CAT 2021QASlot 2 · Afternoon

CAT 2021 Slot 2 QA Question Paper with Solutions

40 Minutes22 QuestionsNov 28, 20213 marks correct · −1 wrong

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Q1CAT 2021 Slot 2 QA

A person buys tea of three different qualities at ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹ 700 per kg. The price, in INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

Q2CAT 2021 Slot 2 QA

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A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

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Q3CAT 2021 Slot 2 QA

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Raj invested ₹ 10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹ 5000. This balance, when invested for another year, grew and the percentage of growth in the second year was five times the percentage of loss in the first year. If the gain of Raj from the initial investment over the two year period is 35%, then the percentage of loss in the first year is

Q4CAT 2021 Slot 2 QA

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For all real values of

x

, the range of the function

f(x)=\dfrac{x^2+2x+4}{2x^2+4x+9}

Q5CAT 2021 Slot 2 QA

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For all possible integers

n

satisfying

2.25 \leq 2+2^{n+2} \leq 202

, the number of integer values of

3+3^{n+1}

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Q6CAT 2021 Slot 2 QA

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In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is

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Q7CAT 2021 Slot 2 QA

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If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

Q8CAT 2021 Slot 2 QA

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\log_2 \left[ 3 + \log_3 \left\{ 4 + \log_4 (x-1) \right\} \right] - 2 = 0

then

4x

equals

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Q9CAT 2021 Slot 2 QA

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Two pipes A and B are attached to an empty water tank. Pipe A fills the tank while pipe B drains it. If pipe A is opened at 2 pm and pipe B is opened at 3 pm, then the tank becomes full at 10 pm. Instead, if pipe A is opened at 2 pm and pipe B is opened at 4 pm, then the tank becomes full at 6 pm. If pipe B is not opened at all, then the time, in minutes, taken to fill the tank is

Q10CAT 2021 Slot 2 QA

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For a real number

x

the condition

\left|3x-20\right|+\left|3x-40\right|=20

necessarily holds if

Q11CAT 2021 Slot 2 QA

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Two trains A and B were moving in opposite directions, their speeds being in the ratio 5 : 3. The front end of A crossed the rear end of B 46 seconds after the front ends of the trains had crossed each other. It took another 69 seconds for the rear ends of the trains to cross each other. The ratio of length of train A to that of train B is

Q12CAT 2021 Slot 2 QA

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For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

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Q13CAT 2021 Slot 2 QA

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Three positive integers

x, y

and

z

are in arithmetic progression. If

y - x > 2

and

xyz = 5(x + y + z)

, then

z - x

equals

Q14CAT 2021 Slot 2 QA

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Consider the pair of equations:

x^2 - xy - x = 22

and

y^2 - xy + y = 34

. If

x > y

, then

x - y

equals

Q15CAT 2021 Slot 2 QA

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Suppose one of the roots of the equation

ax^2 - bx + c = 0

2 + \sqrt{3}

, where

a, b

and

c

are rational numbers and

a \ne 0

. If

b = c^3

then

\left|a\right|

equals

Q16CAT 2021 Slot 2 QA

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Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

Q17CAT 2021 Slot 2 QA

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For a sequence of real numbers

x_1, x_2, \ldots, x_n

, if

x_1 - x_2 + x_3 - \ldots + (-1)^{n+1} x_n = n^2 + 2n

for all natural numbers

n

, then the sum

x_{49}+x_{50}

equals

Q18CAT 2021 Slot 2 QA

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The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is

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Q19CAT 2021 Slot 2 QA

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Anil, Bobby and Chintu jointly invest in a business and agree to share the overall profit in proportion to their investments. Anil’s share of investment is 70%. His share of profit decreases by ₹ 420 if the overall profit goes down from 18% to 15%. Chintu’s share of profit increases by ₹ 80 if the overall profit goes up from 15% to 17%. The amount, in INR, invested by Bobby is

Q20CAT 2021 Slot 2 QA

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Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that

AD : BD = 2 : 1

and

AE : CE = 2 : 3

. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

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Q21CAT 2021 Slot 2 QA

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The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

Q22CAT 2021 Slot 2 QA

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From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

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About CAT 2021 Slot 2 QA

The QA section of CAT 2021 Slot 2 was conducted on November 30, 2021, 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 2021 Slot 2 QA

CAT 2021 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 2021 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 2021 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.