CAT 2024QASlot 2 · Afternoon

CAT 2024 Slot 2 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 24, 20243 marks correct · −1 wrong

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Q1CAT 2024 Slot 2 QA

a

b

and

c

are positive real numbers such that

a > 10 \geq b \geq c

and

\dfrac{\log_8(a+b)}{\log_2 c} + \dfrac{\log_{27}(a-b)}{\log_3 c} = \dfrac{2}{3}

, then the greatest possible integer value of

a

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Q2CAT 2024 Slot 2 QA

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\sqrt{x + 6\sqrt{2}} - \sqrt{x - 6\sqrt{2}} = 2\sqrt{2}

, then

x

equals

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Q3CAT 2024 Slot 2 QA

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A bus starts at 9 am and follows a fixed route every day. One day, it travelled at a constant speed of 60 km per hour and reached its destination 3.5 hours later than its scheduled arrival time. Next day, it travelled two-thirds of its route in one-third of its total scheduled travel time, and the remaining part of the route at 40 km per hour to reach just on time. The scheduled arrival time of the bus is

Q4CAT 2024 Slot 2 QA

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Anil invests Rs 22000 for 6 years in a scheme with 4% interest per annum, compounded half-yearly. Separately, Sunil invests a certain amount in the same scheme for 5 years, and then reinvests the entire amount he receives at the end of 5 years, for one year at 10% simple interest. If the amounts received by both at the end of 6 years are equal, then the initial investment, in rupees, made by Sunil is

Q5CAT 2024 Slot 2 QA

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Bina incurs 19% loss when she sells a product at Rs. 4860 to Shyam, who in turn sells this product to Hari. If Bina would have sold this product to Shyam at the purchase price of Hari, she would have obtained 17% profit. Then, the profit, in rupees, made by Shyam is

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Q6CAT 2024 Slot 2 QA

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The roots

\alpha

\beta

of the equation

3x^2 + \lambda x - 1 = 0

, satisfy

\dfrac{1}{\alpha^2} + \dfrac{1}{\beta^2} = 15

. The value of

(\alpha^3 + \beta^3)^2

Q7CAT 2024 Slot 2 QA

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x

and

y

are real numbers such that

4x^2 + 4y^2 - 4xy - 6y + 3 = 0

, then the value of

(4x + 5y)

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Q8CAT 2024 Slot 2 QA

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A function

f

maps the set of natural numbers to whole numbers, such that

f(xy) = f(x)f(y) + f(x) + f(y)

for all

x

y

and

f(p) = 1

for every prime number

p

. Then, the value of

f(160000)

Q9CAT 2024 Slot 2 QA

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All the values of

x

satisfying the inequality

\dfrac{1}{x+5} \leq \dfrac{1}{2x-3}

are

Q10CAT 2024 Slot 2 QA

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P, Q, R and S are four towns. One can travel between P and Q along 3 direct paths, between Q and S along 4 direct paths, and between P and R along 4 direct paths. There is no direct path between P and S, while there are few direct paths between Q and R, and between R and S. One can travel from P to S either via Q, or via R, or via Q followed by R, respectively, in exactly 62 possible ways. One can also travel from Q to R either directly, or via P, or via S, in exactly 27 possible ways. Then, the number of direct paths between Q and R is

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Q11CAT 2024 Slot 2 QA

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When

3^{333}

is divided by 11, the remainder is

Q12CAT 2024 Slot 2 QA

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A vessel contained a certain amount of a solution of acid and water. When 2 litres of water was added to it, the new solution had 50% acid concentration. When 15 litres of acid was further added to this new solution, the final solution had 80% acid concentration. The ratio of water and acid in the original solution was

Q13CAT 2024 Slot 2 QA

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The coordinates of the three vertices of a triangle are:

(1, 2)

(7, 2)

, and

(1, 10)

. Then the radius of the incircle of the triangle is

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Q14CAT 2024 Slot 2 QA

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A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

Q15CAT 2024 Slot 2 QA

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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

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Q16CAT 2024 Slot 2 QA

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Three circles of equal radii touch (but not cross) each other externally. Two other circles,

x

and

y

, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of

x

is more than that of

y

, the ratio of the radii of x and y is

Q17CAT 2024 Slot 2 QA

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ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If

AB = 2

cm,

CD = 1

cm, and perimeter of

ABCD

6

cm, then the perimeter, in cm, of

\triangle AEB

Q18CAT 2024 Slot 2 QA

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Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

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Q19CAT 2024 Slot 2 QA

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The sum of the infinite series

\dfrac{1}{5}\left(\dfrac{1}{5} - \dfrac{1}{7}\right) + \left(\dfrac{1}{5}\right)^2\left[\left(\dfrac{1}{5}\right)^2 - \left(\dfrac{1}{7}\right)^2\right] + \left(\dfrac{1}{5}\right)^3\left[\left(\dfrac{1}{5}\right)^3 - \left(\dfrac{1}{7}\right)^3\right] + \ldots

is equal to

Q20CAT 2024 Slot 2 QA

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x

and

y

satisfy the equations

|x| + x + y = 15

and

x + |y| - y = 20

, then

(x - y)

equals

Q21CAT 2024 Slot 2 QA

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m

and

n

are natural numbers such that

n > 1

, and

m^n = 2^{25} \times 3^{40}

, then

m - n

equals

Q22CAT 2024 Slot 2 QA

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When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become

About CAT 2024 Slot 2 QA

The QA section of CAT 2024 Slot 2 was conducted on November 30, 2024, the last Sunday of November — consistent with IIM's scheduling across all recent years. The section contains 24 questions to be answered in 40 minutes, carrying 72 marks in total. There is no sectional time limit within the overall exam, but students choosing to switch sections mid-paper lose the ability to return — making pacing within QA critical.

Passage Topics in CAT 2024 Slot 2 QA

CAT 2024 Slot 2 QA featured four reading comprehension passages and a standalone Verbal Ability block. The RC passages spanned complexity theory and global systems, the aesthetics of electronic music, the economics of income inequality, and the legal history of criminal responsibility — a typical CAT spread across the sciences, humanities, and social sciences. The VA section included Para Jumbles, Para Summary, and Odd Sentence Out questions, consistent with the pattern since CAT 2019.

CAT 2024 QA Marking Scheme

Correct answer (MCQ): +3 marks
Wrong answer (MCQ): −1 mark
Unattempted (MCQ): 0 marks
TITA questions (if any): +3 correct, no negative marking

How to Use This Question Paper

Click any answer option to immediately check your answer. The correct option is highlighted in green; if you selected the wrong option, it is shown in red and the correct answer is revealed. A detailed explanation appears below each question after you answer it, along with statistics showing what percentage of students answered correctly in the actual exam.

The question navigator at the top of the page updates in real time — green bubbles indicate correct answers and red indicate wrong. Use this to spot weak areas at a glance. To practice under timed conditions, use the Take Full Mock button to attempt the complete CAT 2024 Slot 2 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QA section. The passages in CAT are dense and argumentative — they reward close reading of the author's position rather than skimming for facts. Practising on past papers is the most reliable way to calibrate your reading speed, improve inference accuracy, and recognise the types of questions IIM setters favour. Use the answer statistics on this page to benchmark yourself; questions where more than 50% of test-takers answered correctly are ones you should aim to get right every time.