IPMAT Indore 2025 — Previous Year Paper

If the polynomial ${\mathrm{ax}}^2+bx+5$ leaves a remainder 3 when divided by $x-1$, and a remainder 2 when divided by $x+1$, then $2b-4a$ equals _____________.

English exam and Math exam were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice the number of students who did not appear for the Math exam. The number of students who passed the Math exam is twice the number of students who appeared but failed the English exam. If the number of students who passed the English exam is twice the number of students who appeared but failed the Math exam, then the number of students who appeared but failed the English exam is _________

The number of factors of $3^5\times 5^8\times 7^2$ that are perfect squares is ____________.

Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one specialty. The total number of biologists, geologists, and explorers are equal.

The following additional information is available:

• Every team has at least 2 members from each of the three skill sets.
• Team C and D have 6 biologists each, and Team A has 6 geologists.
• Every team except A has more biologists than explorers.
• The number of explorers in each team is distinct and decreases in the order A, B, C, D and E.

The number of biologists in team E is ____________.

Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one specialty. The total number of biologists, geologists, and explorers are equal.

The following additional information is available:

• Every team has at least 2 members from each of the three skill sets.
• Team C and D have 6 biologists each, and Team A has 6 geologists.
• Every team except A has more biologists than explorers.
• The number of explorers in each team is distinct and decreases in the order A, B, C, D and E.

The number of teams having more geologists than biologists is ______

If $A=\left[\begin{array}{cc}2& n\\ 4& 1\end{array}\right]$ such that $A^3=27\left[\begin{array}{cc}4& q\\ p& r\end{array}\right]$, then $p+q+r$ equals ______________.

Eight teams take part in a tournament where each team plays against every other team exactly once. In a particular year, one team got suspended after playing 3 matches, due to a disciplinary issue. The organizers decide to proceed, nonetheless, with the remaining matches. The total number of matches that were played in the tournament that year is _____

Arpita and Nikita, working together, can complete an assigned job in 12 days. If Arpita works initially to complete 40% of the job, and the remaining job is completed by Nikita alone, then it takes 24 days to complete the job. The possible number of days that Nikita requires to complete the entire job, working alone, is _________

Five teams – A, B, C, D and E – each consisting of 15 members, are going on expeditions to five different locations. Each team includes members from three different skill sets: biologists, geologists, and explorers. However, the number of members from each skill set varies by team and each member has only one specialty. The total number of biologists, geologists, and explorers are equal.

The following additional information is available:

• Every team has at least 2 members from each of the three skill sets.
• Team C and D have 6 biologists each, and Team A has 6 geologists.
• Every team except A has more biologists than explorers.
• The number of explorers in each team is distinct and decreases in the order A, B, C, D and E.

The median number of biologists across five teams is ________.

If ${\log }_3(x^2-1)$, ${\log }_3(2x^2+1)$ and ${\log }_3(6x^2+3)$ are the first three terms of an arithmetic progression, then the sum of the next three terms of the progression is _______________.

If $m$ and $n$ are two positive integers such that $7m+11n=200$, then the minimum possible value of $m+n$ is _________.

If $a,b,c$ are three distinct natural numbers, all less than 100, such that $|a-b|+|b-c|=|c-a|$, then the maximum possible value of $b$ is______________.

A circle of radius 13 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 18 cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is___________.

If the sum of the first 21 terms of the sequence $\ln \frac{a}{b},\ln \frac{a}{b\sqrt{b}},\ln \frac{a}{b^2},\ln \frac{a}{b^2\sqrt{b}},\dots$ is $\ln \frac{a^m}{b^n}$, then the value of $m+n$ is _____________.

Monica, who is 18 years old, is one-third the age of her father. The age at which she will be half the age of her father is ______

Anindita invests a total of 1 lakh rupees distributed across three schemes A, B and C for a period of two years. These schemes offer an interest rate of 10%, 8% and 12% per annum, respectively, each compounded annually. If the initial investment amount in scheme A is 30000 rupees and the total interest earned from all the three schemes during the first year is 10600 rupees, then the total interest earned, in rupees, from all the three schemes for the second year is _________

Let $S_1=\{100,105,110,115,\dots \}$ and $S_2=\{100,95,90,85,\dots \}$ be two series in arithmetic progression. If $a_k$ and $b_k$ are the $k$-th terms of $S_1$ and $S_2$ respectively, then ${\sum }_{k=1}^{20}{a}_k{b}_k$ equals

If $8x^2-2kx+k=0$ is a quadratic equation in $x$, such that one of its roots is $p$ times the other, and $p,k$ are positive real numbers, then $k$ equals

Let $P(x)$ be a quadratic polynomial such that $\left|\begin{array}{cc}P(0)& P(1)\\ P(0)& P(2)\end{array}\right|=0$. Let $P(0)=2$ and $P(1)+P(2)+P(3)=14$. Then $P(4)$ equals

If ${\log }_{25}[5{\log }_3(1+{\log }_3(1+2{\log }_{2}x))]=\frac{1}{2}$ then $x$ is

The area of the triangle, formed by the straight lines $y=0$, $12x-5y=0$, and $3x+4y=7$, is

Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is

Given that $1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\cdots =\frac{{\pi }^2}{6}$, the value of $1+\frac{1}{3^2}+\frac{1}{5^2}+\frac{1}{7^2}+\cdots$ is

Two swimmers, Ankit and Bipul, start swimming from the opposite ends of a swimming pool at the same time. Ankit can cover the length of the pool once in 10 minutes. Bipul can cover the length of the pool once in 15 minutes. They swim back and forth for 80 minutes without stopping. The number of times they meet each other is _____

If $a_1,a_2,\dots ,a_8$ are the roots of the equation $x^8+x^7+\cdots +x+1=0$, then the value of $a_1^{2025}+a_2^{2025}+\cdots +a_8^{2025}$ is

Which of the following numbers is divisible by $3^{10}+2$?

A circle touches the $y$-axis at $(0,4)$ and passes through the point $(-2,0)$. Then the radius of the circle is

If $y=a+b{\log }_{e}x$ then which of the following is true?

Let $A(1,3)$ and $B(5,1)$ be two points. If a line with slope $m$ intersects $AB$ at an angle of $45°$, then the possible values of $m$ are

The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

Area of a regular octagon inscribed in a circle of radius 1 unit is

The sum of the first 5 terms of a geometric progression is the same as the sum of the first 7 terms of the same progression. If the sum of the first 9 terms is 24, then the $4^{th}$ term of the progression is

The remainder when $11^{1011}+1011^{11}$ is divided by 9 is

The set of all values of $x$ satisfying the inequality ${\log }_{(x+1/x)}[{\log }_2(\frac{x-1}{x+2})]>0$ is

Let $f(x)=a^2{x}^2+2bx+c$ where $a\ne 0$, $b,c$ are real numbers and $x$ is a real variable. Then

A natural number $n$ lies between 100 and 400, and the sum of its digits is 10. The probability that $n$ is divisible by 4 is _________________

In triangle $ABC$, $AB=AC=x$, $\angle ABC=\theta$ and the circumradius is equal to $y$. Then $x/y$ equals

Let $A$ and $B$ be two finite sets such that $n(A-B),n(A\cap B),n(B-A)$ are in an arithmetic progression. Here $n(X)$ denotes the number of elements in a finite set $X$. If $n(A\cup B)=18$, then $n(A)+n(B)$ is

Suppose $a,b$ and $c$ are three real numbers such that $\max (a,b,c)+\min (a,b,c)=15$, and $\text{Median}(a,b,c)-\text{Mean}(a,b,c)=2$. Then the median of $a,b$ and $c$ is

A and B take part in a rifle shooting match. The probability of A hitting the target is 0.4, while the probability of B hitting the target is 0.6. If A has the first shot, post which both strike alternately, then the probability that A hits the target before B hits it is

The table below provides monthly sales (in lakhs of rupees) and the value of products returned by customers (as a percentage of sales) for three product categories for the year 2024. Net sales = Sales − Value of products returned.

By what percentage the net sales for June increased as compared to May in the Footwear category?

The table below provides monthly sales (in lakhs of rupees) and the value of products returned by customers (as a percentage of sales) for three product categories for the year 2024. Net sales = Sales − Value of products returned.

Among the following four months, for which month the value of the Footwear returned (in lakhs of rupees) was the highest?

The table below provides monthly sales (in lakhs of rupees) and the value of products returned by customers (as a percentage of sales) for three product categories for the year 2024. Net sales = Sales − Value of products returned.

Which month had highest percentage decline in monthly sales as compared to previous month for the Apparel category?

The table below provides monthly sales (in lakhs of rupees) and the value of products returned by customers (as a percentage of sales) for three product categories for the year 2024. Net sales = Sales − Value of products returned.

For which categories the value of the products returned (as a percentage of sales) increased for three consecutive months?

The table below provides monthly sales (in lakhs of rupees) and the value of products returned by customers (as a percentage of sales) for three product categories for the year 2024. Net sales = Sales − Value of products returned.

Among the following four months, for which month the contribution of the Apparel category in the total monthly sales was the highest?

The writer implies that

The writer argues that social media

Technologies are enabling social media to

Social media has succeeded in

The writer's conclusion is that information available on social media is linked to

The inherent downside associated with social media is that it

What is Baudrillard's position on consumption?

Which of the following is an argument made by Baudrillard?

How does Baudrillard engage with the cargo myth?

What is Baudrillard's position on total happiness?

How can consumption be made more satisfying?

Why are consumers unhappy with commodities that they have just bought?

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

The labourers who were fired broke into the office building and destroyed some of the machinery. Rather than finding a solution to their problems, they ____________.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

We hope that the government's new policies will ____________ a period of economic growth.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

Everyone wondered how the travel vlogger could go around the world all through the year and ____________.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

Deepak is an unpleasant person, but we all ____________ because his sister is a close friend of ours.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

Without a doubt, the widespread use of renewable energy is a key solution to climate change. However, it is not a ____________, as efforts in conservation are equally crucial.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

When she inherited some jewellery from a distant relative, she had no idea of its worth and decided ____________.

Direction: Complete the following sentence by choosing the most appropriate word/phrase from the options given below.

There are so many instances of one or more deer crossing the road, or just standing in the middle of the road, or else ____________; it is like the deer cannot hear the noise of the engines or see the headlights.

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

If the President knew that his allies would let him down so suddenly, he would have handled them with the greatest care.

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

Among scientists, the discovery of the double helix structure of DNA and the genetic code it incorporates is widely regarded to be one of the most significant scientific discovery of the twentieth century.

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

Thank goodness, the damage to the car was neglectful.

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

When I had to leave town due to office work, I had my brother to give food to my dog twice a day.

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

Although the new policy aims to increase efficiency, reducing costs, and enhancing employee satisfaction, some employees feel that the changes are too abrupt and poorly communicated.

Direction: The paragraph below has a sentence missing (indicated by a blank). Choose the sentence that is most logically appropriate to complete the paragraph.

A report published in Lancet Diabetes and Endocrinology has called for an overhaul of our understanding of obesity. An over-reliance on using Body Mass Index [BMI] as a metric has the peculiar effect of leading to both underdiagnosis and overdiagnosis of the condition. ____________________. BMI does not give accurate information about how fat is distributed in an individual's body. It frequently fails to capture the true state of health of an individual.

Direction: The paragraph below has a sentence missing (indicated by a blank). Choose the sentence that is most logically appropriate to complete the paragraph.

As globalization held sway over the world, communities, which used to live in relative isolation, sought access to the wider world, and in the process, they parted with their own language and adopted a new lingua franca. The loss of language, however, does not merely mean the loss of a mode of communication or the loss of a few thousand words. ___________________. So, when a language dies, a way of thinking dies with it.

Direction: The paragraph below has a sentence missing (indicated by a blank). Choose the sentence that is most logically appropriate to complete the paragraph.

An island in Japan boasts of numerous dairy farms that own nearly one million cows, and supplies 70% of the milk sold in the country. These dairy farms have now begun to use cow manure to produce hydrogen. The methane from cow manure mingles with steam in a high temperature environment to produce hydrogen, which is used to electrify the local zoo._________________.

Direction: The paragraph below has a sentence missing (indicated by a blank). Choose the sentence that is most logically appropriate to complete the paragraph.

On the first day of January 2025, the Indian Meteorological Department [IMD] announced that 2024 was the hottest year on record. A study by the Council on Energy, Environment and Water shows that nearly eight out of ten Indians live in districts that are at risk of either a flood, a cyclone, or a drought. Nearly twenty three States in India are heatwave-prone.__________________. In the summer of 2024, India recorded more than 44,000 cases of heatstroke and over 300 heat-related mortalities, as per the bulletin of the Ministry of Health and Family Welfare. Water reservoirs and the energy demand that keeps India powered are impacted too.

Direction: Choose the best option to fill in the blanks.

The notion of personhood is ____________ on something more than a particular type of genetic material within human beings: it arises only with the larger-scale structural ____________ of that material, which permits capacities like ____________, thought and moral agency.

Direction: Choose the best option to fill in the blanks.

While Curcumin, which is an ________________ found in turmeric helps to reduce ____________, extremely high doses of it can ____________ headache and nausea.

Direction: Choose the best option to fill in the blanks.

Art can be ____________ because it encourages individuals to express their emotions through a creative outlet, allowing them to process complex feelings, reduce stress, and ____________ self-awareness.

Direction: Choose the best option to fill in the blanks.

Psychologists urge users to remember that social media rarely reflects the full complexity of real life. Influencers often ____________ a carefully curated online persona, which can ____________ unrealistic standards and occasionally ____________ negative self-comparisons amongst their followers.

Direction: Choose the best option to fill in the blanks.

Since chronic stress can ____________ the immune system, making individuals more susceptible to illness and ____________ their overall well-being, healthcare practitioners often recommend mindfulness practices and proper sleep to ____________ these negative effects.

Direction: Choose the best option to fill in the blanks.

Astronauts who stayed for an ____________ period of time at the International Space Station displayed a remarkable level of ____________ endurance and mental ____________.

Which of the following best and correctly summarizes the main idea of the conversation?

In the context of the conversation, the term "arenas of competition" refers to

"Wizard" industries are characterized by

In the context of the conversation, "dynamism" most closely refers to

"Muggles" refers to industries that

Which one of the following does "shuffle rate" not measure?

Direction: The sentences given below, when properly sequenced, form a coherent paragraph. Decide on the most logical order and enter the sequence of numbers (no spaces, no punctuation; e.g. "53412").

1. Among its major urban centres, Harappa and Mohenjo-Daro stand out as prime examples of this architectural prowess, revealing large public structures, residential areas, and sophisticated water management systems indicative of a complex societal structure.

2. Showing remarkable sophistication for its time, this ancient culture developed meticulously planned cities, complete with advanced sanitation systems and intricate grid layouts that underscore their profound understanding of urban design and engineering.

3. Economically, the civilization thrived on a foundation of extensive trade networks, connecting them with distant lands, alongside a robust agricultural system that sustained their large populations and facilitated surplus production.

4. Despite its impressive achievements and longevity, the reasons behind the eventual decline of this remarkable civilization remain largely enigmatic, prompting ongoing research and speculation among historians and archaeologists.

5. The Indus Valley Civilization, flourishing in the Bronze Age, represents one of humanity's earliest urban societies, evidenced by archaeological discoveries dating back thousands of years.

Direction: The sentences given below, when properly sequenced, form a coherent paragraph. Decide on the most logical order and enter the sequence of numbers (no spaces, no punctuation; e.g. "53412").

1. When we take time to notice these moments, we discover hidden beauty that sparks our creative thoughts because creativity isn't just about rare, amazing events—it's also about finding the special in the ordinary.

2. Creativity is often seen as the ability to look at the world in a new way—to turn everyday sights, sounds, and experiences into art or ideas.

3. In fact, inspiration can come from small details of daily life: the gentle warmth of morning sunlight on a kitchen counter, the steady sound of traffic outside, or the brief smile of a stranger on a busy street.

4. Many people wrongly think that true creativity only comes from big ideas or exciting adventures.

Direction: The sentences given below, when properly sequenced, form a coherent paragraph. Decide on the most logical order and enter the sequence of numbers (no spaces, no punctuation; e.g. "53412").

1. Seven of the ten worst affected countries (including India) are low- and middle income countries.

2. Between 1993 and 2022, India was the sixth worst-affected country in terms of fatalities and damage sustained from extreme weather events wrought by the climate crisis.

3. High income nations, whose economies are founded in industrial era use of fossil fuels, meanwhile, insist that growing economies, especially India and China, shoulder greater responsibility.

4. This reinforces the developing world's contention that it has had to bear a disproportionate burden of climate afflictions despite having contributed little to the crisis.

Direction: The sentences given below, when properly sequenced, form a coherent paragraph. Decide on the most logical order and enter the sequence of numbers (no spaces, no punctuation; e.g. "53412").

1. Using the wonders of Artificial Intelligence (AI), they quickly improved upon those skills to become far more dexterous.

2. Inside a robotics laboratory of the Toyota Research Institute, a group of robots is busy cooking. There is nothing special about that; robotic chefs have been around for a while.

3. Despite their extraordinary culinary capabilities, these robots are not destined for a career in catering.

4. But these robots are more proficient than most: flipping pancakes, slicing vegetables, and making pizzas with ease.

5. The difference is that instead of being laboriously programmed to carry out their tasks, the Toyota robots have been taught only a basic set of skills.

Direction: The sentences given below, when properly sequenced, form a coherent paragraph. Decide on the most logical order and enter the sequence of numbers (no spaces, no punctuation; e.g. "53412").

1. In drought conditions, water often depletes in the topsoil and remains accessible only in the deeper subsoil layers.

2. A new study gives new insights into how the acid changes root growth angles to enable plants to reach out deeper subsoils in search of water.

3. Plants rely on their root systems, the primary organs for interacting with soil, to actively seek water.

4. Abscisic acid plays an important role in helping plants adapt to these challenging conditions.