5 IPMAT Indore 2022
5.1 Quantitative Ability (SA)
The sum of the coefficients of all the terms in the expansion of \((5x-9)^{4}\) is
A = \(\begin{bmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{bmatrix}\).
Then the absolute value of the determinant of \((A^{9}+A^{6}+A^{3}+A)\) is
The area enclosed by \(2|x|+3|y|\le6\) is ___ sq. units
If \(\sin \alpha + \sin \beta = \frac{\sqrt{2}}{\sqrt{3}}\) and \(\cos \alpha + \cos \beta = \frac{1}{\sqrt{3}}\) then the value of \((20\cos(\frac{\alpha-\beta}{2}))^{2}\) is
Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is
Let \(P(X)\) denote power set of a set \(X\). If \(A\) is the null set, then the number of elements in \(P(P(P(P(A))))\) is
Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is
Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150. Then the number of apples purchased by Aruna is
If \(\log_{(x^{2})}y+\log_{(y^{2})}x=1\) and \(y=x^{2}-30\) then the value of \(x^{2}+y^{2}\) is
The numbers -16, \(2^{x+3}\), \(-2^{2x-1}-16\), \(2^{2x-1}+16\) are in an arithmetic progression. Then x equals
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
A new sequence is obtained from the sequence of positive integers (1, 2, 3,…) by deleting all the perfect squares. Then the \(2022^{nd}\) term of the new sequence is
When Geeta increases her speed from 12 km/hr to 20 km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___ km.
The \(3^{rd}\), \(14^{th}\) and \(69^{th}\) terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the \(n^{th}\) term of the arithmetic progression, then n equals
Given that \(f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|\), \(x \in (-\infty, \infty)\) the minimum value of \(f(x)\) is
5.2 Quantitative Ability (MCQ)
The sum of the first 15 terms in an arithmetic progression in 200, while the sum of the next 15 terms in 350, then the common difference is
For \(0<\theta<\frac{\pi}{4}\) let \(a=((sin~\theta)^{sin~\theta})(log_{2}cos~\theta)\), \(b=((cos~\theta)^{sin~\theta})(log_{2}sin~\theta)\), \(c=((sin~\theta)^{cos~\theta})(log_{2}cos~\theta)\) and \(d=((sin~\theta)^{sin~\theta})(log_{2}sin~\theta)\). Then, the median value in the sequence a, b, c, d is
In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is
In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m: n is
The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is
In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?
The set of all possible values of f(x) for which \((81)^{x}+(81)^{f(x)}=3\)
The value of k for which the following lines are concurrent: \(x-y-1=0\), \(2x+3y-12=0\), \(2x-3y+k=0\) is
The curve represented by the equation \(\frac{x^{2}}{\sin\sqrt{2}-\sin\sqrt{3}}+\frac{y^{2}}{\cos\sqrt{2}-\cos\sqrt{3}}=1\) is
Let \(A={1,2,3}\) and \(B={a,b}\). Assuming all relations from set A to set B are equally likely, what is the probability that a relation from A to B is also a function?
In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?
The sum of the squares of all the roots of the equation \(x^{2}+|x+4|+|x-4|-35=0\) is
If for all non-negative integers x and y, \(f(x^{2}+f(y))=xf(x)+y\) then the value of \([f(0)]^{2}+f(0)\) equals
The set of real values of x for which the inequality holds \(\log_{27}8 \le \log_{3}x < \frac{1}{9\,\log_{2}3}\) is
A set of all possible values the function \(f(x)=\frac{|x|}{|x|}\), where \(x\ne0\), takes is
In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?
Suppose a, b and c are integers such that \(a>b>c>0\) and \(A=\begin{bmatrix}a&b&c\\ b&c&a\\ c&a&b\end{bmatrix}\). Then the value of the determinant of A
Let A and B be two sets such that the Cartesian product \(A\times B\) consists of four elements. If two elements of \(A\times B\) are (1, 4) and (4, 1), then
If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?
The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is
If \(A=\begin{bmatrix}1&0\\ \frac{1}{2}&0\end{bmatrix}\). Then \(A^{2022}\) is
If one of the factors of the number \(3^{7}2^{8}17^{3}\) is randomly chosen, then the probability that the chosen factor will be a perfect square is
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
When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get
Ayesha is standing atop a vertical tower 200m high and observes a car moving away from the tower on a straight, horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be \(45^{\circ}\). At 11:02 AM, she observes the angle of depression of the car to be \(30^{\circ}\). The speed at which the car is moving is approximately
5.3 Instructions [41–45]
A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees are required while on Sunday three employees need to work. Every employee works for three days in a week. Some additional information is also provided:
- Every employee works on two consecutive days while the third day is not consecutive.
- Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them.
- Neither Bhabha nor Cathy works with Alex on any day.
- Cathy does not work either on Saturday or on Monday.
Which among the following employees do not work together on any of the days?
Employees who work on Sunday are
One of the days Alex works on is
Number of days Bhabha and Cathy work together in a week is
The consecutive days on which Ethan works are
5.4 Verbal Ability
Instructions [46–51]:
Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.
Bananas, apples, and avocados continue to ripen after they are picked. Cherries, blackberries, and grapes do not. The difference between climacteric fruits (the former) and non-climacteric fruits (the latter) matters to fruit growers and greengrocers, who must make sure their wares are in tip-top condition when they arrive at the marketplace. But how those differences originally came about remains unclear.
Two biologists of the University of Tokyo offer a suggestion. Fruits, they observe, exist to solve a problem faced by all plants—how best to spread their progeny around. Wrapping their seeds in a sugary pulp to provide a tasty meal serves as a way to get animals to do this for them. They do, however, need to make sure that their fruits favour the animals most likely to do the distributing. The biologists propose that climacterism, or its absence, is a way to achieve this. If ground-dwelling animals are the main distributors, then the continuing ripening of fallen fruit (i.e., climacterism) is beneficial. If, by contrast, those distributors are arboreal or aerial, and so can feed on unfallen fruit, then non-climacteric fruits will do well.
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
The origins of the distinguishing characteristics between the two types of fruits, climacteric and non-climacteric are
The study has been based on
Which one of the following options means “arboreal” and “camouflage”?
Consider the following two Findings: (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 or aerial animals respectively. According to the passage,
Instructions [52-57]:
Read the following passage and choose the answer that is closest to each of the questions that are based on the passage.
On the 14th of May 1796, vaccine matter was taken from the hand of a dairy maid, Sarah Nelmes, and inserted by two superficial incisions in the arms of James Phipps, a healthy boy of about eight years of age. The boy went through an attack of cowpox as expected. After this, however, it was necessary to determine whether he was protected from smallpox. After waiting two months Jenner inoculated him with material from a smallpox patient. He was delighted to note that the boy was not affected by smallpox.
By 1798, Jenner had succeeded in demonstrating the protective quality of the cowpox virus against smallpox, by putting on record details of 23 cases, contracted either casually or by direct inoculation. Sixteen of these had occurred accidentally among dairy workers in the course of occupations connected with cows and horses; the rest were done under Jenner’s direction. Among the persons inoculated was Jenner’s own little second son, Robert Harding Jenner, an infant eleven months old. Jenner demonstrated conclusively that the cowpox protects the human constitution from the infection of smallpox.
After Dr. Jenner had made his tests, he prepared a pamphlet for publication. He also went to London, so that he might have the opportunity to introduce the subject personally to friends and demonstrate the truth of his assertion to them. He remained in London for nearly three months without being able to find anyone who would submit to vaccination. Jenner went back to Gloucestershire, disappointed. It happened, however, that soon after his return home, a distinguished London surgeon named Cline resolved to make a trial of the vaccine material which Jenner had left with his friends.
The patient was a child suffering from a form of chronic hip-joint disease. The vaccine material was inoculated, and the vaccine vehicle ran rather a normal course and healed fully. The little patient was afterward inoculated with smallpox virus and found to be incapable of acquiring that disease. This case attracted considerable attention. The child was in a rundown condition, and the vaccine material might very well have provoked a rather serious local reaction. In a way, the fate of vaccination hung in the balance and good luck was in its favour.
Mr. Cline, however, after this, became a strong advocate of vaccination, and brought it very decidedly before the London physicians. It was not long before the opposition to the practice of vaccination took definite form. One of the best-known London physicians of the time, Dr. Ingenhouz, became the leader of a strong faction of the medical profession of London, who not only would have nothing to do with vaccination, but proclaimed openly that it was a dangerous innovation, absolutely unjustifiable, and communicated a disease without protecting against any other.
According to the author, the main idea in the passage is
On returning from London, Dr. Jenner was disappointed because
Jenner received a lot of recognition from medical bodies because
By calling the vaccine unjustifiable, Dr. Ingenhouz meant that vaccination
Twenty-three cases were put on record with the objective to explain very clearly that
‘Local reaction’ refers to
Instructions [58-64]:
Complete the following sentences by choosing the most appropriate word/phrase from the options given below.
She ________ her classmates because she comes from a very rich, aristocratic family
Ever since Girish won the prestigious Infosys prize, he has been behaving________
Some of the best spies take the guise of innocuous secretaries or researchers and are able to send large amounts of information to their heads of espionage, as they a________
I still have two more difficult exams left, but I’m trying to _______; after these I won’t have any more for a year!
For the past three decades, this chain of coffee shops has been committed to building a culture where everyone is welcome. They are an ally to the LGBTQ community, and this is just one instance of their _______
Leela is always nasty and inconsiderate with her colleagues; now that she has a rude superior, she is getting _______
Flying this simple aeroplane is a _______ for the experienced pilot.
Instructions [65-69]:
In each of the following sentences, the incorrect part of the sentence is underlined. Choose an alternative from the four given options so that the sentence is rendered correct.
His talk on heritage sites has picked up my interest.
He was having a difficult time, but never once he complained
The Principal and professors are authorized to sanction leave to a student provided she will have a good attendance record.
If I had known that you needed to go to the airport yesterday, I could drive you there.
When all the words on the page got scrambled, she quickly pressed undo, after which the document reverted back to its original state.
Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete 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.
Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete 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, and most students take a huge number of them during their school career.
Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete 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 and have some good beach-view hotels and plenty of shops selling touristy things such as beach robes, hats, jewellery, bags, and more.
Each of the paragraphs given below has a sentence missing which is indicated by a blank. From the choices given below each paragraph, choose the sentence that seems most logically appropriate to complete 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.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. Visually strong, ______ films of the 1920s are ______ preserved and suffer from censorship cuts, leading to the ______ that they were primitive and barely watchable.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. The beauty of ______ is that it poses thought-provoking questions and inspires us to think deeply about ______ about the ideas and perspectives outlined by different thinkers of the world we live in, and life in general. Further, ______ can help us to gain a better ______.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. 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.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. 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.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. The investigators have ______ that he had leaked confidential ______ information about the acquisition, thereby allowing associates to profit from the ______ deal.
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence. 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 ______.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
One of the statements below contains a word used incorrectly. Choose the option which has the incorrect or inappropriate usage of the word.
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.
- A sub-par monsoon cuts farm yields, output, and farm incomes,
increasing the country’s dependence on food imports.
- A robust monsoon will help put a lid on food inflation by increasing
domestic output of a variety of goods and commodities.
- This is because half the Indian population depends upon farm-derived
income.
- The June-to-September rain-bearing system is often called the
lifeblood of the country’s economy.
- Unfortunately, however, nearly 40% of India’s net sown area does not have access to irrigation.
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.
- The popularity of these creations grew along with that of the tea
ceremony in the 16th century.
- However, savvy tourists find the best bargains for ceramics in
Tokyo’s Kitchen Town.
- Modern shops in touristy spots display thousands of them, both hand
crafted and factory made.
- Japanese artisans have been making ceramics, known as Yakimono since prehistoric times.
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.
- The Central African Republic has approved Bitcoin as an official
currency.
- Experts foresee that this will damage the environment as well as the
economy.
- Others claim that this may make money laundering easy and also use
up a lot of electricity.
- Economists criticised this move as a potential risk to the financial stability of the nation.
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.
- This means the brain receives less input over the course of a
day.
- Youthful eyes jiggle regularly to take in new or unfamiliar
stimuli.
- As the person attached to those eyes ages, the eye muscles grow
slower and the pathways between the eye and the brain grow longer, more
complex, or, in some cases, get damaged.
- Our eyes quickly scan the surroundings and then send the data to the
brain.
- Human eyes perform jiggles, more formally called saccades, in response to a change in the field of vision.
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.
- Located in the foothills of the Sion Fort, the lake is a Grade II-A
heritage structure, dating back to the 17th century.
- Once home to several marine creatures, the lake is now surrounded by
high-rise residential buildings.
- 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.
- Over the years, the lake has lost its prominence.
- Earlier the talao was a known natural water tank with the Sion hillock expanding around it like an enclosing wall.