IPMAT 2023 Question Paper With Detailed PDF Solutions

IPMAT 2023 Paper With Answers & Explanation

QA (SA)

Q. 1 In a chess tournament, there are four groups, each containing an equal number of players. Each player plays
• against every other player belonging to one's own group exactly once;
• against each player belonging to one of the remaining three groups exactly twice;
• against each player belonging to one of the remaining two groups exactly three times; and
• against each player belonging to the remaining group exactly four times. If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is __________.

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Explanation

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Explanation

Q. 2

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Explanation

Correct Answer

199

Explanation

Q. 3 If three consecutive coefficients in the expansion of (x + y)ⁿ are in the ratio 1:9:63, then the value of n is __________.

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Explanation

Correct Answer

Explanation

Q. 4 If f(1) = 1 and f (n) = 3n – f (n – 1) for all integers n > 1, then the value of f(2023) is __________.

Correct Answer
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Explanation

Correct Answer

3034

Explanation

f(1) = 1
f(n) = 3n – f(n – 1)
f(2023) = ?
We can see a pattern when we note down the values:
f(1) = 1 ; f(2) = 5
f(3) = 4 ; f(4) = 8
f(5) = 7 ; f(6) = 11
f(7) = 10 ; f(8) = 14
So, f(2023) = 1 + (1011) × 3 = 3034.

Q. 5 Let a, b, c, d be positive integers such that a + b + c + d = 2023. If a : b = 2 : 5 and c : d = 5 : 2, then the maximum possible value of a + c is __________.

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Explanation

Correct Answer

1442

Explanation

Q. 6 Assume it is the beginning of the year today. Ankita will earn INR 10,000 at the end of the year, which she plans to invest in a bank deposit immediately at a fixed simple interest of 0.5% per annum. Her yearly income will increase by INR 10,000 every year, and the fixed simple interest offered by the bank on new deposits will also increase by 0.5% per annum every year. If Ankita continues to invest all her yearly income in new bank deposits at the end of each year, the total interest earned by her, in INR, in five years from today will be __________.

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Explanation

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1500

Explanation

Q. 7 The total number of positive integer solutions of 21 ≤ a + b + c ≤ 25 is __________.

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Explanation

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1160

Explanation

Q. 8 The remainder when 1! + 2! + 3! + ··· + 95! is divided by 15 is __________·

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Explanation

Correct Answer

Explanation

1! + 2! + 3! + 4! + … + 95!, when divided by 15 leaves the same remainder as 1! + 2! + 3! + 4! will do when divided by 15.
This is because all numbers from 5! onwards are divisible by 15.
So 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33
Hence, 33 leaves a remainder 3 when divided by 15.

Q. 9 Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be __________.

Correct Answer
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Explanation

Correct Answer

Explanation

Let Amisa put in 2 units per day.
So, the work consists of 2 × 2 = 40 units.
At the end of 4 days, 8 units of work is done.
Work done by Amisa in 12 days after returning = 1 × 12 = 12 units.
So Amisa does 20 units and the rest of 20 units are done by the co-worker.
The co-worker worked only for 12 days to complete 20 units.
Hence, time taken to complete 40 units = 24 days.

Q. 10 In the xy-plane let A = (–2, 0), B = (2, 0). Define the set S as the collection of all points C on the circle x² + y² = 4 such that the area of the triangle ABC is an integer. The number of points in the set S is __________.

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Explanation

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Explanation

Q. 11 The polynomial 4x¹⁰ – x⁹ + 3x⁸ – 5x⁷ + cx⁶ + 2x⁵ – x⁴ + x³ – 4x² + 6x – 2 when divided by x – 1 leaves a remainder 2. Then the value of c + 6 is __________.

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Explanation

Correct Answer

Explanation

Q. 12 Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be __________.

Correct Answer
and
Explanation

Correct Answer

312

Explanation

Q. 13 In an election with only two contesting candidates, 15% of the voters did not turn up to vote, and 50 voters cast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting Iist is __________.

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Explanation

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5000

Explanation

Q. 14

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Explanation

Q. 15 The length of the line segment joining the two intersection points of the curves y = 4970 – lxl and y = x² is __________.

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Explanation

Correct Answer

140

Explanation

QA (MCQ)

Q. 16 Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

1) 8

2) 8!

3) 7

4) 7!

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Explanation

Correct Answer

Explanation

Q. 17 In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be:

1) 4√10 : 11

2) 12 : 11

3) 11 : 12

4) 11 : 4√10

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Explanation

Correct Answer

Explanation

Q. 18 If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is

1) 150000

2) 170000

3) 15000

4) 17000

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Explanation

Correct Answer

Explanation

Q. 19 The probability that a randomly chosen positive divisor of 10²⁰²³ is an integer multiple of 10²⁰⁰¹ is

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Explanation

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Explanation

Q. 20 The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is:

1) 5

2) 3

3) 6

4) 7

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Explanation

Correct Answer

Explanation

Q. 21 If log_{cos x}(sin x) + log_{sin x}(cos x) = 2, then the value of x is

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Q. 22

1) 4 + √5

2) 4 - √5

3) 2

4) 3

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Explanation

Correct Answer

Explanation

Q. 23 In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?

1) 4, 4, 1, 1, 0

2) 3, 2, 2, 2, 1

3) 2, 2, 2, 2, 2

4) 3, 3, 2, 1, 1

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Explanation

Correct Answer

Explanation

Q. 24 Which of the following straight lines are both tangent to the circle x² + y² – 6x + 4y – 12 = 0?

1) 4x + 3y + 19 = 0, 4x + 3y + 31 = 0.

2) 4x + 3y – 19 = 0, 4x + 3y – 31 = 0.

3) 4x + 3y – 19 = 0, 4x + 3y + 31 = 0.

4) 4x + 3y + 19 = 0, 4x + 3y – 31 = 0.

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Explanation

Correct Answer

Explanation

Q. 25 A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?

1) 32 meters

2) 64/√5 meters

3) 64 meters

4) 32/√5 meters

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Explanation

Correct Answer

Explanation

Q. 26 Let p be a positive integer such that the unit digit of p³ is 4. What are the possible unit digits of (p + 3)³?

1) 1, 3, 7

2) 3

3) 1, 7, 9

4) 4, 7

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Explanation

Correct Answer

Explanation

Q. 27

1) a = c, or a + b + c + d = 0

2) a = c, and b = d

3) a + b + c + d = 0

4) a = c

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Explanation

Correct Answer

Explanation

Q. 28 A polynomial P(x) leaves a remainder 2 when divided by (x – 1) and a remainder 1 when divided by (x – 2). The remainder when P(x) is divided by (x – 1)(x – 2) is

1) 2

2) 3

3) x – 3

4) 3 – x

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Explanation

Correct Answer

Explanation

Q. 29 A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is

1) 89

2) 55

3) 144

4) 34

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Explanation

Correct Answer

Explanation

Q. 30 Let a, b, c be real numbers greater than 1, and n be a positive real number not equal to 1. If log_n(log₂ a) = 1, log_n(log₂ b) = 2 and log_n(log₂ c) = 3, then which of the following is true?

1) a + b = c

2) aⁿ + bⁿ = cⁿ

3) (b – a)ⁿ = (c – b)

4) (aⁿ + b)ⁿ = ac

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Explanation

Correct Answer

Explanation

Q. 31

1) 5

2) 1

3) 4

4) 6

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Explanation

Correct Answer

Explanation

Q. 32 Let [x] denote the greatest integer not exceeding x and {x} = x – [ x ]. If n is a natural number, then the sum of all values of x satisfying the equation 2[x] = x + n{x} is

2) 3/2

3) n

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Explanation

Correct Answer

Explanation

Q. 33 In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who are supporters of Mumbai Indians is

1) Between 20 and 25

2) 30 or more

3) Between 15 and 25

4) Exactly 20

Correct Answer
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Explanation

Correct Answer

Explanation

Total number of students = 120
Students from Science stream = 80
So students from Commerce stream = 40
Number of students supporting Mumbai Indians = 70
So number of students supporting Chennai Super King = 50
The least number of Science students supporting Mumbai Indians = 80 – 50 = 30.

Q. 34 A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

1) 192 kmph

2) 200 kmph

3) 184 kmph

4) 250 kmph

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Explanation

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Explanation

Q. 35

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Explanation

Q. 36 If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

1) 1/2

2) 1/4

3) 1/3

4) 2/3

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Explanation

Correct Answer

Explanation

Q. 37 If cosα + cosβ = 1, then the maximum value of sinα – sinβ is

1) 2

2) 1

3) √2

4) √3

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Explanation

Correct Answer

Explanation

Q. 38 A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price of each golden bead, in INR, was

1) 48000

2) 24000

3) 12000

4) 9600

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Explanation

Correct Answer

Explanation

Q. 39 The equation x² + y² – 2x – 4y + 5 = 0 represents

1) a point

2) a circle

3) an ellipse

4) a pair of straight lines

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Explanation

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Q. 40

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Explanation

Directions for questions 41 to 45: A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Following additional information is available:
• Each drug works on at least one organism but not more than two organisms.
• Each organism can be treated with at least two and at most three of these five drugs.
• On whichever organism A works, B also works. Similarly, on whichever organism C works, D also works.
• D and E do not work on the same organism.

Q. 41 Drug D works on

1) Only P

2) Q and R

3) P and Q

4) Only Q

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Explanation

Correct Answer

Explanation

Drug D works on P and Q.

Q. 42 Organism P can be treated with

1) Only C and D

2) B, C and D

3) Only B and D

4) A, B, and D

Correct Answer
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Explanation

Correct Answer

Explanation

Organism P can be treated with only C and D.

Q. 43 Organism R can be treated with

1) Only A and B

2) A, B and E

3) A, B and C

4) Only A and E

Correct Answer
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Explanation

Correct Answer

Explanation

Organism R can be treated with A, B, E.

Q. 44 The organism(s) that can be treated with three of these five drugs is(are)

1) Only Q

2) P and Q

3) Q and R

4) Only P

Correct Answer
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Explanation

Correct Answer

Explanation

Organism(s) that can be treated with three drugs are Q and R.

Q. 45 Drug E works on

1) Only P

2) Q and R

3) Only R

4) P and R

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Explanation

Correct Answer

Explanation

Drug E works on only R.

VARC

Directions for questions 46 to 51: Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.

The general idea of being fit is usually assumed to be exercising regularly and having a healthy diet. It’s true to some extent. But this is not always the case. People don’t realise that sleep also plays a crucial part when it comes to physical and mental well-being. It’s a restorative process, which shouldn’t be negotiable.

Hectic working hours, increasing stress levels, and an unhealthy lifestyle can cause irregular sleep patterns. These not only disturb one’s daily routine, but can also hamper one’s health, leading to lifestyle conditions like deranged cholesterol and diabetes. It’s a preconceived notion that cholesterol and diabetes are usually genetic diseases, and unhealthy eating patterns and lifestyle exacerbate them. It is not generally known that sleep deprivation can put a person at risk of both deranged cholesterol and diabetes.

Sleep helps your body and mind repair and recharge themselves. But things can go awry if one is sleepdeprived. Insomnia can generally make the body work abnormally. It affects the mental and physical abilities to prepare the body for the next day. It leaves the brain exhausted, affecting the natural functioning of the body.

Lack of sleep can lead to higher cholesterol and blood pressure. Sleep deprivation can lower levels of leptin, a hormone that stabilises metabolism and appetite. This can also lead to obesity, if left unchecked. Sleep deprivation has been found to raise levels of ghrelin, the hunger hormone, and decrease levels of leptin, the satiety hormone. That’s why people seek relief in foods that raise blood sugar. The American Academy of Sleep Medicine recommends that adults should get a minimum of seven to eight hours of sleep each night. Staying up late can lead to consuming unhealthy snacks and junk food high in carbs and sugar. All this increases the risk of Type 2 diabetes and is equally connected to obesity.

Just like any other routine, having a definite sleeping pattern can help a person maintain a cycle of rest and activity. Sleeping at the same time every day and waking up on time will encourage quality sleep. Proper relaxation of body and mind before sleeping means that one should keep the mobile phone aside for at least half an hour before bed. It helps if the room is dark and quiet. Plus, one can always read a good book or listen to soothing music which can lull one into deep sleep.

Q. 46 The objective of the passage is to

1) advise the reader.

2) present psychological insights to the reader.

3) expose the reader to disinformation.

4) provide medical input to the reader.

Correct Answer
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Explanation

Correct Answer

Explanation

The passage discusses in detail the need for sleep. The use of “you” in the passage makes it evident.

Q. 47 Being deprived of sleep can result in

1) hunger satiation.

2) mental exhaustion.

3) metabolism loss.

4) terminal illness.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “People don’t realise that sleep also plays a crucial part when it comes to physical and mental well-being.”

Q. 48 As per the passage which of these sentences is not correct?

1) One’s body and mind should be properly relaxed to ensure good sleep.

2) Regular exercising and eating healthy food alone ensure fitness.

3) Insufficient sleep can lead to obesity.

4) Irregular sleep patterns can result in health problems.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to the opening paragraph.

Q. 49 The main focus of the passage is on the

1) dangers of high levels of cholesterol and diabetes.

2) perils of insomnia and irregular sleep patterns.

3) stability of leptin and ghrelin in the human body.

4) ill effects of junk food high in carbs and sugars.

Correct Answer
and
Explanation

Correct Answer

Explanation

The entire passage talks about the importance of sleep and what happens if we don’t sleep regularly, and how it leads to insomnia.

Q. 50 In what way does sleep contribute to a person’s well-being?

1) By regularising a person’s daily routine.

2) By increasing a person’s appetite.

3) By helping the body replenish its resources.

4) By adding power and strength to the muscles.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “Sleep helps your body and mind repair and recharge themselves.”

Q. 51 In order to remain physically fit one must

1) snack frequently.

2) raise levels of ghrelin.

3) read a good book every night.

4) maintain a set sleep pattern.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to the last paragraph.

Directions for questions 52 to 57: Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.

Two Apple stores in Delhi and in Mumbai - opened in April 2023. Until now, Indians could buy Apple products in the country either online or through a vast network of what the company call’s premium resellers’. Will the new-found ability to sell products directly to customers in India - the world's second largest smartphone market - impact its fortunes here? Apple has long tried to open physical retail stores in India. In 2019, the Indian government relaxed some investment rules, exempting companies selling ‘cutting-edge’ items, such as Apple's iPhones and iPads, from restrictions.

Apple first launched an online store in India through a website which allows users to request for customised products. Apple’s decision to open physical stores in India could be the next step in its branding strategy. It is not as if this will change Apple’s sales in any dramatic way, but it is still a key milestone, one that will allow Apple to deliver to Indian customers the full Apple experience.

The iPhone is still an aspirational product in the pricesensitive Indian market. When you launch an Apple store, you are basically giving a premium experience to your premium consumers. It might not pull up sales, but it pulls more people into the Apple ecosystem.

Setting up an Apple store in India is also a statement that the country is now big enough for Apple to be actually interested in expanding operations here, and comes at a time when India is rising fast as a manufacturing base for the iPhone.

Apple first began making a lower-end model of the iPhone in India in 2017. Last year, it began producing its latest model of iPhone 14 in the country, which now accounts for 5 percent of total iPhone production.

For years, Apple had relied on China's sophisticated manufacturing network to produce the bulk of its products. But analysts predict that by 2025, a quarter of all iPhones the company makes could be produced in India. Apple was already making between 5-7 percent of its products in India, and they are targeting to go up to 25 percent of their manufacturing capacity.

In 2022, Apple had a 60 percent market share in the Indian ‘premium smartphone’ market - which refers to mobiles that cost INR 40,000 or more, ahead of Samsung's 21 percent share. Apple is doing well across categories. The real issue will be to pull consumers to these flagship centres without alienating the partner sellers.

Apple has finally understood that India’ s premium market is growing, so why not be serious about it.

Q. 52 The Apple retail stores in India will

1) not materially impact sales of iPhones.

2) not have any impact on Apple’s image.

3) drive healthy competition in the smartphone market.

4) bring in more customers and increase sales.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “It is not as if this will change Apple’s sales in any dramatic way,...”

Q. 53 India is now the focus of Apple operations because

1) American technology companies want to reduce their reliance on China.

2) it offers the benefit of a manufacturing base in addition to a market.

3) it has the world’s second largest population.

4) no other country has the same ease of doing business.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “Apple is actually interested in expanding operations here, and comes at a time when India is rising fast as a manufacturing base for the iPhone.”

Q. 54 “Apple’s aim is not only to increase sales of its iPhones, but to draw people into Apple’s ecosystem.” In the context of the passage, this statement means that Apple seeks to

1) be the market leader in the world of premium smartphones.

2) bring customers into a network of related products which it offers.

3) attract customers to buy its phones through innovative means.

4) attract customers by displaying a wide range of aesthetically designed products.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “It might not pull up sales, but it pulls more people into the Apple ecosystem.”

Q. 55 Based on the passage which one of the following is not true?

1) iPhone 14 is being manufactured in India.

2) Currently 5 to 7 percent of all iPhones are manufactured in India.

3) Manufacturing of iPhones in India commenced in 2017.

4) Regulatory restrictions were eased in 2023.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to,” In 2019, the Indian government relaxed some investment rules…” This makes 4 incorrect.

Q. 56 The main point the passage makes is that Apple

1) iPhone was already popular in India.

2) has realised the strategic importance of the Indian market.

3) needs new branding and marketing strategies to compete with Samsung.

4) needs physical stores to expand sales to more buyers of premium products.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to the last line of the paragraph.

Q. 57 Apple’s challenge while opening physical stores is to

1) retain links with their partner sellers while drawing customers to their stores.

2) offer parallel products packaged more attractively.

3) provide stimulation that draws customers away from other sellers.

4) subtly alienate customers away from competitors.

Correct Answer
and
Explanation

Correct Answer

Explanation

Refer to, “The real issue will be to pull consumers to these flagship centres without alienating the partner sellers.”

Directions for questions 58 to 64: Complete the following sentences by choosing the most appropriate word/phrase from the options given below.

Q. 58 The new car has disappointed its buyers in many ways, and good mileage is its only __________.

1) saving case

2) saving praise

3) saving grace

4) saving face

Correct Answer
and
Explanation

Correct Answer

Explanation

saving grace is the correct choice for the blank. Other options are all grammatically incorrect.

Q. 59 The nasty comments made by strangers on the social media platforms about the actor made him __________.

1) ill and ache

2) ill at heart

3) ill in heart

4) ill at ease

Correct Answer
and
Explanation

Correct Answer

Explanation

ill at ease means uncomfortable or embarrassed. Other options are incorrect.

Q. 60 If you ask me to give you a rough estimate for the cost of the project, __________ I would say thirty lakhs.

1) off-the-grid

2) off-the-cuff

3) off-the-mark

4) off-the-mike

Correct Answer
and
Explanation

Correct Answer

Explanation

off the cuff means approximation without any concrete details.

Q. 61 It grieved me __________my friend’s serious illness.

1) hearing regarding

2) to hear of

3) to hear regarding

4) in hearing

Correct Answer
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Explanation

Correct Answer

Explanation

to hear of is the correct usage here.

Q. 62 Meena is very arrogant and class-conscious; she refuses to acknowledge Sunil because she feels he is a man __________.

1) of great importance

2) of no importance

3) of some importance

4) of less importance

Correct Answer
and
Explanation

Correct Answer

Explanation

of no importance is the correct usage.

Q. 63 A few brands tailor their pants in such a way that it is easy for people with prosthetic legs to put them on. This is how they __________.

1) go the extra mile

2) go to the extra level

3) go the entire mile

4) go to the extreme level

Correct Answer
and
Explanation

Correct Answer

Explanation

Going the extra mile is the correct idiomatic expression.

Q. 64 Some big shots know how to escape the law even after they violate it. It is, however, the __________ who are more often apprehended and punished.

1) tiny shots

2) tiny fish

3) small fry

4) small fish

Correct Answer
and
Explanation

Correct Answer

Explanation

Small fry means insignificant people are the ones who get caught.

Directions for questions 65 to 69: In each of the following sentences, the incorrect part of the sentence is underlined. Choose an alternative from the four given options so that the sentence is rendered correct.

Q. 65 The setting of a story effects the storys plot.

1) affects the story plots.

2) affect the story’s plot.

3) effects the stories’ plot.

4) affects the story’s plot.

Correct Answer
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Explanation

Correct Answer

Explanation

Affects the story’s plot, it should be.

Q. 66 Listening to the recording of cricket commentary from the past can be great fun. Especially, the last few overs, when the best players are gone, and the tailenders try their best to run between the wickets without getting out. This is when you realise that nothing much has changed, hasn’t it?

1) nothing much has changed, hasn’t it?

2) nothing much is changed, isn’t it?

3) nothing much has changed, has it?

4) nothing much has changed, would it?

Correct Answer
and
Explanation

Correct Answer

Explanation

nothing much has changed, has it? is the correct expression.

Q. 67 Justin couldn’t understand why his friend had refused to work in a company that offered him a huge salary. If it had been him in his friend’s place, he would definitely accepted such an offer.

1) have definitely have accepted such an offer.

2) have definitely accepted such an offer.

3) have definitely accept such an offer.

4) definitely accepted such an offer.

Correct Answer
and
Explanation

Correct Answer

Explanation

It should be that he would have definitely accepted such an offer.

Q. 68 My aunt Seema was the most generous of all the members of our family. Whenever we went out for dinner, she always insisted to pay for the meal.

1) that she had paid for the meal.

2) that she pay for the meal.

3) on and paid for the meal.

4) that she will be paying for the meal.

Correct Answer
and
Explanation

Correct Answer

Explanation

that she pay for the meal, is the correct expression. Other options are all grammatically incorrect.

Q. 69 When you play the ‘Secret Santa’, you are expected to buy a gift for whoever you are assigned, without letting them know that you are the one buying the gift.

1) whom you are assigned

2) who you are assigned

3) whoever you are assigned

4) whomever you are assigned

Correct Answer
and
Explanation

Correct Answer

Explanation

Whomever is the correct usage here. Hence whomever you are assigned is the correct option.

Directions for questions 70 to 73: Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete the paragraph.

Q. 70 A study of the social and cultural context of Indian poetry in English reveals several important insights into its origin. Indian poetry in English began in Bengal, the province where the British first gained a stronghold. In addition, this poetry was a largely urban phenomenon, centered in Calcutta. __________. Then, gradually, it moved to other urban centres such as Madras and Bombay. Even today, Indian poetry in English remains largely urban. Moreover, because English was an elite language, Indian poets writing in English came from the upper classes.

1) In fact, poetry writing for the first fifty years was confined to a few families who were residents of Calcutta

2) The rulers encouraged the natives to write poetry about India only if their mother tongue was English

3) English was seen as an elite language and so the British felt that only they could use it for poetry

4) The British had decided that poetry about India could reach a larger audience if written in Calcutta

Correct Answer
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Explanation

Correct Answer

Explanation

“In fact, poetry writing for the first fifty years was confined to a few families who were residents of Calcutta” is the correct answer as it elaborates on the previous statement tha poetry basically was an urban phenomenon.

Q. 71 In the late 1960s, architect Charles Correa began his career as an urban planner, creating New Bombay (now Navi Mumbai), an urban area that provided housing and job opportunities for many who lived across the harbour from the original city. In the midst of overpopulated cities, he tried to create quasirural housing environments. In all of his urban planning commissions, Correa avoided highrise housing solutions. __________.

1) He is particularly noted for his sensitivity to the needs of the urban poor

2) Considerations of the Indian climate drove many of his decisions

3) His early work combined traditional architectural values with the Modernist use of materials

4) He focused on low-rise dwelling solutions that emphasized the human scale and created a sense of community.

Correct Answer
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Explanation

Correct Answer

Explanation

The last sentence before the blank discusses avoiding high- rise housing solutions. Hence 4 is the correct answer.

Q. 72 __________. Conflicts are now brewing over rivers and river basins shared by many countries around the world. This is not unexpected, given the fact that more than two hundred water bodies are shared by two or more countries. Strife over water, for example, is erupting throughout the Middle East, from the watersheds of the Nile to the Tigris and Euphrates Rivers.

1) Fresh water is increasingly in short supply, with nearly two-thirds of the global population living in water-stressed conditions

2) The world does not consider water to be the scarce resource it is

3) With water becoming increasingly scarce and development of new sources of water extremely costly, international water tensions are expected to rise

4) It might be a cliche, but given how scarce it is, water is the new oil of the 21st century

Correct Answer
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Explanation

Correct Answer

Explanation

3 fits the given blank correctly as it introduces the topic concerning water scarcity.

Q. 73 The concept of the ‘Villa’ and other European ideas came to Lucknow with foreign soldiers, travellers and adventurers. For the Nawabs of Lucknow, architecture became the physical manifestation of their new status, and a way of proclaiming their alignment to the new power bloc. __________. Villas, hence, provided an ideal substitute. Europeans sold to the Nawabs the idea of villas, based on designs in publications carried by them, and often aided by memory. The building chosen as the prototype for the famous Dilkusha Kothi was a country house in Northumberland.

1) The Nawabs of Lucknow fancied building palaces that resembled British ancestral homes

2) The Villa became the backdrop to both the private as well as the court life of the Nawabs

3) The Nawabs chose to live in Villas because they were easier to construct than palaces

4) The Nawabs were attracted to European ideas in architecture because of their ‘foreignness’

Correct Answer
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Explanation

Correct Answer

Explanation

The previous sentence discusses the need for the Nawabs to maintain the status quo through architecture. Hence option 1 follows the sentence logically.

Directions for questions 74 to 79: Some of the sentences below have words that are missing. Choose the best option from those given below to complete them.

Q. 74 The culture of the 21st century – on an increasingly scale – is oriented around the practical principles of utility, effectiveness, and impact. Things are good to the extent that they are instrumental, with instrumentality usually defined as the capacity to produce money or things. The worth of anything – an idea, an activity, an artwork, a with another person – is determined __.

1) nominal; dinner; meaningfully

2) global; relationship; pragmatically

3) conspicuous; dialogue; diligently

4) ordinal; conversation; imaginatively

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “The culture of the 21st century – on an increasingly global scale – is oriented around the practical principles of utility, effectiveness, and impact. Things are good to the extent that they are instrumental, with instrumentality usually defined as the capacity to produce money or things. The worth of anything – an idea, an activity, an artwork, a relationship with another person – is determined pragmatically.”

Q. 75 The human resource chief said that the company will not on investing in people and has spending on employee needs in order to __ them and provide them with a sense of stability and certainty.

1) delay; assured; empower

2) compromise; prioritised; reassure

3) debate; assured; confront

4) prioritise; compromised; include

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “The human resource chief said that the company will not compromise on investing in people and has prioritised spending on employee needs in order to reassure them and provide them with a sense of stability and certainty.”

Q. 76 Working from home requires that you may have to put your life on . Some people find this very __ as they like to keep their work and home lives separate.

1) private; screen; disconcerting

2) entire; camera; complicated

3) actual; video; uncomfortable

4) family; microscope; disturbing

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “Working from home requires that you may have to put your private life on a screen. Some people find this very disconcerting as they like to keep their work and home lives separate.”

Q. 77 In its early stages, dementia is often from normal ageing, in which the older brain may naturally begin to show signs of cognitive impairment. Neither dementia nor cognitive ageing is currently , though they may be slowed through diet, exercise, and keeping the mind agile with social and intellectual activity.

1) irreversible; manageable

2) indistinguishable; reversible

3) distinguishable; permanent

4) differentiated; visible

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “In its early stages, dementia is often indistinguishable from normal ageing, in which the older brain may naturally begin to show signs of cognitive impairment. Neither dementia nor cognitive ageing is currently reversible, though they may be slowed through diet, exercise, and keeping the mind agile with social and intellectual activity.”

Q. 78 have to label their posts in order to bring about transparency and __ the interests of the customers.

1) Promoters; social media; incite

2) Influencers; promotional; safeguard

3) Advertisers; commercials; capture

4) Distributors; Facebook; multiply

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “Influencers have to label their promotional posts in order to bring about transparency and safeguard the interests of the customers.”

Q. 79 In the alleyways of old Cairo, in its cafes, warehouses and barbershops, framed portraits of Egyptian icons are . Kings, presidents, religious and political figures are all on fading walls, held up as symbols of a glorious past.

1) fashionable; confounded

2) rare; abundant

3) ubiquitous; immortalised

4) substantial; dispersed

Correct Answer
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Explanation

Correct Answer

Explanation

The sentence would read: “In the alleyways of old Cairo, in its cafes, warehouses, and barbershops, framed portraits of Egyptian icons are ubiquitous. Kings, presidents, religious, and political figures are all immortalised on fading walls, held up as symbols of a glorious past.”

Q. 80 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) The politician was so flustered by the animosity of the crowd that he refused to answer further questions.

2) I live farther away from college than all my classmates.

3) We need to discuss this problem right away and avoid letting it fester any further.

4) If you need to farther your career, you should avoid all kinds of distractions.

Correct Answer
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Explanation

Correct Answer

Explanation

The correct word that should be used here is “further,” not “farther.” The correct sentence would be: “If you need to further your career, you should avoid all kinds of distractions.”

Q. 81 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) To keep the key safe, she wore it on a cord around her neck.

2) He purchased a cord of wood from the market.

3) Teenagers may feel a need to cut the umbilical cord tying them to their homes.

4) The musician would hear a cord in his head and play each note individually.

Correct Answer
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Explanation

Correct Answer

Explanation

The correct word that should be used here is “chord,” not “cord.” The correct sentence would be: “The musician would hear a chord in his head and play each note individually.”

Q. 82 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) They found that all the flowers placed on their mother’s grave had withered within a week.

2) The landlord issued a warning to the tenants that non-payment of rent was a grave matter and would lead to a court case.

3) The pet dog could not come to terms with his master’s death and went to grave for him, even refusing to eat for several days.

4) When the witness was summoned by the lawyer, he made grave allegations against the accused.

Correct Answer
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Explanation

Correct Answer

Explanation

The word “grave” is used incorrectly in this sentence. The correct word should be “grieve.” The correct sentence would be: “The pet dog could not come to terms with his master’s death and grieved for him, even refusing to eat for several days.”

Q. 83 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) She had left home for the first time, so her parents made her promise that she would ring them up every day.

2) They were all soaking wet and their mother told them to ring their clothes first and then put them out to dry.

3) The witch waved her wand, recited a magical verse, pressed the blue stone on her ring and vanished into thin air.

4) To catch the terrorist the security forces formed a ring around the house where he was hiding.

Correct Answer
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Explanation

Correct Answer

Explanation

The correct word that should be used here is “wring,” not “ring.” The correct sentence would be: “They were all soaking wet, and their mother told them to wring their clothes first and then put them out to dry.”

Q. 84 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) I have a good chance of a promotion since my firm has recently tied up with a global conglomerate.

2) The bags placed on the carrier were not securely tied, which led to an unfortunate accident.

3) It was a full moon night and the tied was high, but he went boating and, unfortunately, he drowned.

4) After many years of knowing one another, they eventually tied the knot.

Correct Answer
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Explanation

Correct Answer

Explanation

The correct word that should be used here is “tide,” not “tied.” The correct sentence would be: “It was a full moon night, and the tide was high, but he went boating and, unfortunately, he drowned.”

Q. 85 Directions for questions 80 to 85: One of the statements below contains a word used incorrectly or inappropriately. Choose the option which has the incorrect or inappropriate usage of the word.

1) Our products have to function in extreme weather conditions, which is why we put them through climatic testing.

2) The passengers in the bus were sweating profusely because of the hot climatic conditions.

3) The climatic moment of the match was when the captain got caught behind the wicket.

4) Under certain climatic conditions, hailstorms are formed in the atmosphere, resulting in unexpected accidents.

Correct Answer
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Explanation

Correct Answer

Explanation

The word “climatic” is used incorrectly in this sentence. The correct word that should be used here is “climatic”. The correct sentence would be: “The climatic moment of the match was when the captain got caught behind the wicket.”

Q. 86 Directions for questions 86 to 90: The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.

(1) Once they reach a high altitude, they manage to travel all over the world.
(2) An expert from the team explained that the bacteria usually lived on the surface of vegetation, such as leaves.
(3) The wind carries them off the surface and into the atmosphere.
(4) A group of researchers were surprised to find that clouds had carried drug resistant bacteria over a long distance.

Correct Answer
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Explanation

Correct Answer

4231

Explanation

Correct Order- (4) A group of researchers were surprised to find that clouds had carried drugresistant bacteria over a long distance.
(2) An expert f rom the team explained that the bacteria usually lived on the surface of vegetation, such as leaves.
(3) The wind carries them off the surface and into the atmosphere.
(1) Once they reach a high altitude, they manage to travel all over the world.

Q. 87 Directions for questions 86 to 90: The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.

(1) But the mutiny of Visakhapatnam predates this.
(2) Instead of going against their heroic leader, the sepoys attacked the British soldiers and managed to escape from the town.
(3) The Sepoy Mutiny of 1857 in the garrison town of Meerut is regarded as the First War of Independence.
(4) It happened in 1780 when the British officers asked the local sepoys to join the fight against Hyder Ali.

Correct Answer
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Explanation

Correct Answer

3142

Explanation

Correct Order- (3) The Sepoy Mutiny of 1857 in the garrison town of Meerut is regarded as the First War of Independence.
(1) But the mutiny of Visakhapatnam predates this.
(4) It happened in 1780 when the British officers asked the local sepoys to join the fight against Hyder Ali.
(2) Instead of going against their heroic leader, the sepoys attacked the British soldiers and managed to escape from the town.

Q. 88 Directions for questions 86 to 90: The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.

(1) This instance highlights how young people from different backgrounds can make important contributions to climate change.
(2) Participation in environmental education programmes can motivate children to act responsibly towards the environment.
(3) They were motivated to act in ways that would help the environment, like using a reusable water bottle or refusing to use plastic straws.
(4) Six hundred elementary school children from varied social and linguistic groups participated in an ocean pollution education programme.

Correct Answer
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Explanation

Correct Answer

2431

Explanation

Correct Order- (2) Participation in environmental education programmes can motivate children to act responsibly towards the environment.
(4) Six hundred elementary school children from varied social and linguistic groups participated in an ocean pollution education programme.
(3) They were motivated to act in ways that would help the environment, like using a reusable water bottle or refusing to use plastic straws.
(1) This instance highlights how young people from different backgrounds can make important contributions to climate change.

Q. 89 Directions for questions 86 to 90: The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.

(1) What is more shocking to observe is how often such strokes lead to death.
(2) When the body temperature rises, our vital organs swell, and this causes death.
(3) One main reason for this is that people underestimate how badly heat can affect the body.
(4) Heat strokes have become more common in our country than ever before.

Correct Answer
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Explanation

Correct Answer

4132

Explanation

Correct Order- (4) Heat strokes have become more common in our country than ever before.
(1) What is more shocking to observe is how often such strokes lead to death.
(3) One main reason for this is that people underestimate how badly heat can affect the body.
(2) When the body temperature rises, our vital organs swell, and this causes death.

Q. 90 Directions for questions 86 to 90: The sentences given below, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the most logical order and enter the sequence of numbers in the space provided. Only numbers are to be entered in the space provided for the answer, and no letters, characters, or spaces should be entered. For example, a response such as 3412 is valid, and responses such as 3412. or 3 41 2 are invalid.

(1) Yet, even as TikTok delights consumers and advertisers, others believe the sunny app has a dark side.
(2) Since launching just five years ago, the app has brought a warm glow to its 1 billion plus users, as well as an icy dash of competition to the social media incumbents of Silicon Valley.
(3) ByteDance, its owner, has its headquarters in China, whose government is addicted to surveillance and propaganda-making it a worrying place for a media app to be placed.
(4) With its wholesome dancing and lip-syncing videos, TikTok once billed itself as the “last sunny corner on the Internet.”

Correct Answer
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Explanation

Correct Answer

4213

Explanation

Correct Order- (4) With its wholesome dancing and lip-syncing videos, TikTok once billed itself as the “last sunny corner on the Internet.”
(2) Since launching just five years ago, the app has brought a warm glow to its 1 billion plus users, as well as an icy dash of competition to the social media incumbents of Silicon Valley.
(1) Yet, even as TikTok delights consumers and advertisers, others believe the sunny app has a dark side.
(3) ByteDance, its owner, has its headquarters in China, whose government is addicted to surveillance and propaganda-making it a worrying place for a media app to be placed.

IPMAT 2023 Question Paper With Detailed PDF Solutions

IPMAT 2023 Paper With Answers & Explanation

QA (SA)

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Explanation

Q. 2

Correct Answer

Explanation

Q. 3 If three consecutive coefficients in the expansion of (x + y)n are in the ratio 1:9:63, then the value of n is __________.

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Explanation

Q. 4 If f(1) = 1 and f (n) = 3n – f (n – 1) for all integers n > 1, then the value of f(2023) is __________.

Correct Answer

Explanation

Q. 5 Let a, b, c, d be positive integers such that a + b + c + d = 2023. If a : b = 2 : 5 and c : d = 5 : 2, then the maximum possible value of a + c is __________.

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Explanation

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Explanation

Q. 7 The total number of positive integer solutions of 21 ≤ a + b + c ≤ 25 is __________.

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Q. 8 The remainder when 1! + 2! + 3! + ··· + 95! is divided by 15 is __________·

Correct Answer

Explanation

Correct Answer

Explanation

Q. 10 In the xy-plane let A = (–2, 0), B = (2, 0). Define the set S as the collection of all points C on the circle x2 + y2 = 4 such that the area of the triangle ABC is an integer. The number of points in the set S is __________.

Correct Answer

Explanation

Q. 11 The polynomial 4x10 – x9 + 3x8 – 5x7 + cx6 + 2x5 – x4 + x3 – 4x2 + 6x – 2 when divided by x – 1 leaves a remainder 2. Then the value of c + 6 is __________.

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Explanation

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Explanation

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Q. 14

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Q. 15 The length of the line segment joining the two intersection points of the curves y = 4970 – lxl and y = x2 is __________.

Correct Answer

Explanation

QA (MCQ)

Q. 16 Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

Correct Answer

Explanation

Q. 17 In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be:

Correct Answer

Explanation

Q. 18 If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at an annual interest rate of 10% is INR 527, then the amount invested in INR is

Correct Answer

Explanation

Q. 19 The probability that a randomly chosen positive divisor of 102023 is an integer multiple of 102001 is

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Explanation

Q. 20 The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is:

Correct Answer

Explanation

Q. 21 If logcos x(sin x) + logsin x(cos x) = 2, then the value of x is

Correct Answer

Explanation

Q. 22

Correct Answer

Explanation

Q. 23 In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?

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Explanation

Q. 24 Which of the following straight lines are both tangent to the circle x2 + y2 – 6x + 4y – 12 = 0?

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Explanation

Correct Answer

Explanation

Q. 26 Let p be a positive integer such that the unit digit of p3 is 4. What are the possible unit digits of (p + 3)3?

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Explanation

Q. 27

Correct Answer

Explanation

Q. 28 A polynomial P(x) leaves a remainder 2 when divided by (x – 1) and a remainder 1 when divided by (x – 2). The remainder when P(x) is divided by (x – 1)(x – 2) is

Q. 3 If three consecutive coefficients in the expansion of (x + y)ⁿ are in the ratio 1:9:63, then the value of n is __________.

Q. 10 In the xy-plane let A = (–2, 0), B = (2, 0). Define the set S as the collection of all points C on the circle x² + y² = 4 such that the area of the triangle ABC is an integer. The number of points in the set S is __________.

Q. 11 The polynomial 4x¹⁰ – x⁹ + 3x⁸ – 5x⁷ + cx⁶ + 2x⁵ – x⁴ + x³ – 4x² + 6x – 2 when divided by x – 1 leaves a remainder 2. Then the value of c + 6 is __________.

Q. 15 The length of the line segment joining the two intersection points of the curves y = 4970 – lxl and y = x² is __________.

Q. 19 The probability that a randomly chosen positive divisor of 10²⁰²³ is an integer multiple of 10²⁰⁰¹ is

Q. 21 If log_{cos x}(sin x) + log_{sin x}(cos x) = 2, then the value of x is

Q. 24 Which of the following straight lines are both tangent to the circle x² + y² – 6x + 4y – 12 = 0?

Q. 26 Let p be a positive integer such that the unit digit of p³ is 4. What are the possible unit digits of (p + 3)³?

Q. 30 Let a, b, c be real numbers greater than 1, and n be a positive real number not equal to 1. If log_n(log₂ a) = 1, log_n(log₂ b) = 2 and log_n(log₂ c) = 3, then which of the following is true?

Q. 39 The equation x² + y² – 2x – 4y + 5 = 0 represents