IPMAT Indore 2026 question paper

1. A.
   $13\frac{2}{3}$
2. B.
   $13\frac{1}{2}$
3. C.
   $13\frac{3}{4}$
4. D.
   $7\frac{6}{7}$

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1. A.
   711
2. B.
   800
3. C.
   765
4. D.
   781

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1. A.
   10
2. B.
   21
3. C.
   20
4. D.
   19

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1. A.
   $\frac{221}{5}$
2. B.
   $\frac{441}{10}$
3. C.
   $\frac{220}{5}$
4. D.
   $\frac{216}{5}$

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1. A.
   exactly one real solution
2. B.
   exactly two real solutions
3. C.
   no real solution
4. D.
   exactly three real solutions

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

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

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

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1. A.
   12
2. B.
   13
3. C.
   36
4. D.
   37

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1. A.
   26
2. B.
   13
3. C.
   169
4. D.
   91

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1. A.
   $\frac{1}{54}$
2. B.
   $\frac{1}{108}$
3. C.
   $\frac{1}{27}$
4. D.
   $\frac{7}{216}$

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

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1. A.
   only 1
2. B.
   5 and 13
3. C.
   only 13
4. D.
   only 5

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1. A.
   3000
2. B.
   2000
3. C.
   5000
4. D.
   4000

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1. A.
   7
2. B.
   35
3. C.
   21
4. D.
   49

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1. A.
   45 percent
2. B.
   25 percent
3. C.
   35 percent
4. D.
   55 percent

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1. A.
   2
2. B.
   3
3. C.
   $2 - \log_3 2$
4. D.
   1

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

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1. A.
   1
2. B.
   $2\sqrt{2}$
3. C.
   2
4. D.
   $\sqrt{2}$

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1. A.
   50
2. B.
   40
3. C.
   48
4. D.
   44

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1. A.
   $x^2 + y^2 = 16a^2$
2. B.
   $x^2 + y^2 = 4a^2$
3. C.
   $x^2 + y^2 = 32a^2$
4. D.
   $x^2 + y^2 = a^2$

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1. A.
   $\frac{3\pi}{4\sqrt{2}}$
2. B.
   $\frac{12}{\pi}$
3. C.
   $\frac{4\pi}{3\sqrt{2}}$
4. D.
   $\frac{3\pi}{2\sqrt{2}}$

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1. A.
   3 and 4
2. B.
   1 and 5
3. C.
   2 and 5
4. D.
   1, 2 and 5

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1. A.
   6
2. B.
   7
3. C.
   8
4. D.
   9

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1. A.
   28
2. B.
   46
3. C.
   33
4. D.
   25

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

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1. A.
   Only Almonds, and Spinach
2. B.
   Only Almonds, and Oats
3. C.
   Only Almonds, Spinach, and Oats
4. D.
   Only Almonds

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1. A.
   17
2. B.
   15
3. C.
   24
4. D.
   22

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1. A.
   Protein with 65% MDR
2. B.
   Calcium with 65% MDR
3. C.
   Calcium with 70% MDR
4. D.
   Protein with 70% MDR

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

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1. A.
   thought much about each other throughout the day.
2. B.
   communicated with each other about everything.
3. C.
   romped and foraged together in the yard.
4. D.
   played with each other and hunted together.

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1. A.
   is widely spoken in France.
2. B.
   humans cannot learn or understand.
3. C.
   is the common one for people with different native languages.
4. D.
   is used by all birds and animals to communicate within their species.

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1. A.
   via sounds inaudible to humans and gestures that one could not understand.
2. B.
   the direction each dog would take and what each would do.
3. C.
   with their heads in close contiguity for two or three minutes.
4. D.
   with an understanding beyond words and sounds.

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1. A.
   the brethren of the sparrow flocked to the defence against the alien.
2. B.
   the sparrows communicated with an ear-piercing harangue for which they are particularly noted.
3. C.
   the robins who were getting the better of the two parties also got help from several other birds.
4. D.
   more than a score of robins in the immediate vicinity chased away the sparrows.

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1. A.
   is as useful as a robin, bluebird or martin.
2. B.
   occupies whatever space it can find to bring up its young ones.
3. C.
   is a native species driven to fight for its rights.
4. D.
   seeks quarters in the rural districts which other birds do not infect.

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1. A.
   is an expression of fear of humans and predators.
2. B.
   makes the sportsman realise that he has lost his only chance of a shot.
3. C.
   is distinct enough for several species to interpret correctly.
4. D.
   could be that of a dog, crow, jay or magpie.

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1. A.
   consuming more news on social media.
2. B.
   algohacking content that is designed to produce anger.
3. C.
   turning one's attention more closely to hateful propaganda.
4. D.
   blocking sites that propagate inflammatory content.

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1. A.
   a battle of classes within society.
2. B.
   the existential foundations of a society.
3. C.
   a change into a new and better type of society.
4. D.
   the outward forms of social beliefs and behaviour.

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1. A.
   Misuse of anger can negatively impact general wellbeing.
2. B.
   Anger has been used by companies to gain monetary benefits.
3. C.
   Constant anger has a function in certain situations.
4. D.
   Anger has no useful purpose as it has no outcome.

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1. A.
   the seemingly weak can succeed in unequal fights.
2. B.
   resistance to large negative forces fails.
3. C.
   if powerful forces are defeated, they will revive.
4. D.
   actions that seem unnecessary can be successful.

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1. A.
   reading responsible accounts of pollution, terror or elections provides social media users food for thought.
2. B.
   social media content fuels public anger to bring about constructive social change.
3. C.
   tech platforms deliberately supply distorted content that incentivises hate.
4. D.
   users actively chase news content that conforms to their political biases.

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1. A.
   the response of users does not vary according to the media consumed.
2. B.
   the reaction of users cannot be controlled by media.
3. C.
   social media reports more widely and responsibly.
4. D.
   reading responsible media reports promotes thoughtfulness.

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1. A.
   and this report on the business was calumnious
2. B.
   and this report on the business was calamitous
3. C.
   and this report on the business was callous
4. D.
   and this report on the business was careless

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1. A.
   befuddle me
2. B.
   add to my complexities
3. C.
   perplex me further
4. D.
   make matters worse

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1. A.
   as she is very gracious
2. B.
   as she is very gregarious
3. C.
   as she is very egregious
4. D.
   as she is very garrulous

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1. A.
   let the cat out of the bag
2. B.
   sent the cat out of the house
3. C.
   played cat and mouse with her
4. D.
   set the cat among the pigeons

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1. A.
   large bushelful
2. B.
   incredulous bombshell
3. C.
   entire legacy
4. D.
   arm and a leg

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1. A.
   hirsute
2. B.
   obsequious
3. C.
   didactic
4. D.
   plausible

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1. A.
   got his cool
2. B.
   got reasonable
3. C.
   remained woke
4. D.
   kept his head

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1. A.
   to create a link and sent it
2. B.
   create a link and send it
3. C.
   created a link and sent it
4. D.
   creating a link and sending it

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1. A.
   should she be winning this match against
2. B.
   imagine if she win this match against
3. C.
   should she win this match against
4. D.
   imagine that she is winning this match against

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1. A.
   councilor
2. B.
   consoler
3. C.
   counsellor
4. D.
   controller

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1. A.
   along came the last batsman and superannuated
2. B.
   alone came the last batsman and surprised
3. C.
   along came the last batsman and surprised
4. D.
   alone came the last batsman and superannuated

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1. A.
   recanted
2. B.
   recused
3. C.
   refrained
4. D.
   recouped

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1. A.
   Governments should bear the additional electricity costs, as AI will provide greater security.
2. B.
   This way the additional electricity costs will not be passed on to other local consumers.
3. C.
   Not all tech companies will be able to afford the additional electricity costs.
4. D.
   This way the anger of the public will not be directed at the tech companies.

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1. A.
   For writers, the help provided by AI is essential for the formation of lucid thoughts.
2. B.
   Without human effort, however, difficult concepts cannot be easily communicated to the reader.
3. C.
   When that process is delegated to an outside agency, thinking itself becomes superficial.
4. D.
   Thinking is a process expressed best by smooth, frictionless prose assisted by AI.

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1. A.
   Since a large proportion of OTT viewers in India use smart phones to view videos, the content has to be discerning.
2. B.
   Yet, this past year, Indian producers have gravitated towards content that entertains a wider section of viewers.
3. C.
   Now that smart phones are commonplace, viewing videos is no longer part of the shared and family time.
4. D.
   Without a discerning viewership, Indian producers have had to use social media to promote and sell their stories.

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1. A.
   This creates a false sense of complacency about the drugs notwithstanding their side-effects.
2. B.
   Weight loss drugs have allowed celebrities to parade their thin age-defying bodies.
3. C.
   The once-a-week jab is seen as a convenience obviating the need for any other action.
4. D.
   Weight loss is a path to thinness, a healthier lifestyle and a more attractive image.

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1. A.
   enthuse; difficult; undisciplined
2. B.
   encourage; withdrawn; indifferent
3. C.
   inspire; belligerent; uninstructed
4. D.
   engage; deficient; diffident

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1. A.
   credulity; groundless; objective
2. B.
   hysteria; jingoistic; logical
3. C.
   credibility; faulty; possible
4. D.
   indifference; strong; obvious

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1. A.
   community; societies; exploits
2. B.
   conglomeration; armies; annihilates
3. C.
   collection; socialism; admits
4. D.
   congregation; objectivity; rejects

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1. A.
   philosophy; consequential; unsuspectingly
2. B.
   tradition; significant; wrongfully
3. C.
   culture; universal; uncannily
4. D.
   habit; wilful; erroneously

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1. A.
   climate; vistas; ordinary
2. B.
   excitement; locations; overachieving
3. C.
   atmosphere; vacations; superficial
4. D.
   madness; destinations; embarrassing

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1. A.
   irrevocably; indispensable; survival
2. B.
   invaluably; opportunistic; determination
3. C.
   incredibly; reliable; concerns
4. D.
   unimaginably; immutable; subculture

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1. A.
   To measure riverine levels to predict agricultural yields and fix tax rates.
2. B.
   To calculate distances using the flow of water in the Nile.
3. C.
   To measure the consumption of water by the capital city.
4. D.
   To track the speed of trade ships travelling downstream.

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1. A.
   It was a corpuscular thread that ran from the North to the South of the country.
2. B.
   It was the perennial source of water for most citizens.
3. C.
   It served as the singular, vital channel for all movement and survival in the region.
4. D.
   It was a complex network of hundreds of small, aortic streams.

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1. A.
   ability of individual citizens to import and export on behalf of the government.
2. B.
   mercantile belief that the government controlled all commerce.
3. C.
   government's ability to exert power and organise resources within its territory.
4. D.
   department responsible for calculation and collection of taxes.

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1. A.
   Input: Prayers and sacrifices; Output: Increased harvest.
2. B.
   Input: Environmental data; Output: Administrative action.
3. C.
   Input: Agriculture; Output: Exports.
4. D.
   Input: Nilometer; Output: Inference.

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1. A.
   The quantum of arable land would remain unchanged that year.
2. B.
   Food reserves would need to be managed strictly to prevent famine.
3. C.
   They should immediately increase the volume of grain exports.
4. D.
   Tax revenues for the coming year would likely increase.

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1. A.
   It minimized the need for a complex governance structure by forcing all citizens to live in a single city.
2. B.
   It provided a natural defence against both land as well as sea-based invasions.
3. C.
   It restricted the population to a narrow, observable corridor, facilitating administrative oversight of movement and resources.
4. D.
   It allowed for the easy expansion of the Egyptian state into landlocked territories.

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