CAT 2025 Question Paper with Solutions: 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. With CAT 2025 Slot 1, Slot 2, and Slot 3 now completed, students have started sharing their experiences, helping everyone get a clearer sense of the overall difficulty, section-wise trends, and question patterns. 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 estimate their scores and get a fair idea of their expected percentile.
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.
CAT 2025 Slot 1 Question Paper with Solutions (Memory-Based Questions)
Q 1. The number of distinct pairs of integers satisfying $x>y\ge 3$ and $x+y<14$ is __.
Solution:
We need integer pairs $(x,y)$ with $y\ge 3$, $x>y$, and $x+y<14$, i.e. $x+y\le 13$.
For a fixed $y$ we need integers $x$ satisfying $y+1\le x\le 13-y$.
This requires $y+1\le 13-y$, so $2y\le 12$ and hence $y\le 6$. 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:
$10\cdot\frac{1}{24} + 10\cdot\frac{1}{15} > 1$
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 $x^2 - 5x + k = 0$ has real roots is __.
CAT 2025 Slot 2 Memory-Based Question Paper with Solutions
Q1. If $N=23\times 37\times 57\times 79\times 10!$, how many factors of $N$ are perfect squares and also multiples of $420$?
First compute prime exponents in $10!$: $,v_2(10!)=\left\lfloor\frac{10}{2}\right\rfloor+\left\lfloor\frac{10}{4}\right\rfloor+\left\lfloor\frac{10}{8}\right\rfloor=5+2+1=8.$ $,v_3(10!)=\left\lfloor\frac{10}{3}\right\rfloor+\left\lfloor\frac{10}{9}\right\rfloor=3+1=4.$ $,v_5(10!)=\left\lfloor\frac{10}{5}\right\rfloor=2,\qquad v_7(10!)=\left\lfloor\frac{10}{7}\right\rfloor=1.$
Note $57=3\times 19$, and $23,37,79$ are primes, so multiplying by $23,37,57,79$ adds $+1$ to exponents of $23,37,79,3,19$. Thus $,N=2^8\cdot 3^{4+1}\cdot 5^2\cdot 7^1\cdot 19^1\cdot 23^1\cdot 37^1\cdot 79^1 =2^8\cdot 3^5\cdot 5^2\cdot 7^1\cdot 19^1\cdot 23^1\cdot 37^1\cdot 79^1.$
Prime factorization of $420$ is $420=2^2\cdot 3^1\cdot 5^1\cdot 7^1$.
Let a divisor $d$ of $N$ have exponent $e_p$ at prime $p$. Requirements for $d$: $,d\mid N\Rightarrow 0\le e_p\le$ exponent in $N$. $,d$ a multiple of $420\Rightarrow e_2\ge2,\ e_3\ge1,\ e_5\ge1,\ e_7\ge1$. $,d$ a perfect square$\Rightarrow$ every $e_p$ is even.
Look at prime $7$: exponent of $7$ in $N$ is $1$. There is no even integer $e_7$ with $1\le e_7\le1$. Hence it is impossible to satisfy both “perfect square” and “multiple of $420$” simultaneously.
Therefore the number of such divisors is $ \boxed{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 $,\text{Adam's expenditure}=3k-50{,}000,\quad \text{Ben's expenditure}=50{,}000,\quad \text{Mary's expenditure}=4k-50{,}000.$
Feasibility requires Ben's income $\ge$ Ben's expenditure, so $,k\ge 50{,}000.\quad(1)$
Given: Mary’s expenditure is less than thrice Adam’s expenditure: $,4k-50{,}000<3(3k-50{,}000).$ So $,4k-50{,}000<9k-150{,}000\Rightarrow 100{,}000<5k\Rightarrow k>20{,}000.\quad(2)$
Given: Twice Adam’s expenditure is less than two times Ben’s income: $,2(3k-50{,}000)<2k.$ So $,6k-100{,}000<2k\Rightarrow 4k<100{,}000\Rightarrow k<25{,}000.\quad(3)$
From (2) and (3): $,20{,}000<k<25{,}000.$
This contradicts (1) $k\ge 50{,}000$. Hence no $k$ satisfies all conditions. The data are inconsistent, so the correct choice is $ \boxed{\text{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 $=4\cdot(5/36)=20/36=5/9$. Remaining work $=1-5/9=4/9$.
B's rate is $1/18$, so days for B to finish $=(4/9)\div(1/18)=(4/9)\cdot 18=8$.
$\boxed{8\text{ days}}$
Q 4. If the quadratic $ax^2+bx+c=0$ has roots that differ by $4$, and $a+b+c=12$, what is the value of $b^2-4ac$?
For a quadratic $ax^2+bx+c=0$ the difference of roots satisfies $|r_1-r_2|=\dfrac{\sqrt{b^2-4ac}}{|a|}$. Given $|r_1-r_2|=4$, we have $4=\dfrac{\sqrt{b^2-4ac}}{|a|}$, so
$b^2-4ac=16a^2$
Thus the discriminant is $b^2-4ac=16a^2$. (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 $=\tfrac{1}{2}\cdot 3k\cdot 4k=6k^2$.
Given $6k^2=96\Rightarrow k^2=16\Rightarrow k=4$. Perimeter $=(3+4+5)k=12k=12\cdot 4=48$.
$\boxed{48\text{ units}}$
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 Percentile Predictor
Use the CAT Percentile Predictor to estimate your score, gauge your performance, and know your chances of getting shortlisted by IIMs.
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
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.
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.
Hello,
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Hope this helps you.
NIT Rourkela CAT cutoff range is between 70-85 percentiles for the general category. 70 is the minimum percentile needed to apply, and 85 is the highest percentile. However, the maximum percentile depends on the particular year competition. It can be changed.
If you filled the UGC NET form under EWS but you don’t have a valid EWS certificate, then forget using the EWS category. They won’t accept it. You’ll automatically be treated as General category during document verification.
And no, this won’t make your form “invalid” or “illegal.” It just means you won’t get the EWS benefit.
So yes — you can still go for General category posts and Professor recruitment. Just don’t try to submit a fake/invalid certificate; that will get you disqualified.
Hello,
If your CAT admit card shows your surname first followed by your first name as entered in the form, it is correct. You do not need to worry about this format as long as it matches the details you provided. Ensure all other information on the admit card is accurate and carry it to the exam along with the required identification documents.
Hope this helps you.
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