2 IPMAT Indore 2025
2.1 Quantitative Ability (SA)
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, 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 speciality. The total number of biologists, geologists, and explorers is equal. The following additional information is available:
- Every team has at least 2 members from each skill set.
- Teams 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?
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?
Eight teams participate 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 organisers decided to proceed, nonetheless, with the remaining matches. The total number of matches that were played in the tournament that year is?
If the sum of the first 21 terms of the sequence: \(\ln \frac{a}{b}\), \(\ln \frac{a}{b\sqrt{b}}\), \(\ln \frac{a}{b^{2}}\), … is \(\ln \frac{a^{m}}{b^{n}}\) then the value of \(m+n\) is?
The English and Math exams were conducted separately for a class of 120 students. The number of students who did not appear for the English exam is twice that of those who did not appear for the Math exam. The number of students who passed the Math exam is twice that of those 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?
If \(A=\begin{bmatrix}2 & n \\ 4 & 1\end{bmatrix}\) such that \(A^{3}= 27 \begin{bmatrix}4 & q \\ p & r\end{bmatrix}\), then \(p+q+r\) equals?
Five teams - A, B, C, D, and E - each consisting of 15 members, are going on expeditions to five different locations. The following additional information is available:
- Every team has at least 2 members from each skill set.
- Teams 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 \(\log_{3}(x^{2}-1), \log_{3}(2x^{2}+1)\) 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?
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?
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?
Five teams - A, B, C, D, and E - each consisting of 15 members, are going on expeditions to five different locations. The following additional information is available:
- Every team has at least 2 members from each skill set.
- Teams 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 5 teams is?
If m and n are two positive integers such that \(7m+11n=200\) then the minimum possible value of \(m + n\) is?
The number of factors of \(3^{5}\times5^{8}\times7^{2}\) that are perfect squares is?
If the polynomial \(ax^{2}+bx+5\) leaves a remainder 3 when divided by \(x-1\) and a remainder 2 when divided by \(x+1\), then \(2b-4a\) equals?
2.2 Quantitative Ability (MCQ)
Given that \(1+\frac{1}{2^{2}}+\frac{1}{3^{2}}+\frac{1}{4^{2}}+......=\frac{\pi^{2}}{6}\), the value of \(1+\frac{1}{3^{2}}+\frac{1}{5^{2}}+\frac{1}{7^{2}}+.........\) is?
If \(y=a+b \log_{e}x\), which of the following is true?
If \(a_{1},a_{2},........,a_{8}\) are the roots of the equation \(x^{8}+x^{7}+.....+x+1=0\), then the value of \(a_{1}^{2025}+a_{2}^{2025}+....+a_{8}^{2025}\) is?
Suppose a, b and c are three real numbers such that \(Max(a,b,c)+Min(a,b,c)=15\), and \(Median(a, b, c) - Mean(a,b,c)=2\). Then the median of a, b and c is?
If \(\log_{25}[5 \log_{3}(1+\log_{3}(1+2 \log_{2}x))]=\frac{1}{2}\), then x is:
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 \(\frac{x}{y}\) 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 \(A(1,3)\) and \(B(5,1)\) be two points. If a line with slope \(m\) intersects AB at an angle of \(45^{\circ}\), then the possible values of m are?
Let \(P(x)\) be a quadratic polynomial such that \(\begin{vmatrix}P(0)&P(1)\\ P(0)&P(2)\end{vmatrix}=0\). Let \(P(0)=2\) and \(P(1)+P(2)+P(3)=14\). Then \(P(4)\) equals?
A circle touches the y-axis at (0, 4) and passes through the point (-2, 0). Then the radius of the circle 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?
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 three schemes during the first year is 10600 rupees, then the total interest earned, in rupees, from all three schemes for the second year is?
Let \(f(x)=a^{2}x^{2}+2bx+c\) where, \(a\ne0,b,\) c are real numbers and x is a real variable then?
The area of the triangle, formed by the straight lines \(y = 0\), \(12x-5y = 0\), and \(3x+4y=7\) is?
Area of a regular octagon inscribed in a circle of radius 1 unit 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?
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 4th term of the progression is?
The set of all values of x satisfying the inequality \(\log_{(x+\frac{1}{x})}[\log_{2}(\frac{x-1}{x+2})]>0\) is?
Let \(S_{1}=\{100,105,110,115,...\}\) and \(S_{2}=\{100,95,90,85,...\}\) 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?
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?
Which of the following numbers is divisible by \(3^{10}+2\)?
Let A and B be two finite sets such that \(n(A-B)\), \(n(A\cap B)\), and \(n(B-A)\) 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?
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?
The remainder when \(11^{1011}+1011^{11}\) is divided by 9 is?
Instructions [41-45]:
The table given below provides the details of monthly sales (in lakhs of rupees) and the value of products returned by the customers (as a percentage of sales) of an e-commerce company for three product categories for the year 2024. Net sales (in lakhs of rupees) is de«ned as the difference between sales (in lakhs of rupees) and the value of products returned (in lakhs of rupees).
| Month | Sales (in lakhs of rupees) | Value of products returned (as a percentage of Sales) | ||||
|---|---|---|---|---|---|---|
| Apparel | Footwear | Electronics | Apparel | Footwear | Electronics | |
| January | 262 | 104 | 289 | 13% | 7% | 2% |
| February | 279 | 113 | 387 | 16% | 9% | 3% |
| March | 236 | 121 | 283 | 20% | 7% | 2% |
| April | 258 | 58 | 325 | 16% | 8% | 1% |
| May | 249 | 69 | 359 | 12% | 6% | 4% |
| June | 230 | 111 | 321 | 19% | 5% | 3% |
| July | 244 | 119 | 341 | 17% | 9% | 4% |
| August | 252 | 60 | 336 | 16% | 6% | 2% |
| September | 288 | 118 | 355 | 10% | 9% | 5% |
| October | 222 | 108 | 383 | 15% | 8% | 2% |
| November | 228 | 93 | 282 | 14% | 9% | 4% |
| December | 221 | 86 | 268 | 18% | 10% | 1% |
Which month had the highest percentage decline in monthly sales as compared to the previous month for the Apparel category?
For which categories did the value of the products returned (as a percentage of sales) increase for three consecutive months?
By what percentage did the net sales for June increase as compared to May in the Footwear category?
Among the following four months, for which month was the contribution of the Apparel category in the total monthly sales the highest?
Among the following four months, for which month was the value of the Footwear returned (in lakhs of rupees) the highest?
2.3 Verbal Ability
Instructions [46-51]:
Read the following passage and answer the questions.
Meta is recalibrating content on its social media platforms as the political tide has turned in Washington, with Mark Zuckerberg announcing last week that his company plans to fire its US fact-checkers. Fact-checking evolved in response to allegations of misinformation and is being watered down in response to accusations of censorship. Social media does not have solutions to either. Community review-introduced by Elon Musk at X and planned by Zuckerberg for Facebook and Instagram - is not a significant improvement over fact-checking. Having Washington lean on foreign governments over content moderation does not benefit free speech. Yet, that is the nature of the social media beast, designed to amplify bias.
Information and misinformation continue to jostle on social media at the mercy of user discretion. Social media now has enough control over all other forms of media to broaden its reach. It is the connective tissue for mass consumption of entertainment, and alternative platforms are reworking their engagement with social media. Technologies are shaping up to drive this advantage further through synthetic content targeted precisely at its intended audience. Meta’s algorithm will now play up politics because it is the flavour of the season.
The Achilles’ Heel of social media is informed choice which could turn against misinformation. Its move away from content moderation is driven by the need to be more inclusive, yet unfiltered content can push users away from social media towards legacy forms that have better moderation systems in place. Lawmakers across the world are unlikely to give social media a free run, even if Donald Trump is working on their case. Protections have already been put in place across jurisdictions over misinformation. These may be difficult to dismantle, even if the Republicans pull US-owned social media companies further to the right.
Media consumption is, in essence, evidence-based judgement that mediums must adapt to. Content moderation, not free speech, is the adaptation mechanism. Musk and Zuckerberg are not exempt.
The writer implies that…
The writer argues that social media…
The writer’s conclusion is that the information available on social media is linked to…
Social media has succeeded in…
Technologies are enabling social media to…
The inherent downside associated with social media is that it…
Instructions [52-57]:
Read the following passage and answer the questions.
According to the French philosopher Jean Baudrillard, commodities available for consumption are not inherently negative things. Baudrillard tried to interpret consumption in modern societies by engaging with the ‘cargo myth’ prevalent among the indigenous Melanesian people living in the South Pacific. The Melanesians did not know what aeroplanes were. However, they saw that these winged entities descended from the air for white people and appeared to make them happy. They also noted that aeroplanes never descended for the Melanesian people.
The Melanesian natives noted that the white people had placed objects similar to the aeroplane on the ground. They concluded that these objects were attracting the aeroplanes in the air and bringing them to the ground. Through a magical process, the aeroplanes were bringing plenty to the white people and making them happy. The Melanesian people concluded that they would need to place objects that simulated the aeroplane on the ground and attract them from the air. Baudrillard believes that the cargo myth holds an important analogy for the ways in which consumers engage with objects of consumption.
According to Baudrillard, the modern consumer “sets in place a whole array of sham objects, of characteristic signs of happiness, and then waits for happiness to alight”. For instance, modern consumers believe that they will get happiness if they buy the latest available version of a mobile phone or automobile. However, consumption does not usually lead to happiness. While consumers should ideally be blaming their heightened expectations for their lack of happiness, they blame the commodity instead.
They feel that they should have waited for the next version of a mobile phone or automobile before buying the one they did. The version they bought is somehow inferior and therefore cannot make them happy. Baudrillard argues that consumers have replaced ‘real’ happiness with ‘signs’ of happiness. This results in the endless deferment of the arrival of total happiness.
In Baudrillard’s words, “in everyday practice, the blessings of consumption are not experienced as resulting from work or from a production process; they are experienced as a miracle”. Modern consumers view consumption in the same magical way as the Melanesian people viewed the aeroplanes in the cargo myth. Television commercials also present objects of consumption as miracles. As a result, commodities appear to be distanced from the social processes which lead to their production. In effect, objects of consumption are divorced from the reality which produces them.
How can consumption be made more satisfying?
Which of the following is an argument made by Baudrillard?
How does Baudrillard engage with the cargo myth?
Why are consumers unhappy with commodities that they have just bought?
What is Baudrillard’s position on total happiness?
What is Baudrillard’s position on consumption?
Deepak is an unpleasant person, but we all ______.
We hope that the government’s new policies will ______ a period of economic growth.
When she inherited some jewellery from a distant relative, she had no idea of its worth and decided ______.
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.
Everyone wondered how the travel vlogger could go around the world all through the year and ______.
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.
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 ______.
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.
Thank goodness, the damage to the car was neglectful.
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.
so suddenly, he would have handled them with the greatest care.
When I had to leave town due to office work, I had my brother to give food to my dog twice a day.
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. A person’s BMI may indicate they are “obese”, but their organs and bodily functions may be absolutely normal. Every individual is a unique constellation — not only of genes and other biological variables, but also socio-economic conditions and habits.
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.
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.
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. During a ten-day-long heatwave in Delhi, peak power demand was 16% than the previous year.
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.
Astronauts who stayed for an ______ period of time at the International Space Station displayed a remarkable level of ______ endurance and mental ______.
While Curcumin, which is an ______ found in turmeric helps to reduce ______, extremely high doses of it can ______ headache and nausea.
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.
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.
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.
Instructions [80-85]:
CONVERSATION ANALYSIS: Read the following transcript and choose the answer that is closest to each of the questions that are based on the transcript.
Lucia Rahilly (Global Editorial Director, The McKinsey Podcast): Today we’re talking about the next big arenas of competition, about the industries that will matter most in the global business landscape, which you describe as arenas of competition. What do we mean when we use this term?
Chris Bradley (Director, McKinsey Global Institute): If I go back and look at the top ten companies in 2005, they were in traditional industries such as oil and gas, retail, industrials, and pharmaceuticals. The average company was worth about 250 billion. If I advance the clock forward to 2020, nine in ten of those companies have been replaced, and by companies that are eight times bigger than the old guards. And this new batch of companies comes from these new arenas or competitive sectors. In fact, they’re so different that we have a nickname for them. If you’re a fan of Harry Potter, it’s wizards versus muggles. Arena industries are wizard-ish; we found that there’s a set of industries that play by very different set of economic rules and get very different results, while the rest, the muggles (even though they run the world, finance the world, and energize the world), play by a more traditional set of economic rules.
Lucia Rahilly: Could we put a finer point on what is novel or different about the lens that you applied to determine what’s a wizard and what’s a muggle?
Chris Bradley: Wizards are defined by growth and dynamism. We looked at where value is flowing and the places where value is moving. And where is the value flowing? What we see is that this set of wizards, which represent about ten percent of industries, hog 45 percent of the growth in market cap. But there’s another dimension or axis too, which is dynamism. That is measured by a new metric we’ve come up with called the “shuffle rate.” How much does the bottom move to the top? It turns out that in this set of wizard-ish industries, or arenas, the shuffle rate is much higher than it is in the traditional industry.
Lucia Rahilly: So, where are we seeing the most profit?
Chris Bradley: The economic profit, which is the profit you make minus the cost for the capital you employ is in the wizard industries. It’s where R&D happens; they’re two times more R&D intensive. They’re big stars, the nebulae, where new business is born.
In the context of the conversation, “dynamism” most closely refers to…
In the context of the conversation, the term “arenas of competition” refers to…
“Muggles” refers to industries that…
Which one of the following does “shuffle rate” not measure?
“Wizard” industries are characterized by…
Which of the following best and correctly summarises the main idea of the conversation?
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.
- 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.
- Showing remarkable sophistication for its time, this ancient culture developed meticulously planned cities, complete with advanced sanitation systems and intricate grid layouts that underscore its profound understanding of urban design and engineering.
- Economically, the civilisation thrived on a foundation of extensive trade networks, connecting them with distant lands, alongside a robust agricultural system that sustained its large populations and facilitated surplus production.
- Despite its impressive achievements and longevity, the reasons behind the eventual decline of this remarkable civilisation remain largely enigmatic, prompting ongoing research and speculation among historians and archaeologists.
- The Indus Valley Civilisation, flourishing in the Bronze Age, represents one of humanity’s earliest urban societies, evidenced by archaeological discoveries dating back thousands of years.
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.
- Using the wonders of Artificial Intelligence (Al), they quickly improved upon those skills to become far more dexterous.
- 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.
- Despite their extraordinary culinary capabilities, these robots are not destined for a career in catering.
- But these robots are more proficient than most: flipping pancakes, slicing vegetables, and making pizzas with ease.
- 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.
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.
- Seven of the ten worst-affected countries (including India) are low- and middle-income countries.
- 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.
- High-income nations, whose economies are founded in the industrial era use of fossil fuels, meanwhile, insist that growing economies, especially India and China, shoulder greater responsibility.
- 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.
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.
- 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.
- 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.
- 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.
- Many people wrongly think that true creativity only comes from big ideas or exciting adventures.
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.
- In drought conditions, water often depletes in the topsoil and remains accessible only in the deeper subsoil layers.
- 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.
- Plants rely on their root systems, the primary organs for interacting with soil, to actively seek water.
- Abscisic acid plays an important role in helping plants adapt to these challenging conditions.