IPMAT Indore 2024 — Previous Year Paper

The number of factors of 1800 that are multiple of 6 is ________

The number of real solutions of the equation $(x^2-15x+55{)}^{x^2-5x+6}=1$ is _________

Companies table:

The age of all employees are integers. Age of every employee in A is strictly less than every employee in B; in B less than C; ... in G less than H.

The highest possible age of an employee of company A is ______

In a group of 150 students, 52 like tea, 48 like juice and 62 like coffee. If each student likes at least one drink, then the maximum number of students that like more than one drink is _____

Let ABC be a triangle right-angled at B with AB = BC = 18. The area of the largest rectangle that can be inscribed in this triangle and has B as one of the vertices is ______

A fruit seller has oranges, apples and bananas in the ratio 3:6:7. If the number of oranges is a multiple of both 5 and 6, then the minimum number of fruits the seller has is ______

The number of pairs (x, y) of integers satisfying the inequality $|x-5|+|y-5|\le 6$ is _____

The price of a chocolate is increased by x% and then reduced by x%. The new price is 96.76% of the original price. Then x is _____

Let f and g be two functions defined by $f(x)=|x+|x||$ and $g(x)=1/x$ for x ≠ 0. If $f(a)+g(f(a))=13/6$ for some real a, then the maximum possible value of $f(g(a))$ is ______

Companies table:

The age of all employees are integers. Age of every employee in A is strictly less than every employee in B; in B less than C; ... in G less than H.

The median age of an employee across the eight companies is ______

Companies table:

The age of all employees are integers. Age of every employee in A is strictly less than every employee in B; in B less than C; ... in G less than H.

In company F, the lowest possible sum of the ages of all employees is ______

If $4^{{\log }_{2}x}-4x+9^{{\log }_{3}y}-16y+68=0$, then $y-x$ equals _______

Person A borrows Rs. 4000 from B for 4 years. A portion is at 3% simple interest per annum, the rest at 4% simple interest. If B gets Rs. 520 as total interest, then the amount borrowed at 3% per annum is _______

The number of triangles with integer sides and with perimeter 15 is _______

If $A=\left[\begin{array}{ccc}{x}_1& x_2& 7\\ y_1& y_2& y_3\\ z_1& 8& 3\end{array}\right]$ is a matrix such that the sum of all three elements along any row, column or diagonal are equal to each other, then the value of determinant of A is ______

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle changes to 45° after moving 20 metres towards the base. Then the height of the pole, in metres, is

If $|x+1|+(y+2{)}^2=0$ and $ax-3ay=1$, then the value of $a$ is

If ${\log }_{4}x=a$ and ${\log }_{25}x=b$ then ${\log }_{x}10$ is

Let ABC be an equilateral triangle, with each side of length $k$. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

Let ABC be a triangle with AB = AC and D be a point on BC such that ∠BAD = 30°. If E is a point on AC such that AD = AE, then ∠CDE equals

If 5 boys and 3 girls randomly sit around a circular table, the probability that there will be at least one boy sitting between any two girls is

The side AB of a triangle ABC is $c$. The median BD is of length $k$. If $\angle BDA=\theta <90°$, then the area of triangle ABC is

Let $a=\frac{({\log }_{7}4)({\log }_{7}5-{\log }_{7}2)}{({\log }_{7}25)({\log }_{7}8-{\log }_{7}4)}$. Then $5^a$ is

For some non-zero real values of $a,b,c$, it is given that $|c/a|=4$, $|a/b|=1/3$ and $b/c=-3/4$. If $ac>0$, then $(b+c)/a$ equals

The difference between the maximum real root and the minimum real root of the equation $(x^2-5{)}^4+(x^2-7{)}^4=16$ is

If $\theta$ is the angle between the pair of tangents drawn from the point $A(0,7/2)$ to the circle $x^2+y^2-14x+16y+88=0$, then $\tan \theta$ equals

The numbers $2^{2024}$ and $5^{2024}$ are expanded and their digits are written out consecutively on one page. The total number of digits written is

A boat goes 96 km upstream in 8 hours and covers the same distance downstream in 6 hours. The next day boat starts from A, goes downstream for 1 hour, then upstream for 1 hour, and repeats 4 more times (5 upstream and 5 downstream). Then the boat would be

If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is

In a survey of 500 people, 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither. The number of people who owned both is

The sum of an infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of n for which the sum of its first n terms is closest to 100 is

Let n be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy. Then n is

The greatest number among $2^{300},3^{200},4^{100},2^{100}+3^{100}$ is

The number of values of $x$ for which $\left(\genfrac{}{}{0ex}{}{17-x}{3x+1}\right)$ is defined as an integer is

The number of solutions of $x_1+x_2+x_3+x_4=50$ where $x_1,x_2,x_3,x_4$ are integers with $x_1\ge 1,x_2\ge 2,x_3\ge 0,x_4\ge 0$ is

Sagarika divides her savings of 10000 rupees across schemes A and B. Scheme A offers 10% p.a. compounded half-yearly; Scheme B offers 12% p.a. simple interest. If at end of year 1, value in B exceeds A by 2310 rupees, then the total interest earned is

A fruit seller had apples, bananas, oranges. Bananas were 10 more than apples; (apples + bananas) was a multiple of 11. She sold 70% of apples, 60% of bananas, and 50% of oranges. If she sold 55% of total fruits, then the minimum number of oranges she had was

The terms of a geometric progression are real and positive. If the $p$th term is $q$ and the $q$th term is $p$, then the logarithm of the first term is

The number of real solutions of the equation $x^2-10|x|-56=0$ is

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is

Direction (Q.41-Q.45): In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each, all of whom voted. Three parties A, B and C contested. The party that gets the maximum number of votes in a constituency wins that seat; there was a clear winner in every constituency. Additional info:

• Total votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C; A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

The constituency in which B got lower number of votes compared to A and C is

Direction (Q.41-Q.45): In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each, all of whom voted. Three parties A, B and C contested. The party that gets the maximum number of votes in a constituency wins that seat; there was a clear winner in every constituency. Additional info:

• Total votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C; A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

The number of votes obtained by B in S2 is

Direction (Q.41-Q.45): In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each, all of whom voted. Three parties A, B and C contested. The party that gets the maximum number of votes in a constituency wins that seat; there was a clear winner in every constituency. Additional info:

• Total votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C; A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

If A and C formed an alliance, the number of seats this alliance would have won is

Direction (Q.41-Q.45): In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each, all of whom voted. Three parties A, B and C contested. The party that gets the maximum number of votes in a constituency wins that seat; there was a clear winner in every constituency. Additional info:

• Total votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C; A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

The number of votes obtained by A in S5 is

Direction (Q.41-Q.45): In an election there were five constituencies S1, S2, S3, S4 and S5 with 20 voters each, all of whom voted. Three parties A, B and C contested. The party that gets the maximum number of votes in a constituency wins that seat; there was a clear winner in every constituency. Additional info:

• Total votes obtained by A, B and C across all constituencies are 49, 35 and 16 respectively.
• S2 and S3 were won by C; A won only S1.
• Number of votes obtained by B in S1, S2, S3, S4 and S5 are distinct natural numbers in increasing order.

The lowest number of votes by A was in constituency

Based on the information in the passage, who has endorsed the right to clean air?

In the last sentence, "This is the battle for our future", the writer is

Based on the information in the passage, which one of the following statements is correct?

The first sentence mentions that India was in the news again as a world leader. What is the writer's intention?

Which of the following points is NOT made by the writer?

The phrase "that kicks in" (para 3) means

Which of the following best indicates the relationship between anxiety and survival?

In what way might the relationship between exercise and anxiety relief suggest a potential solution for individuals with anxiety disorders?

The information about anxiety treatments is organized in which of the following ways?

Which best describes the potential danger associated with anxiety disorder?

The passage is chiefly concerned with

Which one of the following statements is correct?

Direction: Choose the most appropriate word/phrase to complete the sentence.

My supervisor seemed to be in a bad mood because he __________ when I asked if I could leave an hour early.

Direction: Choose the most appropriate word/phrase to complete the sentence.

In a circus where performers share dressing rooms and work in a fast-paced environment, the success of a show __________ fostering team-work and collaboration.

Direction: Choose the most appropriate word/phrase to complete the sentence.

Anil could not go to his friend's party, as he had fever and was __________.

Direction: Choose the most appropriate word/phrase to complete the sentence.

The Principal said, "If you want others to take you seriously then you must __________ on issues like gender bias and inclusivity."

Direction: Choose the most appropriate word/phrase to complete the sentence.

The students' picnic plans __________ when it started raining heavily in the morning.

Direction: Choose the most appropriate word/phrase to complete the sentence.

All the employees agreed that the new regulations had __________ positive changes in the workplace.

Direction: Choose the most appropriate word/phrase to complete the sentence.

Sheila keeps interrupting Manohar when he is playing, but he __________ because she is his younger sister.

Direction: The underlined part of the sentence may be incorrect. Choose the option that renders the sentence correct.

He is very careless and has loosed his keys all the time.

Direction: The underlined part of the sentence may be incorrect. Choose the option that renders the sentence correct.

I had been having a headache, so I will not attend the meeting.

Direction: The underlined part of the sentence may be incorrect. Choose the option that renders the sentence correct.

The negotiations are unsuccessful, and the Boards' hopes to continuing talks on a future deal seems to be increasingly improbable.

Direction: The underlined part of the sentence may be incorrect. Choose the option that renders the sentence correct.

In my opinion, the psychological thrillers of Alfred Hitchcock, who is a master of suspense and horror, have more lasting impact than any other filmmaker in history.

Direction: The underlined part of the sentence may be incorrect. Choose the option that renders the sentence correct.

While the bustling city streets were filled with the cacophony of honking horns and chatter of pedestrians, the serene countryside, where time seemed to move at a slower pace, provide a welcome retreat for their seeking solace amidst the chaos of urban living.

Direction: Choose the sentence that most logically completes the paragraph.

Most artificial intelligence (AI) applications in the fields of healthcare, industry, finance, transportation, and writing, rely heavily on deep learning and natural language processing. However, while AI systems can mimic existing styles and patterns, there is an ongoing debate about whether AI can truly possess creativity in the same sense as humans. ______________________________.

Direction: Choose the sentence that most logically completes the paragraph.

In an era where privacy and individualism are often prized above all else, Japanese architect Riken Yamamoto blurs the boundary between public and private. ______________________________. His work is a testament to the power of architecture to break down barriers and to foster a sense of community.

Direction: Choose the sentence that most logically completes the paragraph.

The pursuit of a career in sports offers individuals opportunities for personal fulfilment and professional success. _______________________. Athletes must therefore undergo rigorous training regimens to maintain peak physical condition and hone their skills.

Direction: Choose the sentence that most logically completes the paragraph.

______________________________. This happened after a lorry laden with tomatoes worth 21 lakh rupees went missing. One of the three traders who had sent his tomatoes on the lorry said that they had lost contact with the driver in Nashik and that his GPS had been switched off.

Direction: Choose the best option to fill the blanks.

An ______________ found that one of the marathon runners had ______________ slowed down in the last two kilometres and after ______________ to the one behind him had let him cross the finish line just one second before he did.

Direction: Choose the best option to fill the blanks.

The outbreak of COVID-19 resulted in a health crisis and a drop in economic activity that were without ________________________ in history. While containing and _____________________ the spread of the virus was the first priority, reducing the ______________ of the disease and limiting the pressure on healthcare systems were also considered equally important.

Direction: Choose the best option to fill the blanks.

In today's fast-paced world, individuals are inundated with information, necessitating the cultivation of critical thinking skills to navigate the influx of data ______________. Additionally, the prevalence of fake news presents a ________________ challenge, undermining people's trust. Promoting media literacy is vital for _____________________ informed citizenship.

Direction: Choose the best option to fill the blanks.

Conspiracy theorists suggest that if climate change is slowly turning the planet into an oven, then this must have been the outcome of our enemies' intentional _____________. If there are no coincidences in the world, then everything, including _____________ events, can be controlled. It is only a matter of power and ____________.

Direction: Choose the best option to fill the blanks.

It is widely argued that social media can benefit aspiring ______________. Populists in particular latch on to social media today as a way to connect directly with people, ______________ restraints on their behaviour that political parties would have provided. They can also profit from echo chambers, which reinforce the sense that a whole people ______________ supports a populist leader.

Direction: Choose the best option to fill the blanks.

In an era of globalization, cultural diversity is celebrated. However, the rise of xenophobia poses a ______________ challenge to social cohesion. Building inclusive communities and promoting intercultural dialogue are essential for ______________ mutual understanding. Educating individuals and challenging ______________ are crucial steps toward creating inclusive societies.

Which option has the incorrect or inappropriate usage of 'callus'?

Which option has the incorrect or inappropriate usage of 'diffuse'?

Which option has the incorrect or inappropriate usage of 'ban'?

Which option has the incorrect or inappropriate usage of 'stay'?

Which option has the incorrect or inappropriate usage of 'proscribe'?

Which option has the incorrect or inappropriate usage of 'train'?

Direction: The sentences below, when properly sequenced, form a coherent paragraph. Enter the sequence as a digit string (e.g. "53412").

1. By contrast, in America, it is estimated that even after post-COVID decline, total giving came to almost $500 billion in 2022.

2. There are no comparable data on different countries. But one report by Dasra, a Mumbai-based NGO, estimates total private giving in India came to about $13 billion in 2022.

3. A strategic sort of giving, involving philanthropy professionals, a long-term lens, and big ambitions of transforming society is gradually emerging. It differs, of course, between countries.

4. Researchers at the Chinese Academy of Social Sciences, put total giving in China at $21 billion in 2020.

5. By any measure, however, organised philanthropy across Asia is on a much smaller scale than in the West.

Direction: The sentences below, when properly sequenced, form a coherent paragraph. Enter the sequence as a digit string (e.g. "53412").

1. Farmers, however, especially during the peak farming season, ignore the warnings of the weather forecast.

2. People from some states of India have demanded that families of those who have been killed by lightning strikes should receive compensation.

3. The Minister for Disaster Management announced that over 2800 people have died after being struck by lightning last year.

4. The Minister responded that pamphlets on the dangers of lightning and precautions to be taken are being distributed in villages.

Direction: The sentences below, when properly sequenced, form a coherent paragraph. Enter the sequence as a digit string (e.g. "53412").

1. Meanwhile, people are posting less. The share of Americans who say they enjoy documenting their life online has fallen from 40% to 28% since 2020.

2. The striking feature of the new social media is that they are no longer very social.

3. Some of the consequences of this are welcome. Political campaigners say they have to tone down their message to win over private groups.

4. Debate is moving to closed platforms such as WhatsApp and Telegram.

5. Inspired by TikTok, apps like Facebook increasingly serve a diet of clips selected by AI according to a user's viewing behaviour, not their social connections.

Direction: The sentences below, when properly sequenced, form a coherent paragraph. Enter the sequence as a digit string (e.g. "53412").

1. In this microgravity environment, your blood also tends to move towards the heart and head.

2. Both effects are only short-lived and, after a brief period of readjustment on arriving back home, the heart and spine return to normal.

3. The heart interprets this as an increase in the amount of blood in the body and that it needs to pump less, so it shrinks.

4. In space with less gravitational force than on Earth, there's less pressure on your spine and so it'll get a bit longer, effectively making you as much as two inches taller.

Direction: The sentences below, when properly sequenced, form a coherent paragraph. Enter the sequence as a digit string (e.g. "53412").

1. The muddy concoction – made by grinding the kava plant's roots and mixing it with water to create a dark, earthy liquid – holds a deep cultural significance throughout the region, and the drink is often shared between friends, guests, and colleagues.

2. Regular kava drinkers often describe this blissful state as a sort of peace, a way for the body and mind to uncoil from itself.

3. Called yaqona in Fiji, 'ava in Samoa and sakau in Micronesia, kava has occupied a sacred role in Pacific countries for centuries.

4. A swig (or two) taken from a bowl or shell – sometimes quite literally a coconut shell cut in half – can lead to profound relaxation, a sort of numbness that trickles down from your mouth through your shoulders and spine.