CAT 2025 Question Paper with Solutions: The Common Admission Test (CAT) 2025, conducted by IIM Kozhikode, has officially wrapped up across all three slots for admission to MBA and other management programmes for the 2026–2028 batch. Now, the IIM has released the CAT result 2025 online along with the scorecard. Candidates who have appeared for the exam can download CAT scorecard 2025 with their login credentials. Earlier, we have shared the CAT 2025 question paper with solutions as well. Candidates can download the CAT 2025 Slot 1, Slot 2, and Slot 3 along with the official answer key.
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CAT 2025 Question Paper with Solutions
CAT 2025 Answer Key
CAT 2025 Slot-wise Question Paper with Solutions
CAT 2025 All Slot Analysis
CAT 2025 Overview
CAT 2025 Question Paper with Solutions
The official answer key is also provided below, aspirants can also use this article to go through the detailed slot-wise analysis, memory-based questions, and solutions to calculate their scores and get a fair idea of their expected percentile.
CAT 2025 Question Paper with Solutions
The CAT 2025 Slot 1 question paper with solutions has now been released. This page has been updated with memory-based questions, and expert solutions from Slot 1 to help candidates evaluate their performance accurately.
This section will give you quick access to the official answer key for CAT 2025 Slot 1, helping you verify your responses and estimate your scores with confidence.
The CAT 2025 exam will be conducted across multiple slots on the same day. Although the level of difficulty may vary slightly across slots, the overall paper pattern and structure remain the same. Reviewing the CAT 2025 slot-wise question paper is extremely important as it helps candidates evaluate:
Section-wise difficulty levels
Types of questions asked in each slot
Areas where mistakes were made
Comparison across slots
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The CAT 2025 question paper and solutions for all three slots are being updated here. Slot 1, Slot 2, and Slot 3 have now been successfully concluded, and memory-based questions along with detailed solutions are being added slot-wise. Candidates are advised to bookmark this page and check back regularly for the latest PDFs, answer keys, and expert solution updates.
feeling overwhelmed:
CAT 2025 Slot 1 Question Paper with Solutions (Memory-Based Questions)
Q 1. The number of distinct pairs of integers satisfying x>y≥3 and x+y<14 is __.
Solution:
We need integer pairs (x,y) with y≥3, x>y, and x+y<14, i.e. x+y≤13.
For a fixed y we need integers x satisfying y+1≤x≤13−y.
This requires y+1≤13−y, so 2y≤12 and hence y≤6. Thus y=3,4,5,6.
Number of x values for each y is (13−y)−(y+1)+1=13−2y:
Q 2. Arun, Tarun and Varun work for 24, 21 and 15 days and get paid Rs. 2160, Rs. 2400 and Rs. 2160 respectively. If the work has to be completed within 10 days, what is the minimum amount to be paid?
Solution:
Daily pay:
Arun = 2160/24=90 per day, rate = 1/24 Varun = 2160/15=144 per day, rate = 1/15
Tarun costs more, so ignore him.
Together in 10 days:
10⋅124+10⋅115>1
So Arun + Varun can finish within 10 days.
Since both cost ₹2160 per job, using only them costs ₹2160.
Q 3. The number of integer values of k for which x2−5x+k=0 has real roots is __.
Solution:
Real roots require b2−4ac≥0:
(−5)2−4(1)(k)≥0 25−4k≥0 −4k≥−25 k≤25/4 k≤6.25
So integer k≤6.
All integers k≤6 → infinitely many.
Q 4. The number of non-negative values of n for which log1/4(n2−7n+14)>0 is __.
Solution:
Base 1/4<1, so:
log1/4(x)>0⇒0<x<1 Here x=n2−7n+14.
We need:
0<n2−7n+14<1
Step 1: Check n2−7n+14>0
Discriminant: (−7)2−4(1)(14)=49−56=−7<0 So it is always positive.
Step 2: Solve:
n2−7n+14<1 n2−7n+13<0
Discriminant: 49−52=−3<0 Quadratic is always positive → cannot be < 0.
Answer: 0
Q 5. In a cafeteria, there are 5 breads. One can choose 1 bread (small or large) and up to 2 sauces from 6 sauces. How many orders ?
Solution:
Bread choices = 5 Size choices = 2 Sauce choices:
(60)+(61)+(62)=1+6+15=22
Total orders:
5×2×22=220
Answer: 220
Q 6. A rhombus has side 36 cm and area 396 cm². Find |d1−d2|.
CAT 2025 Slot 2 Memory-Based Question Paper with Solutions
Q1. If N=23×37×57×79×10!, how many factors of N are perfect squares and also multiples of 420?
First compute prime exponents in 10!: ,v2(10!)=⌊102⌋+⌊104⌋+⌊108⌋=5+2+1=8. ,v3(10!)=⌊103⌋+⌊109⌋=3+1=4. ,v5(10!)=⌊105⌋=2,v7(10!)=⌊107⌋=1.
Note 57=3×19, and 23,37,79 are primes, so multiplying by 23,37,57,79 adds +1 to exponents of 23,37,79,3,19. Thus ,N=28⋅34+1⋅52⋅71⋅191⋅231⋅371⋅791=28⋅35⋅52⋅71⋅191⋅231⋅371⋅791.
Prime factorization of 420 is 420=22⋅31⋅51⋅71.
Let a divisor d of N have exponent ep at prime p. Requirements for d: ,d∣N⇒0≤ep≤ exponent in N. ,d a multiple of 420⇒e2≥2, e3≥1, e5≥1, e7≥1. ,d a perfect square⇒ every ep is even.
Look at prime 7: exponent of 7 in N is 1. There is no even integer e7 with 1≤e7≤1. Hence it is impossible to satisfy both “perfect square” and “multiple of 420” simultaneously.
Therefore the number of such divisors is 0.
Q2. Adam’s savings = Ben’s expenditure = Mary’s savings =50,000. Incomes are in ratio 3:1:4, so let incomes be 3k, k, 4k.
Then ,Adam's expenditure=3k−50,000,Ben's expenditure=50,000,Mary's expenditure=4k−50,000.
Feasibility requires Ben's income ≥ Ben's expenditure, so ,k≥50,000.(1)
Given: Mary’s expenditure is less than thrice Adam’s expenditure: ,4k−50,000<3(3k−50,000). So ,4k−50,000<9k−150,000⇒100,000<5k⇒k>20,000.(2)
Given: Twice Adam’s expenditure is less than two times Ben’s income: ,2(3k−50,000)<2k. So ,6k−100,000<2k⇒4k<100,000⇒k<25,000.(3)
From (2) and (3): ,20,000<k<25,000.
This contradicts (1) k≥50,000. Hence no k satisfies all conditions. The data are inconsistent, so the correct choice is D: Data Inconsistent.
Q 3. A and B can complete a work in 12 days and 18 days respectively. They start together, but A leaves after 4 days. How many more days will B take to finish the remaining work?
A's rate is 1/12 work/day and B's rate is 1/18 work/day. Together their rate is 1/12+1/18=5/36 work/day.
Work done in 4 days =4⋅(5/36)=20/36=5/9. Remaining work =1−5/9=4/9.
B's rate is 1/18, so days for B to finish =(4/9)÷(1/18)=(4/9)⋅18=8.
8 days
Q 4. If the quadratic ax2+bx+c=0 has roots that differ by 4, and a+b+c=12, what is the value of b2−4ac?
For a quadratic ax2+bx+c=0 the difference of roots satisfies |r1−r2|=b2−4ac|a|. Given |r1−r2|=4, we have 4=b2−4ac|a|, so
b2−4ac=16a2
Thus the discriminant is b2−4ac=16a2. (Using a+b+c=12 alone does not fix a unique numeric value for a, so the discriminant is expressed in terms of a.)
Q 5. In a triangle ABC, the sides are in the ratio 3:4:5. If the area of the triangle is 96 sq units, what is its perimeter?
Let the sides be 3k,4k,5k. This is a right triangle, area =12⋅3k⋅4k=6k2.
Given 6k2=96⇒k2=16⇒k=4. Perimeter =(3+4+5)k=12k=12⋅4=48.
48 units
CAT 2025 Slot 3 Memory-Based Question Paper with Solutions
The CAT 2025 Slot 3 question paper is often perceived as time-pressured due to mental fatigue by the evening. This section will give you brief about CAT Slot 3 analysis. This section will be updated soon with the memory-based questions.
CAT 2025 - Slot 1 vs Slot 2 vs Slot 3 Expected Score Vs Percentile
Percentile
CAT 2025 Slot 1 (Prediction)
CAT 2025 Slot 2 (Prediction)
CAT 2025 Slot 3 (Prediction)
99.95
115+
110+
112+
99.9
103–106
101–105
102–104
99.5
90–92
89–91
88–90
99
78–80
77–79
76–78
97
66–68
65–67
65–67
95
56–58
55–57
55–57
90
45–48
44–46
44–45
85
40–42
39–41
39–40
80
35–36
34–35
34–35
75
32–33
31–32
31–32
70
30–31
29–30
29–30
60
25–26
24–25
24–25
CAT 2025 College Predictor
Use CAT 2025 College Predictor to check your chances for IIM and top MBA calls based on CAT percentile, profile, work experience and cut-off trends.
CAT 2025 slot 2 detailed analysis is provided below with their difficulty level and number of questions in each:
CAT 2025 Slot 2 Exam Analysis
Section
Total Questions
Difficulty Level
Good Attempts
VARC
24
Moderate to Difficult
16 - 18
DILR
22
Difficult
8 - 9
QA
22
Moderate to Difficult
12 - 13
CAT 2025 Analysis: Slot 3
We have given below the slot 3 analysis of CAT 2025, along with the number of questions and difficulty level of each section:
CAT 2025 Slot 3 Exam Analysis
Section
Total Questions
Difficulty Level
Good Attempts
VARC
24
Easy to Moderate
Will be updated
DILR
22
Easy to Moderate
Will be updated
QA
22
Moderate to Difficult
Will be updated
Total
68
Easy to Moderate
Will be updated
CAT 2025 Overview
A
B
The CAT 2025 exam pattern remained the same as last year. As there was no official notification regarding any change in the pattern, the exam followed the same structure and marking scheme as previous year. Below is the CAT 2025 exam pattern and marking scheme.
For every wrong answer in MCQs, a negative mark of -1 will be deducted
Non-MCQs do not have any negative marks
Frequently Asked Questions (FAQs)
Q: How important are mock tests for CAT?
A:
Mocks are essential. They help you understand real exam pressure, identify weak areas, and fine-tune your strategy.
Q: Do I need coaching to prepare for CAT?
A:
Coaching is optional. Many students prepare on their own with books, online resources, and mock tests. What matters most is consistency and practice.
Q: What is the best way to start preparing for CAT?
A:
Begin with understanding the syllabus and pattern, strengthen your basics in quant and reading comprehension, practice regularly with sectional tests, and take full-length mocks to improve speed and strategy.
Q: When will the official CAT 2025 answer key and response sheet be released?
A:
The official CAT 2025 answer key and response sheet are usually released within a few days after the exam by the conducting authority, the Indian Institute of Management.
Q: Are memory-based questions for CAT 2025 reliable?
A:
Yes, the CAT 2025 memory-based questions are compiled from multiple student inputs and verified by experts. While minor variations may exist, they give a very close representation of the actual exam and are useful for analysis and score estimation.
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