IPMAT Indore 2022 — Previous Year Paper

The 3rd, 14th and 69th terms of an AP form three distinct and consecutive terms of a GP. If the next term of the GP is the nth term of the AP, then n equals____________.

The area enclosed by $2|x|+3|y|\le 6$ is____________ sq. units

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is_________.

If $\sin \alpha +\sin \beta =\frac{\sqrt{2}}{\sqrt{3}}$ and $\cos \alpha +\cos \beta =\frac{1}{\sqrt{3}}$, then the value of $(20\cos ((\alpha -\beta )/2){)}^2$ is.

The sum of the coefficients of all the terms in the expansion of $(5x-9{)}^4$ is __________.

Aruna buys apples at INR 20 each and mangoes at INR 25 each. If she sells all apples at 10% profit and all mangoes at 20% loss, no profit/no loss. If instead apples at 20% loss and mangoes at 10% profit, loss is INR 150. Number of apples is_________.

If ${\log }_{x^2}y+{\log }_{y^2}x=1$ and $y=x^2-30$. Then $x^2+y^2$ is___________.

Let $P(X)$ denote power set of set $X$. If $A$ is null set, then the number of elements in $P(P(P(P(A))))$ is_____________.

A new sequence is obtained from the sequence of positive integers (1, 2, 3,...) by deleting all the perfect squares. Then the 2022nd term of the new sequence is___________.

If $A=\left[\begin{array}{ccc}1& 0& 0\\ 0& 0& 1\\ 0& 1& 0\end{array}\right]$, then the absolute value of the determinant of $(A^9+A^6+A^3+A)$ is ______________.

The numbers $-16,2^{x+3}-2^{2x-1}-16,2^{2x-1}+16$ are in arithmetic progression. Then $x$ equals _________.

Given $f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|$, the minimum value of $f(x)$ is_________.

When Geeta increases her speed from 12 km/hr to 20 km/hr, she takes one hour less. The distance between home and office is________km.

50 distinct positive integers, highest is 100, average of largest 25 exceeds average of remaining by 50. Maximum possible sum of all 50 integers is _________.

Mrs and Mr Sharma, Mrs and Mr Ahuja, and 4 other persons sit at a round table for dinner. If Sharmas sit next to each other and Ahujas don't sit next to each other, the number of seating arrangements is _____.

The sum of the squares of all roots of $x^2+|x+4|+|x-4|-35=0$ is

Let $A=\{1,2,3\}$ and $B=\{a,b\}$. Assuming all relations from $A$ to $B$ are equally likely, the probability that a relation is also a function is

If the five-digit number $abcde$ is divisible by 6, then which is NOT necessarily divisible by 6?

The set of real values of $x$ for which ${\log }_{27}8\le {\log }_{3}x<9^{1/{\log }_{2}3}$ holds is

Suppose $a,b,c$ are integers with $a>b>c>0$ and $A=\left[\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right]$. Then the determinant

The lengths of the sides of a triangle are $x,21$ and $40$, where $x$ is the shortest side. A possible value of $x$ is

If $A=\left[\begin{array}{cc}1& 0\\ \frac{1}{2}& 0\end{array}\right]$, then $A^{2022}$ is

The sum of the first 15 terms of an AP is 200, while the sum of the next 15 terms is 350. The common difference is

Cost of jewellery is proportional to square of weight. A 10 gram piece costs INR 3600. Cost of a 4 gram piece is

When the square of the difference of two naturals is subtracted from the square of the sum, and the result divided by four, we get

In a 400m race, Ashok beats Bipin by 15 sec and Chandan by 25 sec. If Ashok beats Bipin by 150m, by how many metres does Bipin beat Chandan?

The set of all possible values of $f(x)$ for which $81^x+81^{f(x)}=3$ is

Let $A$ and $B$ be sets such that $A\times B$ has four elements. If two elements of $A\times B$ are $(1,4)$ and $(4,1)$, then

In right-angled triangle ABC, hypotenuse AC = 13 cm. Midpoints D, E of AB, AC connected by line of length 6 cm. Length of BC is

Bowl: 60ml orange + 40ml water + 100ml apple = fruit punch. Madhu drinks 50ml. How much orange should be added to make orange 50% of the remainder?

Room with n persons avg height 160 cm. m more persons enter with avg height 172 cm. Average becomes 164 cm. Then m:n is

For $0<\theta <\pi /4$, let $a=((\sin \theta {)}^{\sin \theta })({\log }_2\cos \theta )$, $b=((\cos \theta {)}^{\sin \theta })({\log }_2\sin \theta )$, $c=((\sin \theta {)}^{\cos \theta })({\log }_2\cos \theta )$, $d=((\sin \theta {)}^{\sin \theta })({\log }_2\sin \theta )$. The median value is

If $f(x^2+f(y))=xf(x)+y$ for all non-negative integers $x,y$, then $[f(0){]}^2+f(0)$ equals

The curve represented by $\frac{x^2}{\sin \sqrt{2}-\sin \sqrt{3}}+\frac{y^2}{\cos \sqrt{2}-\cos \sqrt{3}}=1$ is

The number of four-digit integers > 1000 and divisible by both 2 and 3, but not by 5, is

Ayesha atop 200m tower sees a car moving on straight horizontal road. At 11:00 angle of depression 45°. At 11:02 angle of depression 30°. The speed is approximately

If a factor of $3^7\cdot 2^8\cdot 17^3$ is randomly chosen, the probability it's a perfect square is

The value of k for which lines x-y-1=0, 2x+3y-12=0, 2x-3y+k=0 are concurrent is

The set of all possible values the function $f(x)=\frac{x}{|x|}$ (x ≠ 0) takes is

In how many ways can the letters of MANAGEMENT be arranged such that no two vowels appear together?

Direction (Q.41-Q.45): A showroom is open all 7 days a week. Five employees Alex, Bhabha, Cathy, Dilip, Ethan work there. Every day except Sunday, two employees work; Sunday three work. Every employee works 3 days a week. Additional info:

• Every employee works on two consecutive days while the third day is not consecutive.
• Alex and Dilip work together on Tuesday and Wednesday; their other working day differs.
• Neither Bhabha nor Cathy works with Alex on any day.
• Cathy does not work on Saturday or Monday.

Number of days Bhabha and Cathy work together in a week is

Direction (Q.41-Q.45): A showroom is open all 7 days a week. Five employees Alex, Bhabha, Cathy, Dilip, Ethan work there. Every day except Sunday, two employees work; Sunday three work. Every employee works 3 days a week. Additional info:

• Every employee works on two consecutive days while the third day is not consecutive.
• Alex and Dilip work together on Tuesday and Wednesday; their other working day differs.
• Neither Bhabha nor Cathy works with Alex on any day.
• Cathy does not work on Saturday or Monday.

The consecutive days Ethan works are

Direction (Q.41-Q.45): A showroom is open all 7 days a week. Five employees Alex, Bhabha, Cathy, Dilip, Ethan work there. Every day except Sunday, two employees work; Sunday three work. Every employee works 3 days a week. Additional info:

• Every employee works on two consecutive days while the third day is not consecutive.
• Alex and Dilip work together on Tuesday and Wednesday; their other working day differs.
• Neither Bhabha nor Cathy works with Alex on any day.
• Cathy does not work on Saturday or Monday.

Which pair do NOT work together on any day?

Direction (Q.41-Q.45): A showroom is open all 7 days a week. Five employees Alex, Bhabha, Cathy, Dilip, Ethan work there. Every day except Sunday, two employees work; Sunday three work. Every employee works 3 days a week. Additional info:

• Every employee works on two consecutive days while the third day is not consecutive.
• Alex and Dilip work together on Tuesday and Wednesday; their other working day differs.
• Neither Bhabha nor Cathy works with Alex on any day.
• Cathy does not work on Saturday or Monday.

Employees who work on Sunday are

Direction (Q.41-Q.45): A showroom is open all 7 days a week. Five employees Alex, Bhabha, Cathy, Dilip, Ethan work there. Every day except Sunday, two employees work; Sunday three work. Every employee works 3 days a week. Additional info:

• Every employee works on two consecutive days while the third day is not consecutive.
• Alex and Dilip work together on Tuesday and Wednesday; their other working day differs.
• Neither Bhabha nor Cathy works with Alex on any day.
• Cathy does not work on Saturday or Monday.

One of the days Alex works on is

According to the passage, the interest in the difference between climacteric and non-climacteric fruits is in the

The main point the writer makes is that fruit-bearing plants

Consider: (i) Non-climacteric fruits tend to have vivid colours. (ii) Thirty-six varieties of climacteric and non-climacteric fruits were eaten predominantly either by ground-dwellers, or by arboreal/aerial animals respectively. According to the passage,

The study has been based on

The origins of the distinguishing characteristics between climacteric and non-climacteric fruits are

Which one of the following options means "arboreal" and "camouflage"?

'Local reaction' refers to

Jenner received a lot of recognition from medical bodies because

Twenty-three cases were put on record to explain that

By calling the vaccine unjustifiable, Dr. Ingenhouz meant that vaccination

According to the author, the main idea in the passage is

On returning from London, Dr. Jenner was disappointed because

Direction: Choose the most appropriate word/phrase.

Flying this simple aeroplane is a _________ for the experienced pilot.

Direction: Choose the most appropriate word/phrase.

Leela is always nasty and inconsiderate with her colleagues; now that she has a rude superior, she is getting ____________.

Direction: Choose the most appropriate word/phrase.

I still have two more difficult exams left, but I'm trying to _______; after these I won't have any more for a year!

Direction: Choose the most appropriate word/phrase.

For the past three decades, this chain of coffee shops has been committed to building a culture where everyone is welcome. This is just one instance of their _________.

Direction: Choose the most appropriate word/phrase.

Ever since Girish won the prestigious Infosys prize, he has been behaving_________.

Direction: Choose the most appropriate word/phrase.

Some of the best spies take the guise of innocuous secretaries or researchers, as they are_________.

Direction: Choose the most appropriate word/phrase.

She ________ her classmates because she comes from a very rich, aristocratic family.

Direction: Choose the option that renders the sentence correct.

His talk on heritage sites has picked up my interest.

Direction: Choose the option that renders the sentence correct.

If I had known that you needed to go to the airport yesterday, I could drive you there.

Direction: Choose the option that renders the sentence correct.

He was having a difficult time, but never once he complained.

Direction: Choose the option that renders the sentence correct.

The Principal and professors are authorized to sanction leave to a student provided she will have a good attendance record.

Direction: Choose the option that renders the sentence correct.

When all the words on the page got scrambled, she quickly pressed undo, after which the document reverted back to its original state.

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

___________________. In Southeast Asia, for example, climate and lifestyle factors mean that people spend much more time in shopping malls than Europeans do, who might go shopping once a fortnight. Then there are gender variations in the way we shop. As descendants of hunter-gatherers, accumulating is in our blood, but how you go about it depends on whether you are male or female.

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

This winter, I wish to go to the beaches for a holiday. I think I will go to Goa, India's most well-known beach holiday destination. It is about 600 km away from Mumbai, so reaching there is not a major problem. ____________. The major Goan beaches are tourist attractions.

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

Nowadays, many teenagers and young adults around the world have to spend most of their time studying in order to get top grades, a university place, and a good job. ___________. There are several causes for this situation, one of the main ones being exams. These are stressful experiences.

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

The people of the Indus Valley civilization wrote with a script. So far scholars have been unable to decipher that script. Archaeologists who have been excavating newly discovered sites in Mesopotamia hope to find a text that has scripts from both the Indus valley and Mesopotamia, the second of which has already been deciphered. ________.

Direction: Choose the best option to fill the blanks.

Achieving spaceflight enabled humans to begin to explore the solar system and the rest of the _________, to understand the many objects and ___________ that are better observed from a space perspective, and to use for human benefit the resources and attributes of the space environment. All of these activities – discovery, scientific understanding, and the ___________________ of that understanding to serve human purposes – are elements of space _________.

Direction: Choose the best option to fill the blanks.

Visually strong, __________ films of the 1920s are ________ preserved and suffer from censorship cuts, leading to the ______________ that they were primitive and barely watchable.

Direction: Choose the best option to fill the blanks.

Everyday more than 1 billion promotional messages are sent that are commercial and ___________________. Although _______________ have used more technology to stop this, ________________ find ways around it.

Direction: Choose the best option to fill the blanks.

The investigators have ______ that he had leaked confidential ______ information about the acquisition, thereby allowing associates to profit _______ from the deal.

Direction: Choose the best option to fill the blanks.

The beauty of _____ is that it poses thought-provoking questions and inspires us to think deeply about ______ and life in general. Further, _______ about the ideas and perspectives outlined by different thinkers can help us to gain a better _______ of the world we live in.

Direction: Choose the best option to fill the blanks.

In an anthropocentric ______, animals are no more than property to human beings. Therefore, the concepts of 'humane' treatment and 'necessary' _______ are economic in nature. The idea that killing animals is not a serious issue as long as animals are not made to suffer rests _____________ on the widely accepted idea that animals do not have a right to life.

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

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

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

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

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

Which option has the incorrect or inappropriate usage of 'collaborate/corroborate'?

Direction: Sequence the sentences and enter as a digit string (e.g. "3412").

1. The Central African Republic has approved Bitcoin as an official currency.

2. Experts foresee that this will damage the environment as well as the economy.

3. Others claim that this may make money laundering easy and also use up a lot of electricity.

4. Economists criticised this move as a potential risk to the financial stability of the nation.

Direction: Sequence the sentences and enter as a digit string (e.g. "3412").

1. Located in the foothills of the Sion Fort, the lake is a Grade II-A heritage structure, dating back to the 17th century.

2. Once home to several marine creatures, the lake is now surrounded by high-rise residential buildings.

3. The Municipal Corporation is set to breathe life back into the city's Sion Talao (Lake) with the rejuvenation and beautification of the centuries-old lake.

4. Over the years, the lake has lost its prominence.

5. Earlier the Talao was a known natural water tank with the Sion hillock expanding around it like an enclosing wall.

Direction: Sequence the sentences and enter as a digit string (e.g. "3412").

1. A sub-par monsoon cuts farm yields, output, and farm incomes, increasing the country's dependence on food imports.

2. A robust monsoon will help put a lid on food inflation by increasing domestic output.

3. This is because half the Indian population depends upon farm-derived income.

4. The June-to-September rain-bearing system is often called the lifeblood of the country's economy.

5. Unfortunately, however, nearly 40% of India's net sown area does not have access to irrigation.

Direction: Sequence the sentences and enter as a digit string (e.g. "3412").

1. The popularity of these creations grew along with that of the tea ceremony in the 16th century.

2. However, savvy tourists find the best bargains for ceramics in Tokyo's Kitchen Town.

3. Modern shops in touristy spots display thousands of them, both hand crafted and factory made.

4. Japanese artisans have been making ceramics, known as Yakimono since prehistoric times.

Direction: Sequence the sentences and enter as a digit string (e.g. "3412").

1. This means the brain receives less input over the course of a day.

2. Youthful eyes jiggle regularly to take in new or unfamiliar stimuli.

3. As the person attached to those eyes ages, the eye muscles grow slower and the pathways grow longer, more complex, or, in some cases, get damaged.

4. Our eyes quickly scan the surroundings and then send the data to the brain.

5. Human eyes perform jiggles, more formally called saccades, in response to a change in the field of vision.