7 IPMAT Indore 2020
7.1 Quantitative Ability (SA)
In a division problem, product of quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then dividend is.
The shortest distance from the point (-4, 3) to the circle \(x^{2}+y^{2}=1\) is
The value of \(0.04^{log\sqrt{5}(\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+....)}\) is.
Suppose \(\begin{bmatrix}a & a^{2} & b^{2} & -1 \\ b & b^{2} & b^{3} & -1 \\ c & c^{2} & c^{3} & -1 \end{bmatrix}=0.\) where a, b and c are distinct real numbers. If \(a=3\), then the value of abc is
The minimum value of \(f(x)=|3-x|+|2-x|+|5-x|\) is equal to
Ashok purchased pens and pencils in the ratio 2:3 during his first visit and paid Rs. 86 to the shopkeeper. During his second visit, he purchased pens and pencils in the ratio 4:1 and paid Rs. 112. The cost of a pen as well as a pencil in rupees is a positive integer. If Ashok purchased four pens during his second visit, then the amount he paid in rupees for the pens during the second visit is
In a four-digit number, the product of thousands digit and units digit is zero while their difference is 7. Product of the middle digits is 18. The thousands digit is as much more than the units digit as the hundreds digit is more than the tens digit. The four-digit number is
Out of 80 students who appeared for the school exams in Mathematics (M), Physics (P) and Chemistry (C), 50 passed M, 30 passed P and 40 passed C. At most 20 students passed M and P, at most 20 students passed P and C and at most 20 students passed C and M. The maximum number of students who could have passed all three exams is
Two friends run a 3 kilometer race along a circular course of length 300 meters. If their speeds are in ratio 3:2, the number of times the winner passes the other is
Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is
7.2 Quantitative Ability (MCQ)
The probability that a randomly chosen factor of \(10^{19}\) is a multiple of \(10^{15}\) is
The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is
The equation of the straight line passing through the point M (-5,4), such that the portion of it between the axes is divided by the point M into two equal halves, is
The value of \(cos^{2}\frac{\pi}{8}+cos^{2}\frac{3\pi}{8}+cos^{2}\frac{5\pi}{8}+cos^{2}\frac{7\pi}{8}\) is
If \(\frac{1}{1^{2}}+\frac{1}{2^{2}}+\frac{1}{3^{2}}+........=\frac{\pi^{2}}{6}\) then value of \(\frac{1}{1^{2}}+\frac{1}{3^{2}}+\frac{1}{5^{2}}+.......\) upto ∞ is
A man is known to speak the truth on an average 4 out of 5 times. He throws a die and reports that it is a five. The probability that it is actually a five is
If \(log_{5}log_{8}(x^{2}-1)=0,\) then a possible value of x is
Consider the following statements: (i) When \(0<x<1\), then \(\frac{1}{1+x}<1-x+x^{2}\) (ii) When \(0<x<1\), then \(\frac{1}{1+x}>1-x+x^{2}\) (iii) When \(-1<x<0\) then \(\frac{1}{1+x}<1-x+x^{2}\) (iv) When \(-1<x<0\) then \(\frac{1}{1+x}>1-x+x^{2}\)
Fifty litres of a mixture of milk and water contains 30 percent of water. This mixture is added to eighty litres of another mixture of milk and water that contains 20 percent of water. Then, how many litres of water should be added to the resulting mixture to obtain a final mixture that contains 25 percent of water?
Three workers working together need 1 hour to construct a wall. The first worker, working alone, can construct the wall twice as fast as the third worker, and can complete the task an hour sooner than the second worker. Then, the average time in hours taken by the three workers, when working alone, to construct the wall is
7.3 Quantitative Ability (MCQ)
In a class, students are assigned roll numbers from 1 to 140. All students with even roll numbers opted for cricket, all those whose roll numbers are divisible by 5 opted for football, and all those whose roll numbers are divisible by 3 opted for basketball. The number of students who did not opt for any of the three sports is
Given \(f(x)=x^{2}+log_{3}x\) and \(g(y)=2y+f(y)\), the value of \(g(3)\) equals
A \(2\times2\) matrix is filled with four distinct integers randomly chosen from the set (1,2,3,4,5,6). Then the probability that the matrix generated in such a way is singular is
Ashok started a business with a certain investment. After few months, Bharat joined him investing half amount of Ashok’s initial investment. At the end of the first year, the total profit was divided between them in ratio 3:1. Bharat joined Ashok after
The average marks of 6 students in a test is 64. All the students got different marks, one of the students obtained 70 marks and all other students scored 40 or above. The maximum possible difference between the second highest and the second lowest marks is
Instructions [26-30]:
The table below presents the quoted buy and sell prices of five stocks during the five trading days of a given week. The quoted sell price is the price at which an investor can sell a stock in the market. The quoted buy price is the price at which an investor can buy a stock from the market. All the quoted numbers are in Indian Rupees.
| Day | Sunday | Tuesday | Wednesday | Thursday | Friday | |||||
|---|---|---|---|---|---|---|---|---|---|---|
| Sell | Buy | Sell | Buy | Sell | Buy | Sell | Buy | Sell | Buy | |
| Dabur | 460 | 462 | 455 | 458 | 432 | 433 | 444 | 447 | 461 | 462 |
| Marico | 345 | 346 | 355 | 336 | 365 | 368 | 372 | 375 | 372 | 374 |
| HUL | 1931 | 1933 | 1952 | 1955 | 1979 | 1981 | 2044 | 2048 | 1966 | 1969 |
| ITC | 237 | 238 | 238 | 239 | 246 | 251 | 221 | 225 | 253 | 256 |
| Britannia | 3044 | 3046 | 3100 | 3101 | 3110 | 3115 | 3025 | 3027 | 3140 | 3144 |
If an investor had Rs. 36,00,000 to invest in any particular single stock, and she could buy the stock only on Monday and sell it off only on Friday, then the stock she should buy on Monday to earn the maximum possible profit during the week is
If an investor planned to invest Rs. 36,00,000 in purchasing the stocks of HUL on Monday, sell them off on Wednesday and use the entire proceeds to purchase the stocks of Britannia on the same day and sell them off again on Friday, then the total investment return during the week would be
The difference between the quoted buy and sell price of a stock is referred to as the spread of the stock. The average spread of the stocks is lowest on
A brokerage firm charges 0.1 percent trading commission on the value of shares bought or sold through its trading platform. If an investor bought 1000 shares of Britannia on Tuesday, and sold all of them on Thursday, then the total brokerage fee that will be charged from the investor is
If you had decided to invest Rs. 36,00,000 worth of ITC stocks on Monday, then the day of the week you should choose to sell the stocks to earn the maximum possible profit would be
7.4 Verbal Ability
Instructions [31-36]:
Read the following passage and choose the answer that is closest for each of the questions that are based on the passage.
“John Muir, Earth-planet, Universe.” - These words are written on the inside cover of the notebook from which the contents of this volume have been taken. They reflect the mood in which the late author and explorer undertook his thousand-mile walk to the Gulf of Mexico a half-century ago. No less does this refreshingly cosmopolitan address, which might have startled any finder of the book, reveal the temper and the comprehensiveness of Mr. Muir’s mind. Even at the early age of twenty-nine his eager interest in every aspect of the natural world had made him a citizen of the universe. On these expeditions he had disciplined himself to endure hardship, for his notebooks disclose the fact that he often went hungry and slept in the woods, or on the open prairies, with no cover except the clothes he wore.
“Oftentimes,” Mr. Muir writes in some unpublished biographical notes, “I had to sleep out without blankets, and also without supper or breakfast. But usually I had no great difficulty in finding a loaf of bread in the widely scattered clearings of the farmers. With one of these big backwoods loaves I was able to wander many a long, wild mile, free as the winds in the glorious forests and bogs, gathering plants and feeding on God’s abounding, inexhaustible spiritual beauty bread. Only once in my long Canada wanderings was the deep peace of the wilderness savagely broken. It happened in the maple woods about midnight, when I was cold and my fire was low. I was awakened by the awfully dismal howling of the wolves, and got up in haste to replenish the fire.”
Had it not been for the accidental injury to his right eye in the month of March, 1867, he probably would have started somewhat earlier than he did. In a letter written to Indianapolis friends on the day after the accident, he refers mournfully to the interruption of a long-cherished plan, “For weeks,” he writes, “I have daily consulted maps in locating a route through the Southern States, the West Indies, South America, and Europe - a botanical journey studied for years. But, alas, I am half blind. My right eye, trained to minute analysis, is lost and I have scarce heart to open the other.” The injury to his eye proved to be less serious than he had at first supposed. In June he was writing to a friend: “I have been reading and botanizing for some weeks, and find that for such work I am not very much disabled.” In an account written after the excursion he says: “I was eager to see Illinois prairies on my way home, so we went to Decatur, near the center of the State, thence, I botanized one week on the prairie about seven miles southwest of Pecatonica….. To me all plants are more precious than before. My poor eye is not better, nor worse, A cloud is over it, but in gazing over the widest landscapes, I am not always sensible of its presence.”
“John Muir, Earth-planet, Universe,” Muir wrote this in his notebook because
Which of these did John Muir have no great difficulty in doing?
How did the experience with nature affect John Muir?
According to the passage, in what way was Muir affected by his injury?
When Muir said that he ‘botanized’, he meant that he
Which of these sentences is not true?
Instructions [37-42]:
Complete the following sentences by choosing the appropriate word/phrase from the options given below
It came as a shock to me that my friend had lost the ____ he had built carefully over the years when in a moment of madness he lent all of it to his neighbour.
During the debate, when the minister appeared to be vague about his stand on the controversial energy project, his opponent asked him to ____ and declare outright if the government would go ahead with the project or not.
It is irritating when co-workers dismiss your ideas as worthless, and later, present those very ideas as their own. They just want to ____
Before the start of the meeting, I am ____ the
Despite statistics to prove that there was a slowdown in the economy of the country, the professor was ____ about it.
After the unearthing of relics at the archaeological site, the historian was asked to ____
Instructions [43-45]:
Choose the alternative so that the underlined part of the sentence is rendered correct.
The pharmaceutical company hired a consultant to supervise a taskforce studying lower salaries as to their effects on employees’ morale.
Besides offering physiological rewards such as toned muscles, when regular karate is practiced the body can be turned into a dangerous weapon.
The animal activist has raised awareness not only on the plight of abandoned dogs, but also on overworked bulls and temple elephants.
Instructions [46-47]:
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.
When people move from one city or country to another, the spread of diseases may result. People often bring in germs which may not have been present there before. These new germs can spread quickly and cause previously unknown diseases. ____ They become ill more easily and could even die. In turn, newcomers may catch diseases which were not present where they came from.
Samar, a young man from a village in Tripura is a social media star who hopes to make it big as a model and actor. While his minute-long videos are very popular, his series titled, “Who wore it better?” showcases his creative side. ____ He uses a variety of filters and visual effects to improve his videos.
Instructions [48-52]:
The sentences below have words that are missing. Choose the best option from those given below to complete the sentence.
Coral reefs are one of the most ____, biologically complex, and diverse marine ecosystems on Earth. This ecosystem is one of the ____ paradoxes of the biosphere: how do clear, and thus nutrient-poor, waters support such ____ and productive communities?
It is a ____ to live in a land without ____. Even with all the technological advancement and economic growth, there are still millions who live in war zones where life every day is filled with ____.
The ability to ____ and ____ a cohesive team is particularly critical in hi-tech firms where the ____ landscape can shift dramatically in the face of disruptive technologies.
Cool-headed and rational, Jo Eun-cha is a talented and driven anchorman who commands as well as demands respect. After ____ to get elected as a news director, he aims to ____ to his job as the top news anchor to increase his ____ of being elected the next year.
A collective investment fund (CIF), also known as a collective investment trust (CIT), is a group of ____ accounts held by a bank or trust company. The financial institution ____ assets from individuals and organizations to ____ a single larger, diversified portfolio.
Instructions [53-57]:
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.
Instructions [58-60]:
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 in the space provided.
- However, they stand out because they help the film maker realize his personal artistic vision.
- An Indie film refers to independent films made outside a major studio system.
- Their release is also limited to a few screens, although there have been films with a wide release.
- Most of such films are low budget films produced and distributed by small companies.
- Mental illness continues to struggle for recognition as a significant contributor to poor health in spite of the existence of the Mental Healthcare Act 2017.
- The data reveals that an estimated one in seven Indians - or 197 million persons - suffered from mental disorders, at varying degrees of severity, in 2017.
- There is always more to human health than meets the eye.
- This is particularly important in the Indian cultural and political context, where the outward appearance of physical well-being is often considered the only visible marker of overall health.
- It was felt that the major polluters had a moral obligation to deliver on the agreements reached some years ago during a similar convention on Climate Change.
- The papers presented indicated that the impacts of current warming are much more severe than previously understood.
- It appears that the planet’s ability to adapt to and cope with how it is being treated is fraying.
- For example, the acceleration of sea level rise and ocean warming, and increasing risks of reaching limits to adaptation.
- This is what emerged at a recent conference attended by the largest scientific community on climate science.