Stalwart Career Institute

Get access to the detailed solutions to the previous years questions asked in IIM IPMAT exam

1 CAT 2024 Slot 1 - Quant

Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is

665

667

537

540




540



2 CAT 2024 Slot 1 - Quant

Let x, y and z be real numbers satisfying
4(x2 + y2 + z2) = a
4(x – y – z) = 3 + a
The a equals

3

4

1




3



3 CAT 2024 Slot 1 - Quant

If the equations x2 + mx + 9 = 0, x2 + nx + 17 = 0 and x2 + (m + n)x + 35 = 0 have a common negative root, then the value of (2m + 3n) is




38



4 CAT 2024 Slot 1 - Quant

Suppose x1, x2, x3 ......... x100 are in arithmetic progression such that x5 = – 4 and 2x6 + 2x9 = x11 + x13. Then, x100 equals

– 194

– 196

204

206




– 194



5 CAT 2024 Slot 1 - Quant

Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is




6



6 CAT 2024 Slot 1 - Quant

When 10100 is divided by 7, the remainder is

1

3

4

6




4



7 CAT 2024 Slot 1 - Quant

The sum of all real values of k for which  is

2/3

4/3

– 2/3

– 4/3




– 2/3



8 CAT 2024 Slot 1 - Quant

For any natural number n let an be the largest integer not exceeding √n. Then the value of a1 + a+ ...... + a50 is




217



9 CAT 2024 Slot 1 - Quant

In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 ? 6 ? 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to

15.18

13.26

14.84

12.75




13.26



10 CAT 2024 Slot 1 - Quant

The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310 + n, where n is a single digit natural number. Then, the value of (a + b + c + d + n) is




31



11 CAT 2024 Slot 1 - Quant

ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of ?ADE is




10



12 CAT 2024 Slot 1 - Quant

In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≥ x + 4 and − 4 ≤ x2 + y2 + 4(x − y) ≤ 0 is

π






13 CAT 2024 Slot 1 - Quant

If x is a positive real number such that 4 log10 x + 4 log100 x + 8 log1000 x = 13, then the greatest integer not exceeding x, is




31



14 CAT 2024 Slot 1 - Quant

The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is

15

14

10

20




14



15 CAT 2024 Slot 1 - Quant

A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is

1 : 27

1 : 81

1 : 26

1 : 80




1 : 80



16 CAT 2024 Slot 1 - Quant

A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is




66



17 CAT 2024 Slot 1 - Quant

Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is

18

16

14

12




12



18 CAT 2024 Slot 1 - Quant

There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is




15



19 CAT 2024 Slot 1 - Quant

An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is

3

4

5

6




6



20 CAT 2024 Slot 1 - Quant

A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is

50

36

42

18




42



21 CAT 2024 Slot 1 - Quant

If (a + b√n) is the positive square root of (29 – 12√5), where a and b are integers, and n is a natural number, then the maximum possible value of (a + b + n) is

18

22

4

6




18



22 CAT 2024 Slot 1 - Quant

The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is

1125 π

750 π

1125 π√2

750 π√2




1125 π√2



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Stalwart Career Institute

Stalwart Career Institute: Your Premier Destination for CAT, IPMAT, CMAT, and CUET Coaching in Indore

Welcome to Stalwart Career Institute, the best coaching institute in Indore, offering specialized coaching for CAT, IPM, CMAT, and CUET. Positioned as your definitive pathway to prestigious B-Schools across the country, we are dedicated to providing unparalleled guidance and support to fuel your MBA aspirations.

Why Opt for Stalwart Career Institute for Your MBA Aspirations?

  1. Proven Excellence: As a trusted name in management education, Stalwart Career Institute empowers students through Best-in-Class Teaching and Technology-Enabled Learning.
  2. Impressive Results: Our commitment to delivering quality education is evidenced by numerous success stories and admissions to renowned B-Schools, including IIMs, IIFT, MDI Gurugram, SCMHRD, SIBM Pune, NMIMS, MICA, GIM Goa, IMT Ghaziabad, and more.
  3. Dedication to Excellence: We showcase our dedication through comprehensive study materials and online tests, designed to instill confidence in every student facing MBA entrance exams.

Why Stalwart Career Institute Excels in CAT, IPMAT, CMAT, and CUET Coaching

  1. Experienced Faculties: Our instructors, CAT/XAT toppers with years of teaching expertise, impart invaluable knowledge to students.
  2. Dynamic Study Material: We annually update our content to align with the latest exam patterns, offering the largest question bank (Online + Offline) to students.
  3. National Online Test Series: Recognizing the significance of online tests, our in-house web portal features a variety of tests, including topic tests, sectional tests, video capsules, full-length tests, online magazines, and more.
  4. Mentorship Program: Beyond academics, we provide guidance and mentorship to students, both academically and mentally, ensuring they are well-prepared to crack national-level tests.
  5. GD/PI/WAT Training: Converting a call into admission is paramount. At Stalwart Career Institute, we place equal emphasis on GD/PI/Essay writing alongside core academic subjects.

Courses Offered:

  • CAT Coaching in Indore: Comprehensive coaching program covering Verbal Ability, Quantitative Aptitude, Data Interpretation, and Logical Reasoning.
  • IPMAT Coaching in Indore: Specialized coaching for Integrated Program in Management Aptitude Test (IPMAT), encompassing Quantitative Ability, Verbal Ability, and Logical Reasoning.
  • CMAT Coaching in Indore: Tailored coaching for the Common Management Admission Test (CMAT), addressing Quantitative Techniques, Data Interpretation, Logical Reasoning, Language Comprehension, and General Awareness.
  • CUET Coaching in Indore: Customized coaching for the Common University Entrance Test (CUET), covering relevant subjects and preparing students for the unique challenges of the exam.

Online Courses:

  • CAT Coaching Online: Interactive sessions covering the entirety of CAT’s syllabus, with recorded sessions for flexible learning.
  • IPMAT Coaching Online: Specialized coaching sessions dedicated to the IPMAT syllabus, accessible anytime, anywhere.
  • CMAT Coaching Online: Engaging online sessions designed to thoroughly prepare you for CMAT, including comprehensive study material and practice tests.
  • CUET Coaching Online: Tailored online coaching sessions for CUET, ensuring comprehensive preparation for this distinct examination.

Preparation Books:

To complement our coaching programs, we recommend the following preparation books:

  • CAT Preparation Books: Curated materials focusing on Verbal Ability, Quantitative Aptitude, Data Interpretation, and Logical Reasoning.
  • IPMAT Preparation Books: Essential resources covering Quantitative Ability, Verbal Ability, and Logical Reasoning for IPMAT.
  • CMAT Preparation Books: Comprehensive guides addressing Quantitative Techniques, Data Interpretation, Logical Reasoning, Language Comprehension, and General Awareness for CMAT.
  • CUET Preparation Books: Specialized books catering to the unique syllabus and requirements of the Common University Entrance Test.

Stalwart Career Institute offers a seamless blend of classroom and online courses, ensuring flexibility and accessibility for students aiming to excel in CAT, IPM, CMAT, CUET, and more. Choose the mode of learning that suits your schedule and preferences while receiving the same high-quality education and guidance. Your aspirations, our expertise – a winning combination for your MBA dreams.