IPMAT Indore 2025 question paper

1. A.
   $\frac{\pi^2}{6} - 1$
2. B.
   $\frac{\pi}{6}$
3. C.
   $\frac{\pi^2}{12}$
4. D.
   $\frac{\pi^2}{8}$

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1. A.
   $\frac{1}{y-a}$ is proportional to $x^{b}$
2. B.
   $y-a$ is proportional to $x^{b}$
3. C.
   $e^{y}$ is proportional to $x^{b}$
4. D.
   $\log _{e} y$ is proportional to $x$

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1. A.
   0
2. B.
   2
3. C.
   8
4. D.
   4

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1. A.
   11
2. B.
   10.5
3. C.
   10
4. D.
   9.5

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1. A.
   4
2. B.
   16
3. C.
   2
4. D.
   8

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1. A.
   $\frac{1}{4}$
2. B.
   $\frac{7}{27}$
3. C.
   $\frac{1}{3}$
4. D.
   $\frac{2}{9}$

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1. A.
   $\sin \theta$
2. B.
   $\cos \theta$
3. C.
   $2 \cos \theta$
4. D.
   $2 \sin \theta$

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1. A.
   $(p + \frac{1}{p})$
2. B.
   $2(p + \frac{1}{p})$
3. C.
   $2(\sqrt{p} + \frac{1}{\sqrt{p}})^2$
4. D.
   $(\sqrt{p} + \frac{1}{\sqrt{p}})^2$

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1. A.
   $7, \frac{1}{7}$
2. B.
   $3, \frac{1}{3}$
3. C.
   $-3, \frac{1}{3}$
4. D.
   $5, -\frac{1}{5}$

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1. A.
   -14
2. B.
   30
3. C.
   -6
4. D.
   16

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1. A.
   4
2. B.
   5
3. C.
   6
4. D.
   7

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1. A.
   $22 + 2\pi$
2. B.
   $19 + 2\pi$
3. C.
   $22$
4. D.
   $22 - 2\pi$

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1. A.
   $10308$
2. B.
   $11748$
3. C.
   $22348$
4. D.
   $19708$

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1. A.
   $f(x)$ has a maximum and a minimum
2. B.
   $f(x)$ has a minimum and no maximum
3. C.
   $f(x)$ has a maximum and no minimum
4. D.
   $f(x)$ has no minimum and no maximum

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1. A.
   $\frac{35}{27}$
2. B.
   $\frac{14}{9}$
3. C.
   $\frac{28}{9}$
4. D.
   $\frac{35}{54}$

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1. A.
   $2\sqrt{2}$
2. B.
   $2 + \sqrt{2}$
3. C.
   $\dfrac{9}{2\sqrt{2}}$
4. D.
   $\sqrt{10}$

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1. A.
   8
2. B.
   6
3. C.
   7
4. D.
   5

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1. A.
   -48
2. B.
   -24
3. C.
   24
4. D.
   48

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1. A.
   $(2,5)$
2. B.
   $(-5,-2)$
3. C.
   $(5,\infty)$
4. D.
   Null set

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1. A.
   137275
2. B.
   138250
3. C.
   137225
4. D.
   135375

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1. A.
   $\frac{1}{2}$
2. B.
   $\frac{10}{19}$
3. C.
   $\frac{2}{3}$
4. D.
   $\frac{9}{19}$

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1. A.
   $3^{20} + 4$
2. B.
   $3^{30} + 2$
3. C.
   $3^{20} + 8$
4. D.
   $3^{30} + 8$

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1. A.
   24
2. B.
   27
3. C.
   30
4. D.
   36

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1. A.
   276
2. B.
   180
3. C.
   120
4. D.
   240

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1. A.
   0
2. B.
   8
3. C.
   9
4. D.
   7

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1. A.
   June
2. B.
   March
3. C.
   December
4. D.
   October

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1. A.
   Only Electronics
2. B.
   Only Apparel
3. C.
   Both Apparel and Footwear
4. D.
   Only Footwear

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1. A.
   62.58 percent
2. B.
   7.21 percent
3. C.
   18.97 percent
4. D.
   60.87 percent

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1. A.
   January
2. B.
   April
3. C.
   December
4. D.
   August

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1. A.
   September
2. B.
   July
3. C.
   June
4. D.
   March

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1. A.
   20
2. B.
   24
3. C.
   Both (A) and (B)
4. D.
   None of the following

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1. A.
   uncensored content will always have more appeal than controlled content.
2. B.
   social media's innate strength is the user's inability to fact check.
3. C.
   social media can never be discarded by its users.
4. D.
   older forms of media will regain users because of its controls.

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1. A.
   remains unaffected by global debates amongst lawmakers on misinformation.
2. B.
   has become the preferred way to access entertainment.
3. C.
   flourishes because it can publish any material.
4. D.
   is in a difficult position because it cannot adapt to new policies.

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1. A.
   the need for deregulation.
2. B.
   the individual's right to free speech.
3. C.
   the global legal systems' support of free speech.
4. D.
   the policies of the governments in power.

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1. A.
   ignoring technology and artificial content.
2. B.
   finding alternative means for fact-checking.
3. C.
   becoming independent of other media.
4. D.
   controlling other media that depend on it.

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1. A.
   enlarge its sphere of influence and persuasion.
2. B.
   understand that algorithms cannot control its content.
3. C.
   accept the current trends as emphasised by algorithms.
4. D.
   readjust its interaction with competitors.

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1. A.
   does not address the problem of the digital divide.
2. B.
   results in unremitting expansion of freedom of expression.
3. C.
   creates and spreads much innate and acquired prejudice.
4. D.
   reinforces existing objectivity among the users.

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1. A.
   By banning television commercials that promise real happiness.
2. B.
   By understanding the connection between production and consumption.
3. C.
   By recognising that commodities produce miraculous change.
4. D.
   By rejecting colonialism and all other forms of economic oppression.

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1. A.
   Consumers value signs more than the real.
2. B.
   Television commercials are at the heart of unhappiness experienced by consumers.
3. C.
   Production and consumption are magical processes.
4. D.
   Melanesian people coped with the inequality of colonialism by creating myths.

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1. A.
   He uses it to show that consumption is a blessing.
2. B.
   He uses it as a metaphor to critique modern consumption.
3. C.
   He uses it to describe the suffering of Indigenous people.
4. D.
   He uses it to show that consumers should consume more serious objects.

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1. A.
   Because they have exaggerated expectations of commodities.
2. B.
   Because television commercials do not create enough hype about commodities.
3. C.
   Because the Law of Diminishing Marginal Commodities comes into play.
4. D.
   Because they focus on improved functionality of commodities.

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1. A.
   It is perpetually delayed.
2. B.
   It comes with patience and waiting.
3. C.
   It prioritises production over consumption.
4. D.
   It results from ethical consumption.

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1. A.
   It is a utilitarian process.
2. B.
   It is a positive process.
3. C.
   It is an egalitarian process.
4. D.
   It is an irrational process.

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1. A.
   put him down
2. B.
   put him aside
3. C.
   put up with him
4. D.
   put along with him

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1. A.
   usher in
2. B.
   set in
3. C.
   turn up
4. D.
   set forth

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1. A.
   to get an approval
2. B.
   to get it appreciated
3. C.
   to have it appraised
4. D.
   to have it apprised

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1. A.
   jumping under the road
2. B.
   foraging beneath the road
3. C.
   staggering with the road
4. D.
   bounding across the road

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1. A.
   manage his itinerant life style
2. B.
   manage his itinerary life style
3. C.
   manage his iterative life style
4. D.
   manage his itinerary in his life style

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1. A.
   dead ringer
2. B.
   silver lining
3. C.
   red herring
4. D.
   silver bullet

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1. A.
   exacerbated the situation
2. B.
   extended their troubles
3. C.
   exaggerated their hardships
4. D.
   extenuated the circumstance

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1. A.
   regarded for being one of the most significant scientific discoveries
2. B.
   regarded as one of the most significant scientific discoveries
3. C.
   regarded like one of the most significant scientific discovery
4. D.
   regarded being one of the most significant scientific discoveries

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1. A.
   was negligible
2. B.
   was neglecting
3. C.
   was neglectable
4. D.
   was negligent

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1. A.
   increase efficiency, reducing the costs and enhanced employee satisfaction
2. B.
   increasing efficiency, reducing of costs, and enhancing of employee satisfaction
3. C.
   increase the efficiency, reduce the costs and enhancing employee satisfaction
4. D.
   increase efficiency, reduce costs, and enhance employee satisfaction

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1. A.
   Had the President knowledge that his allies would let him down
2. B.
   Had the President known that his allies would let him down
3. C.
   If the President could know beforehand that his allies would let him down
4. D.
   If the President knew that his allies can let him down

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1. A.
   had my brother feed my dog
2. B.
   had my brother giving food to my dog
3. C.
   had my brother who fed my dog
4. D.
   had my brother to feed my dog

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1. A.
   Obesity is the end result of multiple factors and BMI can pinpoint the cause of the problem
2. B.
   Further, much of the information on diabetes, obesity or BMI available on social media is misleading
3. C.
   BMI reading can help the doctor to accurately prescribe the appropriate dosage to reduce fat
4. D.
   This is because BMI does not provide a reliable picture of health, nor any direct measure of fat

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1. A.
   The Indian government too, should replicate this, and use such technology to produce hydrogen
2. B.
   It is a case study of a certain animal that is useful in providing energy for several other animals
3. C.
   This is an exemplary way of creating a sustainable source of energy using innovative technology
4. D.
   This shows how Japan has always used technology to help animals

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1. A.
   A certain school of thought regrets the demise of local languages but in recent times revival movements have emerged across the world, especially in India
2. B.
   A potentially endangered language can sometimes appear to be thriving, or on the other hand, it can show signs of declining
3. C.
   Languages exist not only for the purposes of practical communication; they convey a linguistic community's entire mindset and its culture
4. D.
   Since evolution and change in languages is a part of history, most of the languages spoken today would be scarcely recognizable from what they were a few thousand or maybe even a few hundred years ago

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1. A.
   According to the Council, more than 20% of the population is not affected by climate change
2. B.
   The record-breaking heat of the summer of 2024 resulted in an unpredictable and delayed monsoon
3. C.
   However, the people of these districts are given sufficient compensation for loss of life and property
4. D.
   The increasing heat stress remains a major challenge, affecting public health and economic productivity

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1. A.
   pleasing; decrease
2. B.
   acceptable; disturb
3. C.
   avoidable; mitigate
4. D.
   therapeutic; enhance

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1. A.
   extensive; dysfunctional; agility
2. B.
   explicit; stoic; integrity
3. C.
   expanded; stern; acuity
4. D.
   extended; physical; resilience

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1. A.
   enzyme; abrasion; infuse
2. B.
   alkali; infection; promote
3. C.
   alchemy; injury; cause
4. D.
   ingredient; inflammation; induce

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1. A.
   dependent; disorganisation; deconstruction
2. B.
   interdependent; division; differentiation
3. C.
   built; distribution; calibration
4. D.
   premised; organisation; consciousness

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1. A.
   undermine; elevate; impede
2. B.
   compromise; impair; counter
3. C.
   paralyse; improve; diminish
4. D.
   endanger; preserve; decrease

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1. A.
   endorse; foster; provoke
2. B.
   maintain; generate; trigger
3. C.
   advocate; perpetuate; stimulate
4. D.
   profess; inspire; release

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1. A.
   the slow, gradual growth and morphing of established companies.
2. B.
   the rapid and frequent changes in leadership and market position within an industry.
3. C.
   the never-changing reliance on established and unchanging business practices.
4. D.
   the stability and predictability of traditional industries.

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1. A.
   specific companies that are considered to be powerful competitors.
2. B.
   government regulations that control business competition.
3. C.
   physical locations where businesses compete.
4. D.
   broad categories of industries where companies engage in competitive activities.

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1. A.
   are characterized by rapid and frequent changes.
2. B.
   exhibit high levels of market capitalization growth.
3. C.
   operate under traditional economic principles.
4. D.
   are primarily focused on technological innovation.

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1. A.
   Volatility of market leadership.
2. B.
   Churn within the arena of competition.
3. C.
   Overall profitability of traditional industries.
4. D.
   Relative change within an industry.

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1. A.
   a slower rate of market capitalization growth.
2. B.
   a higher concentration of economic profit and research and development.
3. C.
   a reliance on traditional economic rules and practices.
4. D.
   lower research and development spending.

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1. A.
   The global economy is shifting back towards traditional industries, as they offer more stable returns.
2. B.
   Newer, dynamic industries, termed "wizards," are experiencing significantly greater growth and profit compared to traditional industries.
3. C.
   Traditional industries are consistently more profitable than newer, "wizard-ish" industries.
4. D.
   The terms "wizard" and "muggle" are used to describe the magical elements of business success.

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