CAT 2020QASlot 2 · Afternoon

CAT 2020 Slot 2 QA Question Paper with Solutions

40 Minutes26 QuestionsNov 29, 20203 marks correct · −1 wrong

Questions

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Q1CAT 2020 Slot 2 QA

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is

s

. Then the area of the triangle is

Q2CAT 2020 Slot 2 QA

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Let

f(x) = x^2 + ax + b

and

g(x) = f(x + 1) - f(x - 1)

. If

f(x) \geq 0

for all real

x

, and

g(20) = 72

, then the smallest possible value of

b

Q3CAT 2020 Slot 2 QA

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John takes twice as much time as Jack to finish a job. Jack and Jim together take one-third of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone?

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Q4CAT 2020 Slot 2 QA

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Aron bought some pencils and sharpeners. Spending the same amount of money as Aron, Aditya bought twice as many pencils and 10 less sharpeners. If the cost of one sharpener is ₹ 2 more than the cost of a pencil, then the minimum possible number of pencils bought by Aron and Aditya together is

Q5CAT 2020 Slot 2 QA

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A and B are two points on a straight line. Ram runs from A to B while Rahim runs from B to A. After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram’s speed to Rahim’s speed is

Q6CAT 2020 Slot 2 QA

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Two circular tracks T₁ and T₂ of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T₁ and track T₂ at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

Q7CAT 2020 Slot 2 QA

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Let the

m

-th and

n

-th terms of a geometric progression be

\dfrac{3}{4}

and 12, respectively, where

m < n

. If the common ratio of the progression is an integer

r

, then the smallest possible value of

r + n - m

Q8CAT 2020 Slot 2 QA

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Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of ₹ 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been

Q9CAT 2020 Slot 2 QA

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The number of pairs of integers

(x, y)

satisfying

x \geq y \geq -20

and

2x + 5y = 99

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Q10CAT 2020 Slot 2 QA

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How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

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Q11CAT 2020 Slot 2 QA

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The sum of perimeters of an equilateral triangle and a rectangle is 90 cm. The area,

T

, of the triangle and the area,

R

, of the rectangle, both in sq cm, satisfy the relationship

R = T^2

. If the sides of the rectangle are in the ratio

1 : 3

, then the length, in cm, of the longer side of the rectangle, is

Q12CAT 2020 Slot 2 QA

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In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean by

Q13CAT 2020 Slot 2 QA

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In a car race, car A beats car B by 45 km, car B beats car C by 50 km, and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Q14CAT 2020 Slot 2 QA

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The value of

\log_a \left(\dfrac{a}{b}\right) + \log_b \left(\dfrac{b}{a}\right)

, for

1 < a \leq b

cannot be equal to

Q15CAT 2020 Slot 2 QA

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The number of integers that satisfy the equality

(x^2 - 5x + 7)^{x+1} = 1

Q16CAT 2020 Slot 2 QA

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The distance from B to C is thrice that from A to B. Two trains travel from A to C via B. The speed of train 2 is double that of train 1 while traveling from A to B and their speeds are interchanged while traveling from B to C. The ratio of the time taken by train 1 to that taken by train 2 in travelling from A to C is

Q17CAT 2020 Slot 2 QA

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x

and

y

are non-negative integers such that

x + 9 = z

y + 1 = z

and

x + y < z + 5

, then the maximum possible value of

2x + y

equals

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Q18CAT 2020 Slot 2 QA

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Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Q19CAT 2020 Slot 2 QA

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A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If the difference between the largest and the smallest of these three shares is ₹ 400, then Sunil’s share, in rupees, is

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Q20CAT 2020 Slot 2 QA

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x

and

y

are positive real numbers satisfying

x + y = 102

, then the minimum possible value of

2601 \left(1 + \dfrac{1}{x}\right) \left(1 + \dfrac{1}{y}\right)

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Q21CAT 2020 Slot 2 QA

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In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent ₹ 150 more due to price increase of rice and wheat by 20% and 12%, respectively. If John had spent ₹ 450 on rice in April, then how much did he spend on wheat in May?

Q22CAT 2020 Slot 2 QA

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Let C₁ and C₂ be concentric circles such that the diameter of C₁ is 2 cm longer than that of C₂. If a chord of C₁ has length 6 cm and is a tangent to C₂, then the diameter, in cm, of C₁ is

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Q23CAT 2020 Slot 2 QA

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Students in a college have to choose at least two subjects from chemistry, mathematics and physics. The number of students choosing all three subjects is 18, choosing mathematics as one of their subjects is 23 and choosing physics as one of their subjects is 25. The smallest possible number of students who could choose chemistry as one of their subjects is

Q24CAT 2020 Slot 2 QA

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For real

x

, the maximum possible value of

\dfrac{x}{\sqrt{1 + x^4}}

Q25CAT 2020 Slot 2 QA

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For the same principal amount, the compound interest for two years at 5% per annum exceeds the simple interest for three years at 3% per annum by ₹ 1125. Then the principal amount in rupees is

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Q26CAT 2020 Slot 2 QA

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In how many ways can a pair of integers

(x, a)

be chosen such that

x^2 - 2|x| + |a - 2| = 0

About CAT 2020 Slot 2 QA

The QA section of CAT 2020 Slot 2 was conducted on November 30, 2020, 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 2020 Slot 2 QA

CAT 2020 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 2020 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 2020 Slot 2 paper with a live timer and percentile benchmarking.

Tips for CAT QA Preparation

Reading Comprehension accounts for roughly two-thirds of the QAsection. 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.