, CMAT)
- Strengthen profile with work experience or certifications
- Perform well in GD-PI rounds
You
can
get a good MBA college with
strategic applications
and
high CAT/XAT percentile.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
kumardurgesh1802 27 February,2025
Hi,
As per your given JEE Main percentile which is 88.34 in the SC Category, Your Predicted JEE MAINS 2025 rank may range between 147086 - 170102.
Based on the previous year analysis, According to your JEE MAINS percentile and category you have less possibility of getting a seat for admission in NIT Surathkal.
Some of the other colleges in which you have chances to get admission includes:
- Harcourt Butler Technological University
- G.L Bajaj Institute of Technology and Management
- Galgotais college of engineering and Technology
- Institute of engineering and Technology, Lucknow
- Kamla Nehru Institute of Technology
- Bundelkhand Institute of engineering and Technology
You can predict more colleges using the JEE MAINS 2025 college predictor tool.
Hope this information will help you
Devraj 26 February,2025
With your academic background, you have a good chance of getting into some of the top IIMs. Here's a breakdown of your profile:
- Class 10:91.6% - Excellent!
- Class 12:66% - Average, but not a deal-breaker
- B.Tech Computer Science: 8.4 CGPA - Very good!
Assuming you score well in CAT , here are some IIMs you might have a good chance of getting into:
- IIM Ahmedabad: Although the qualifying CAT cut off is 85 percentile, the final cut off typically goes up to 99-100 percentile.With a good CAT score, you might be considered.
- IIM Kozhikode: The CAT cut off for IIM Kozhikode is typically around 95-98 percentile. Your academic profile and a good CAT score might make you a competitive candidate.
- IIM Indore:The CAT cut off for IIM Indore is typically around 90-95 percentile. With a good CAT score and your academic background, you might have a chance.
Keep in mind that CAT cut offs can vary from year to year, and other factors like work experience, extracurricular activities, and personal interviews also play a significant role in the admission process.
To increase your chances, focus on scoring well in CAT, and make sure you have a strong overall profile.
sadafreen356 24 February,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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