CAT 2024 Question Paper With Solutions (Released): Download Free PDF for Slot 1, 2 and 3

CAT 2024 Question Paper: Students who appeared for CAT 2024 exam on November 24, 2024, can download the answer key of CAT 2024 as the answer key is OUT. This year, the CAT 2024 question paper pattern has been changed. As per the CAT 2024 test takers, the CAT 2024 question paper has 68 questions with a total of 204 marks. The DILR section has 22, QA has 22, and VARC has 24 questions. The para-jumble section was completely removed from the VARC section. The overall difficulty level of the CAT slot 1 question paper was easy to moderate, the CAT slot 2 question paper was moderate, and the CAT slot 3 question paper was also moderate. Know all about the CAT exam.

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This Story also Contains

1. CAT 2024 Question Paper PDF Download Free
2. CAT 2024 Slot 3 Questions (Memory Based)
3. CAT 2024 Slot 2 Questions (Memory Based)
4. CAT 2024 Slot 1 Questions (Memory Based)
5. CAT 2024 Question Paper Analysis
6. CAT Slot 2 Question Paper Analysis
7. CAT 2024 Slot 3 Question Paper Sectional Analysis
8. CAT Score vs Percentile
9. CAT All Slots Analysis

Latest: Download CAT 2024 Question Paper PDF

CAT 2024 Question Paper PDF Download Free

Download CAT 2024 question paper slot-wise for free from the table below.

CAT 2024 Slot 3 Questions (Memory Based)

Q 1. $3^a=4,4^b=5,5^c=6,6^d=7,7^e=8,8^f=9$. abcdef $\Rightarrow ?$

Solution:

From $3^a=4$, take log:

$a=\log _3 4$

From $4^b=5$ :

$b=\log _4 5$

From $5^c=6$ :

$c=\log _5 6$

From $6^d=7$ :

$d=\log _6 7$

From $7^e=8$ :

$e=\log _7 8$

From $8^f=9$ :

$f=\log _8 9$

$a b c d e f=\left(\log _3 4\right)\left(\log _4 5\right)\left(\log _5 6\right)\left(\log _6 7\right)\left(\log _7 8\right)\left(\log _8 9\right)$

Using the change of base formula $\log _a b \cdot \log _b c=\log _a c$, the product simplifies:

$\left(\log _3 4\right)\left(\log _4 5\right)\left(\log _5 6\right)\left(\log _6 7\right)\left(\log _7 8\right)\left(\log _8 9\right)=\log _3 9$

$\log _3 9=\log _3\left(3^2\right)=2$

Q 2. Upto 500, how many numbers has distinct digits

Solution:

Case 1: 1-digit numbers
There are 1 -digit numbers from 1 to 9 (excluding 0 since 0 is not counted in the distinct digits range here): 9 numbers.

Case 2: 2-digit numbers
For a 2-digit number $A B$ :
- The first digit $A$ (tens place) has 9 choices (1 to 9 ).
- The second digit $B$ (units place) must be different from $A$, so it has 9 choices ( 0 to 9, excluding $A$ ).

Thus, $9 \times 9=81 \text { numbers }$

Case 3: 3-digit numbers less than 500
For a 3-digit number $A B C$, with $A$ as the hundreds place:
- $A$ can be $1,2,3$, or 4 (since the number must be less than 500 ). This gives 4 choices for $A$.
- $B$ (tens place) must be different from $A$, so it has 9 choices ( 0 to 9, excluding $A$ ).
- $C$ (units place) must be different from both $A$ and $B$, so it has 8 choices.

Thus, $4 \times 9 \times 8=288 \text { numbers }$

So, the total count of numbers up to 500 with distinct digits is $9+81+288=378$

Q 3. Avg of 3 numbers, is 28 when the largest is decreased by 10, smallest is increased by 7, Avg becomes 2 more than middle term Keeping the order unchanged, the Difference between largest and smallest number is now 64. Find the original largest number.

Solution:

Let a be the smallest, b be the middle and c be the largest number.

Average of $\mathrm{3}$ numbers is $\mathrm{2 8}$

$
\begin{aligned}
& \frac{a+b+c}{3}=28 \\
& a+b+c=84
\end{aligned}$

When the largest number is decreased by 10 and the smallest number is increased by 7, the new average becomes 2 more than the middle term:
- The new numbers are $a+7, b$, and $c-10$.
- The new average is:

$\frac{(a+7)+b+(c-10)}{3}=b+2$
Simplify the left-hand side:

$\frac{a+b+c-3}{3}=b+2$

Substitute $a+b+c=84$ :

$\begin{gathered}
\frac{84-3}{3}=b+2 \\
\frac{81}{3}=b+2 \\
27=b+2 \\
b=25
\end{gathered}$

The difference between the largest and smallest number after modifications is 64:
- The modified numbers are $a+7$ and $c-10$.
- The difference between them is:

$(c-10)-(a+7)=64$

Simplify:

$\begin{gathered}
c-a-17=64 \\
c-a=81
\end{gathered}$

Solve for $a$ and $c$

Substituting $b=25$ in $a+b+c=84$ :

$\begin{gathered}
a+25+c=84 \\
a+c=59
\end{gathered}$

We also have $c-a=81$.

Let's solve these two equations:
1. $a+c=59$
2. $c-a=81$

Add the two equations:

$\begin{gathered}
(a+c)+(c-a)=59+81 \\
2 c=140 \\
c=70
\end{gathered}$

Now substitute $c=70$ in $a+c=59$ :

$
\begin{gathered}
a+70=59 \\
a=-11
\end{gathered}$

The original largest number is c=70

Q 4. Gopi mark up the price by $\mathrm{2 0 \%}$, Ram gets $\mathrm{1 0 \%}$ discount thus saving Rs 15. Find Profit mode by Gopi?

Solution:

Let the cost price (C.P.) of the item be $x$.

Marked Price (M.P.)

Gopi marks up the price by $20 \%$ :

$\text { M.P. }=x+0.2 x=1.2 x$

Ram gets a $10 \%$ discount on the marked price:

$\text { S.P. }=1.2 x-0.1(1.2 x)=1.2 x-0.12 x=1.08 x$

The discount given to Ram is:

$\text { Discount }=\text { M.P. }- \text { S.P. }=1.2 x-1.08 x=0.12 x $

From the problem, Ram saves Rs 15 as the discount:

$0.12 x=15 \Longrightarrow x=\frac{15}{0.12}=125$

The cost price is $x=125$, and the selling price is:

$\text { S.P. }=1.08 x=1.08 \times 125=135$

Profit is the difference between the selling price and the cost price:

$\text { Profit = S.P. }- \text { C.P. }=135-125=10$

Q 5. Sum of all distinct values of $10^x+\frac{4}{10^x}=\frac{81}{2}$

Solution:

Let $y=10^x$. Then, the equation becomes:

$y+\frac{4}{y}=\frac{81}{2}$

$y^2+4=\frac{81}{2} y$

$2 y^2-81 y+8=0$

Use the quadratic formula:

$\begin{gathered}
y=\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}, \quad a=2, b=-81, c=8 . \\
y=\frac{81 \pm \sqrt{81^2-4(2)(8)}}{2(2)} . \\
y=\frac{81 \pm \sqrt{6561-64}}{4} . \\
y=\frac{81 \pm \sqrt{6497}}{4} .
\end{gathered}$
Thus, the solutions for $y$ are:

$y_1=\frac{81+\sqrt{6497}}{4}, \quad y_2=\frac{81-\sqrt{6497}}{4} .$
Since $y=10^x$, the corresponding solutions for $x$ are:

$ x_1=\log _{10}\left(\frac{81+\sqrt{6497}}{4}\right), \quad x_2=\log _{10}\left(\frac{81-\sqrt{6497}}{4}\right)$

Using the property of logarithms:

$\log _{10}(a)+\log _{10}(b)=\log _{10}(a \cdot b)
$
Here, $a=\frac{81+\sqrt{6497}}{4}, \quad b=\frac{81-\sqrt{6497}}{4}$

The product $a \cdot b$ is:

$\begin{gathered}
a \cdot b=\frac{(81+\sqrt{6497})(81-\sqrt{6497})}{16} \\
a \cdot b=\frac{81^2-(\sqrt{6497})^2}{16} \\
a \cdot b=\frac{6561-6497}{16} \\
a \cdot b=\frac{64}{16}=4
\end{gathered}$

Thus, $\log _{10}(a)+\log _{10}(b)=\log _{10}(4)$

$\log _{10}(4)=\log _{10}\left(2^2\right)=2 \log _{10}(2)$.

Q 6. $|x+y|+|x-y|=2$ No. of pairs of $(\mathrm{x}, \mathrm{y})$ possible?

Solution: The absolute values $|x+y|$ and $|x-y|$ depend on the signs of $x+y$ and $x-y$. We consider the following cases:

Case 1: $x+y \geq 0$ and $x-y \geq 0$ :

$|x+y|=x+y, \quad|x-y|=x-y$

Substituting into the equation:

$(x+y)+(x-y)=2 \Longrightarrow 2 x=2 \Longrightarrow x=1$

Substituting $x=1$ into $x+y \geq 0$ and $x-y \geq 0$ :

$1+y \geq 0 \Longrightarrow y \geq-1, \quad 1-y \geq 0 \Longrightarrow y \leq 1$

So, $y \in[-1,1]$.

This gives 3 integer pairs: $(1,-1),(1,0),(1,1)$.

Case 2: $x+y \geq 0$ and $x-y \leq 0$ :

$|x+y|=x+y, \quad|x-y|=-(x-y)$

Substituting into the equation:

$(x+y)-(x-y)=2 \Longrightarrow 2 y=2 \Longrightarrow y=1$

Substituting $y=1$ into $x+y \geq 0$ and $x-y \leq 0$ :

$x+1 \geq 0 \Longrightarrow x \geq-1, \quad x-1 \leq 0 \Longrightarrow x \leq 1$

So, $x \in[-1,1]$.

This gives 3 integer pairs: $(-1,1),(0,1),(1,1)$.

Case 3: $x+y \leq 0$ and $x-y \geq 0$ :

$|x+y|=-(x+y), \quad|x-y|=x-y$
Substituting into the equation:

$-(x+y)+(x-y)=2 \Longrightarrow-2 y=2 \Longrightarrow y=-1$

Substituting $y=-1$ into $x+y \leq 0$ and $x-y \geq 0$ :

$x-1 \geq 0 \Longrightarrow x \geq 1, \quad x+(-1) \leq 0 \Longrightarrow x \leq 1$

So, $x=1$.

This gives 1 integer pair: $(1,-1)$.

Case 4: $x+y \leq 0$ and $x-y \leq 0$ :

$|x+y|=-(x+y), \quad|x-y|=-(x-y) $
Substituting into the equation:

$-(x+y)-(x-y)=2 \Longrightarrow-2 x=2 \Longrightarrow x=-1 $

Substituting $x=-1$ into $x+y \leq 0$ and $x-y \leq 0$ :

$-1+y \leq 0 \Longrightarrow y \leq 1, \quad-1-y \leq 0 \Longrightarrow y \geq-1$
So, $y \in[-1,1]$.

This gives 3 integer pairs: $(-1,-1),(-1,0),(-1,1)$.

However, some pairs are repeated:
- $(1,-1)$ appears in Cases 1 and 3.
- $(-1,1)$ appears in Cases 2 and 4.

Thus, there are:

$3+3+1+3-2=8 \text { distinct pairs }$

CAT 2024 Slot 2 Questions (Memory Based)

Based on slot 2 of the CAT examination, various memory-based questions across the sections are mentioned below.

1. A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is

2. Find the remainder $3^{333}$ ÷ 11

3. When 2 liters of water is added to a mixture of acid and water, the concentration of acid becomes 50%. Then, 15 liters of acid is added to the solution, which makes the concentration of acid 80%. What is the quantity of the initial mixture?

4. If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2+p x+q=0$ find the value of $\left(\alpha^3+\beta^3\right)^2$

5. What is the sum of coefficients of the equation $4 x^2+4 y^2-4 x y+3 y^2-6 y+3=0$

Ans. 7

6. If $|x|+x+y=15$. Find the value of $x-y$

Ans. 15

7. Solve the inequality: $
\frac{1}{x+3} \leq \frac{1}{2 x-3}
$ restricting the solution to $\left(\frac{3}{2}, 8\right]$.

8. If m and n are integers and $m^n=2^{25} \times 3^{40}$ then calculate the value of m−n.

9. $\sqrt{x+6 \sqrt{2}}-\sqrt{x-6 \sqrt{2}}=2 \sqrt{2}$, Find the value of $x$.

CAT Exam 2024: Important Links

CAT 2024 Slot 1 Questions (Memory Based)

CAT 2024 Slot 1 DILR Questions (Memory Based)

Question 1: 3 friends Dheeraj, Samantha and Nitesh visited different countries in Asia, Europe and Row

I. 32 countries visited by at least one of them.

II. USA (in Row) was the only country visited by all.

III. China by Dheeraj and Nitesh

IV. France (in Europe) was visited by Dheeraj and Samantha but not by Nitesh.

V. Half of the countries, visited by Samantha and Nitesh both, are in Europe.

Answer the following questions:

1. How many countries in Asia were visited by at least one of the person.

2. How many countries in Europe were visited by Only Nitesh.

3. How many countries in Row were visited by both Samantha and Nitesh.

4. How many countries in Europe were visited by exactly one of the 3 people.

CAT 2024 Slot 1 QUANT Questions

Q 1. Find the remainder of $\frac{100^{100}}{7}$

2. There are 187 fruits in a basket. The ratio of apples to mangoes is in the ratio 5:2. After selling 75 apples and 26 mangoes and half the number of oranges, the leftover apples and oranges was in the ratio 3:2.

Ans: 66

3. If $a_n$ represents the greatest integer function of $\sqrt{n}$, then sum of $a_1, a_2, a_3, \ldots a_{49}, a_{50}$ is?

Ans: 217

4. S.P of product is fixed to ensure 40% profit. If product cost 40% less, and have been sold for Rs. 5 less, Then Profit would have been 50%, then the original S.P is:

A) 5

B) 10

C) 20

D) 14

Ans: 14

5. A vessel is full of milk $2 / 3^{\text {rd }}$ of the milk is removed and replaced with water. This process is repeated 3 more times. Then find ratio of milk and water in the final solution.

6. $A B=56, C D=45$. Inradius of circle in ADE..

Ans: 10

7. $(1 / 8)^k \times\left(1 / 8^{5}\right)^{1 / 3}=(1 / 8) x$ $\left(1 / 8^{5}\right)^{1 / k}$. Find the sum of all posslble values of ' $\mathbf{k}$ '

8. For any natural Number ' $n$ ', let an be the largest number not exceeding $\sqrt{\mathrm{n}}$, then $\mathrm{a_1}+\mathrm{a_2}+$ $a_3$... $+a_{50}$=

9. $x$ is a +ve real no,$
4 \operatorname{lox}_{10} x+4 \log _{100} x+
$ $8 \log { }_{1000} x=13$, then the greatest integer not exceeding ' $x$ '

10. Let $x, y, z$ be real numbers and $4\left(x^3+y^2+z^2\right)=a, 4(x-y-z)=3+a$, then find the value of ' a '

CAT 2024 Question Paper Pattern

The CAT exam pattern is expected to be the same for this year as well and there have been no official; updates about a change in pattern. Below is the CAT 2024 exam pattern and marking scheme.

CAT 2024 Question Paper Analysis

The CAT 2024 exam analysis of all the slots of the CAT exam is given here. This section also contains the CAT difficulty level analysis of various sections. The candidates are always encouraged to understand the CAT paper analysis for all slots. This can help them understand the difficulty level of each slot and help them devise a possible CAT score and percentile based on their understanding. Along with the slot analysis, CAT sectional analysis is also given for each slot so that the candidates can gain a deeper understanding.

CAT 2024 Slot 1 Question Paper Analysis

The CAT slot 1 analysis helps the candidates to understand the overall picture of the CAT slot 1 examination. Given below is the CAT sectional analysis based on the initial data available from both the students and the faculties.

Verbal Ability and Reading Comprehension

The VARC section had its share of surprises for the CAT 2024 slot 1 examination. There were no para jumble questions in this year's VARC section of the CAT 2024 slot 1 examination. The candidates were asked questions about concepts such as fill-in-the-blanks, summary completion and so on. The difficulty of the section was set between easy to medium as per the student response.

Data Interpretation and Logical Reasoning

In the DILR section, the candidates were asked 3 questions from the Data Interpretation section followed by 2 questions from the Logical Reasoning section. The difficulty as per the responses is medium.

Quantitative Aptitude

In the quantitative aptitude section, the majority of questions were asked from the algebra and arithmetic sections. The difficulty level of the section has reduced considerably when compared with the CAT 2023 slot 1 question paper. There were 2 questions from geometry and one from sets.

To get the detailed Analysis of CAT 2024 Slot 1 Download the ebook - Download Now

CAT Slot 2 Question Paper Analysis

CAT sectional analysis is necessary for the candidates to gain an overall picture of the CAT 2024 slot 2 and to envision a potential CAT 2024 score. Let us go into detail about the various sections and their analysis.

Verbal Ability and Comprehension

In the VARC section, the ordering of the Verbal Ability and Reading Comprehension questions was random and they were not grouped together. This included 2 odd one-out and 3 para summary questions along with three paracompletion questions.

• There were a few tricky questions. There was a bit of reasoning involved in some reading comprehension questions making it a bit complicated.
• The Reading comprehension questions asked on the topics Spice Trade and Unexpected Consequences of Technology were categorised into the easier side.
• The Reading Comprehension questions pertaining to the topics Peer Review of Research and Issues between Carnivore and Human were categorised into medium to difficult levels.
• There were questions on True and False and critical reasoning.
• The notable change in the VARC section was the absence of Para Jumble questions.
• Para Summary questions were not lengthy and doable.

Data Interpretation and Logical Reasoning

The Data Interpretation and Logical Reasoning section of the slot 2 of the CAT 2024 examination was easier when compared to the same of 2023 exam. There were 12 MCQ questions in the CAT 2024 slot 2 question paper followed by 10 TIT questions which had no negative marking. Let us understand in depth about the questions.

• The Logical Reasoning question on gymnasts lied between the easy to moderate level and according the reviews of the candidates was doable.
• The DI question on 6 sets and their profitability had 4 questions which were MCQs. It was also observed to be on the easier side.
• There was one Logical Reasoning question on grid type arrangement in which the numbers lying between 1 and 10 must be arranged in a grid following underlying conditions. This question was a bit time consuming and falls under the moderate to difficult range.
• The Data Interpretation question on Ecommerce was deemed to be easy.

Quantitative Aptitude

The difficulty level of the quantitative aptitude section of the CAT 2024 slot 2 examination was easier when compared to the CAT 2023 slot 2 quantitative aptitude of the 2023 examination. There were similar questions repeated from slot 1 of the examination. There were 14 MCQs and 8 TITA questions under this section. Questions were asked on topics such as percentages, time, speed and distance, circles and so on. Let us see the type of questions asked under the CAT slot 2 quantitative aptitude section.

CAT 2024 Slot 3 Question Paper Analysis

As the last and final, slot 3 of the CAT 2024 ends, the candidates who appeared in all three slots must be awaiting an all-slots analysis and the candidates who have given the examination in slot 3 must be awaiting their CAT 2024 slot 3 analysis. Now let us go deeper into the CAT 202 slot 3 analysis which offers a lot of insights into the examination.

CAT 2024 Slot 3 Question Paper Sectional Analysis

Diving deeper into the sectional analysis helps the candidates to understand the CAT 2024 slot better and helps them to analyse their performances. Hence, it is necessary for the candidates to go through the sectional analysis of the CAT 2024 exam. Let us go through it in detail.

Verbal Ability and Reading Comprehension

The absence of the parajumbles section is a noteworthy observation of the CAT 2024 slot 3 VARC section. The difficulty level of the CAT 2024 slot 3 VARC was moderate and similar to the previous two slots. Let us go into detail about the questions asked in this section.

• There were 16 questions asked under the Reading Comprehension.
• A reading comprehension question was asked on the topic of space exploration. As far as the initial responses of the candidates are concerned, while it was easy to comprehend the passage, the questions asked under the topic were tricky.
• There was another Reading Comprehension question on AI and it was relatively easy and straightforward.
• The inclusion of odd sentence-out questions instead of the para jumbles was a surprise.
• Critical reasoning questions were asked in the passages.
• Para summary questions were slightly challenging while the other sections were doable.

Data Interpretation and Logical Reasoning

The DILR section of slot 3 of the CAT 202 examination is observed to be slightly more difficult than the other slots of the CAT 2024 exams. Particularly the question based on ATMs and the GDP of ten countries particularly seemed to be on the more difficult side. Let us go in-depth about the questions to have a clearer understanding.

• One Logical Reasoning question was on the intersection of 3 horizontal and vertical lines with each intersection representing an ATM in 3 which three were blank. This question was in line with CAT 2020, and 2021 questions and lies more within the moderate to difficult side.
• The Data Interpretation question based on the GDP of 10 countries was also slightly difficult as per the responses of a few candidates. This question assessed the arithmetic skills of the candidates and required more calculations hence placed in the moderate difficulty.
• There also was another DI based on room temperature depicted using a line graph. It was of a moderate level of difficulty.
• There was another DI question based on the App subscription.
• The Logical Reasoning question on Proteins-Carbohydrates in food items was a bit time-consuming because the candidates had to work out the question using the multiples of four and five.

Quantitative Aptitude

CAT Score vs Percentile

Based on the CAT 2024 analysis, a CAT score vs percentile is devised by the experts of Careers360. Based on the score vs percentile analysis the candidates will be able to have a clear understanding of the scores that they must target to achieve their desired percentile and use which they can join their dream institute.

CAT All Slots Analysis

In addition to the information in the article, candidates can download the comprehensive eBook created by Careers360 experts. This eBook includes detailed analysis of all the slots of the CAT 2024 examination. The links to the eBook are provided below for easy access.