IPMAT Indore 2023 — Previous Year Paper

Vinita drives a car which has four gears. The speed in the fourth gear is five times the speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as in the third gear. In a 100 km journey, equal distances in each gear takes 585 minutes. If instead the distances in 1st, 2nd, 3rd, 4th gears are 4, 4, 32, 60 km respectively, then the total time taken is______ minutes.

If three consecutive coefficients in the expansion of $(x+y{)}^n$ are in the ratio 1:9:63, then $n$ is _______.

The total number of positive integer solutions of $21\le a+b+c\le 25$ is______.

The product of the roots of the equation $2^{({\log }_{2}x{)}^2}-5{\log }_{2}x+6=0$ is ________.

If $f(1)=1$ and $f(n)=3n-f(n-1)$ for all integers $n>1$, then $f(2023)$ is _________.

If $f(n)=1+2+3+\cdots +(n+1)$ and $g(n)={\sum }_{k=1}^n\frac{1}{f(k)}$, then the least value of $n$ for which $g(n)$ exceeds $\frac{99}{100}$ is_________.

The polynomial $4x^{10}-x^9+3x^8-5x^7+c{x}^6+2x^5-x^4+x^3-4x^2+6x-2$ when divided by $x-1$ leaves a remainder 2. Then the value of $c+6$ is________.

The remainder when $1!+2!+3!+\cdots +95!$ is divided by 15 is______.

Let $a,b,c,d$ be positive integers such that $a+b+c+d=2023$. If $a:b=2:5$ and $c:d=5:2$, then the maximum possible value of $a+c$ is________.

In the xy-plane let $A=(-2,0)$, $B=(2,0)$. Define $S$ as the collection of all points $C$ on the circle $x^2+y^2=4$ such that the area of triangle ABC is an integer. The number of points in $S$ is________.

Amisha can complete a task in twenty days. After four days she fell sick for four days and resumed on the ninth day but with half her original work rate. She completed the task in another twelve days with a co-worker who joined from day nine. The number of days required for the co-worker to complete the task alone would be ______.

In an election with two candidates, 15% did not turn up to vote, and 50 voters cast invalid votes. 44% of all voters in the voting list voted for the winner. If the winner got 200 votes more than the other, then the number of voters in the voting list is_________.

Ankita earns INR 10,000 at the end of the year, invests in a deposit at 0.5% simple interest. Yearly income increases by 10,000 every year, interest rate also increases by 0.5% on new deposits. If she invests all yearly income at end of each year, total interest in 5 years from today is__________ INR.

In a chess tournament, there are four groups of equal size. Each player plays once against own group, twice against one of remaining groups, three times against another, and four times against the last. If more than 1000 matches are played, the minimum possible number of players in each group is_______.

The length of the line segment joining the two intersection points of the curves $y=4970-|x|$ and $y=x^2$ is_________.

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

A goldsmith bought a solid golden ball at INR 1,000,000 and melted it to make spherical beads each with radius one-fifth of the original. If sold at 20% discount with 20% profit, the listed price per bead, in INR, was

Let $a,b,c$ be real numbers greater than 1, and $n$ a positive real ≠ 1. If ${\log }_n({\log }_{2}a)=1$, ${\log }_n({\log }_{2}b)=2$, ${\log }_n({\log }_{2}c)=3$, then which is true?

If the harmonic mean of the roots of $(5+\sqrt{2})x^2-bx+8+2\sqrt{5}=0$ is 4 then $b$ is

Consider an 8×8 chessboard. The number of ways 8 rooks can be placed such that no two are in the same row or column is

The set of all real values of $x$ satisfying $\frac{x^2(x+1)}{(x-1)(2x+1{)}^3}>0$ is

If $A=\left[\begin{array}{cc}1& 2\\ 3& a\end{array}\right]$ where $a$ is real, and $\det (A^3-3A^2-5A)=0$, then one possible value of $a$ is

If compound interest minus simple interest for 3 years at 10% annual rate equals INR 527, then the amount invested in INR is

Group of 120 students: 80 Science, rest Commerce. 70 support Mumbai Indians, others support CSK. Number of Science students who support Mumbai Indians is

Minimum number of times a fair coin must be tossed so that P(at least one head) > 0.8 is

A polynomial $P(x)$ leaves remainder 2 when divided by $(x-1)$ and remainder 1 when divided by $(x-2)$. The remainder when $P(x)$ is divided by $(x-1)(x-2)$ is

Let $[x]$ denote the greatest integer not exceeding $x$ and $\{x\}=x-[x]$. If $n$ is a natural number, then the sum of all values of $x$ satisfying $2[x]=x+n\{x\}$ is

If $\frac{a+b}{b+c}=\frac{c+d}{d+a}$, which statement is always true?

If ${\log }_{\cos x}(\sin x)+{\log }_{\sin x}(\cos x)=2$, then $x$ is

A helicopter flies along the sides of a square field of side 100 km. First side at 100 kmph; each subsequent side speed increases by 100 kmph. The average speed is

In triangle ABC, D is midpoint of BC, AM is altitude on BC. If AB:BC:CA = 2:4:3, then ratio of BM:AD is

In a chess tournament with 5 contestants, each plays all others once, no draws. Winner gets 1, loser 0. Which sequence cannot represent scores?

A rabbit sits at base of staircase with 10 steps. It proceeds to top by climbing one or two steps at a time. The number of ways it can reach top is

Let $a_1,a_2,a_3$ be three distinct real numbers in geometric progression. If equations $a_1{x}^2+2a_{2}x+a_3=0$ and $b_1{x}^2+2b_{2}x+b_3=0$ have a common root, then which is necessarily true?

Which of the following straight lines are both tangent to the circle $x^2+y^2-6x+4y-12=0$?

A person at the center of open ground walks 32m east, right turn 16m, right turn 8m, and so on. How far from start after infinite walks?

The equation $x^2+y^2-2x-4y+5=0$ represents

If $\cos \alpha +\cos \beta =1$, then the maximum value of $\sin \alpha -\sin \beta$ is

Let $p$ be a positive integer such that the unit digit of $p^3$ is 4. What are the possible unit digits of $(p+3{)}^3$?

The probability that a randomly chosen positive divisor of $10^{2023}$ is an integer multiple of $10^{2001}$ is

Direction (Q.41-Q.45): A pharmaceutical company tested five drugs on three organisms. The table reports if a drug works. For example, drug A works on R; B and C work on Q.

• Each drug works on at least one organism, max two.
• Each organism treatable with 2 or 3 of these drugs.
• Wherever A works, B also works. Wherever C works, D also works.
• D and E do not work on the same organism.

Organism R can be treated with

Direction (Q.41-Q.45): A pharmaceutical company tested five drugs on three organisms. The table reports if a drug works. For example, drug A works on R; B and C work on Q.

• Each drug works on at least one organism, max two.
• Each organism treatable with 2 or 3 of these drugs.
• Wherever A works, B also works. Wherever C works, D also works.
• D and E do not work on the same organism.

Drug E works on

Direction (Q.41-Q.45): A pharmaceutical company tested five drugs on three organisms. The table reports if a drug works. For example, drug A works on R; B and C work on Q.

• Each drug works on at least one organism, max two.
• Each organism treatable with 2 or 3 of these drugs.
• Wherever A works, B also works. Wherever C works, D also works.
• D and E do not work on the same organism.

The organism(s) that can be treated with three drugs is/are

Direction (Q.41-Q.45): A pharmaceutical company tested five drugs on three organisms. The table reports if a drug works. For example, drug A works on R; B and C work on Q.

• Each drug works on at least one organism, max two.
• Each organism treatable with 2 or 3 of these drugs.
• Wherever A works, B also works. Wherever C works, D also works.
• D and E do not work on the same organism.

Drug D works on

Direction (Q.41-Q.45): A pharmaceutical company tested five drugs on three organisms. The table reports if a drug works. For example, drug A works on R; B and C work on Q.

• Each drug works on at least one organism, max two.
• Each organism treatable with 2 or 3 of these drugs.
• Wherever A works, B also works. Wherever C works, D also works.
• D and E do not work on the same organism.

Organism P can be treated with

Being deprived of sleep can result in

In what way does sleep contribute to a person's well-being?

In order to remain physically fit one must

The main focus of the passage is on the

As per the passage which of these sentences is NOT correct?

The objective of the passage is to

Apple's challenge while opening physical stores is to

The Apple retail stores in India will

"Apple's aim is not only to increase sales of its iPhones, but to draw people into Apple's ecosystem." This means Apple seeks to

The main point the passage makes is that Apple

India is now the focus of Apple operations because

Based on the passage which one of the following is NOT true?

Direction: Choose the most appropriate word/phrase.

If you ask me to give you a rough estimate for the cost of the project, _________________ I would say thirty lakhs.

Direction: Choose the most appropriate word/phrase.

The nasty comments made by strangers on the social media platforms about the actor made him __________.

Direction: Choose the most appropriate word/phrase.

The new car has disappointed its buyers in many ways, and good mileage is its only ______________.

Direction: Choose the most appropriate word/phrase.

Meena is very arrogant; she refuses to acknowledge Sunil because she feels he is a man _______________.

Direction: Choose the most appropriate word/phrase.

Some big shots know how to escape the law. It is, however, the _______________ who are more often apprehended.

Direction: Choose the most appropriate word/phrase.

A few brands tailor pants for people with prosthetic legs. This is how they_____________.

Direction: Choose the most appropriate word/phrase.

It grieved me _______________ my friend's serious illness.

Direction: Choose the option that renders the sentence correct.

My aunt Seema was the most generous of all the members of our family. Whenever we went out for dinner, she always insisted to pay for the meal.

Direction: Choose the option that renders the sentence correct.

Listening to the recording of cricket commentary from the past can be great fun. This is when you realise that nothing much has changed, hasn't it?

Direction: Choose the option that renders the sentence correct.

When you play 'Secret Santa', you are expected to buy a gift for whoever you are assigned, without letting them know.

Direction: Choose the option that renders the sentence correct.

Justin couldn't understand why his friend had refused a job. If it had been him in his friend's place, he would definitely accepted such an offer.

Direction: Choose the option that renders the sentence correct.

The setting of a story effects the storys plot.

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

_______________________. Conflicts are now brewing over rivers and river basins shared by many countries. This is not unexpected, given that more than two hundred water bodies are shared by two or more countries. Strife over water, for example, is erupting throughout the Middle East.

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

Indian poetry in English began in Bengal, the province where the British first gained a stronghold. This poetry was a largely urban phenomenon, centered in Calcutta. ____________. Then, gradually, it moved to other urban centres. Even today, Indian poetry in English remains largely urban.

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

In the late 1960s, architect Charles Correa began as an urban planner, creating New Bombay. In the midst of overpopulated cities, he tried to create quasi-rural housing environments. In all of his urban planning commissions, Correa avoided high-rise housing solutions. __________________.

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

The concept of the 'Villa' came to Lucknow with foreign soldiers, travellers and adventurers. For the Nawabs of Lucknow, architecture became the physical manifestation of their new status. _____________________. Villas, hence, provided an ideal substitute. Europe sold to the Nawabs the idea of villas, based on designs and memory. The building chosen as the prototype for Dilkusha Kothi was a country house in Northumberland.

Direction: Choose the best option to fill the blanks.

_________________have to label their ____________________ posts in order to bring about transparency and ________________ the interests of the customers.

Direction: Choose the best option to fill the blanks.

Working from home requires that you may have to put your __________________ life on ______________________. Some people find this very ________________ as they like to keep their work and home lives separate.

Direction: Choose the best option to fill the blanks.

In its early stages, dementia is often _______________ from normal ageing. Neither dementia nor cognitive ageing is currently _________________, though they may be slowed through diet, exercise, and keeping the mind agile.

Direction: Choose the best option to fill the blanks.

The culture of the 21st century – on an increasingly ___________ scale – is oriented around utility, effectiveness, and impact. The worth of anything – an idea, an activity, an artwork, a _______ with another person – is determined _______________.

Direction: Choose the best option to fill the blanks.

The HR chief said the company will not _____________________ on investing in people and has _______________ spending on employee needs to ______________ them and provide a sense of stability.

Direction: Choose the best option to fill the blanks.

In the alleyways of old Cairo, framed portraits of Egyptian icons are ______________. Kings, presidents, religious figures are all _________________ on fading walls, held up as symbols of a glorious past.

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

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

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

Which option has the incorrect or inappropriate usage of 'tied/tide'?

Which option has the incorrect or inappropriate usage of 'further/farther'?

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

Direction: Sequence the sentences and enter as a digit string (e.g. "53412").

1. But the mutiny of Visakhapatnam predates this.

2. Instead of going against their heroic leader, the sepoys attacked the British soldiers and managed to escape from the town.

3. The Sepoy Mutiny of 1857 in the garrison town of Meerut is regarded as the First War of Independence.

4. It happened in 1780 when the British officers asked the local sepoys to join the fight against Hyder Ali.

Direction: Sequence the sentences and enter as a digit string (e.g. "53412").

1. Yet, even as TikTok delights consumers and advertisers, others believe the sunny app has a dark side.

2. Since launching just five years ago, the app has brought a warm glow to its 1 billion plus users, as well as an icy dash of competition to the social media incumbents of Silicon Valley.

3. ByteDance, its owner, has its headquarters in China, whose government is addicted to surveillance and propaganda – making it a worrying place for a media app to be placed.

4. With its wholesome dancing and lip-syncing videos, TikTok once billed itself as the "last sunny corner on the Internet."

Direction: Sequence the sentences and enter as a digit string (e.g. "53412").

1. What is more shocking to observe is how often such strokes lead to death.

2. When the body temperature rises, our vital organs swell, and this causes death.

3. One main reason for this is that people underestimate how badly heat can affect the body.

4. Heat strokes have become more common in our country than ever before.

Direction: Sequence the sentences and enter as a digit string (e.g. "53412").

1. Once they reach a high altitude, they manage to travel all over the world.

2. An expert from the team explained that the bacteria usually lived on the surface of vegetation, such as leaves.

3. The wind carries them off the surface and into the atmosphere.

4. A group of researchers were surprised to find that clouds had carried drug resistant bacteria over a long distance.

Direction: Sequence the sentences and enter as a digit string (e.g. "53412").

1. This instance highlights how young people from different backgrounds can make important contributions to climate change.

2. Participation in environmental education programmes can motivate children to act responsibly towards the environment.

3. They were motivated to act in ways that would help the environment, like using a reusable water bottle or refusing to use plastic straws.

4. Six hundred elementary school children from varied social and linguistic groups participated in an ocean pollution education programme.