List of top Questions asked in XAT

Consider the function f(x) = (x + 4)(x + 6)(x + 8) ⋯ (x + 98). The number of integers x for which f(x) < 0 is:

Let ABC be an isosceles triangle. Suppose that the sides AB and AC are equal and let the length of AB be x cm. Let b denote the angle ∠ABC and \(sin\ b = \frac 35\). If the area of the triangle ABC is M square cm, then which of the following is true about M?

We have two unknown positive integers m and n, whose product is less than 100.
There are two additional statement of facts available:
mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
m + n is a perfect square.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?

A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one fifth that of the circular base of the cylinder, then how many conical ingots can be made?

A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag.
There are two additional statement of facts available:
If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.
Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?

The figure below shows two right angled triangles ∆OAB and ∆OQP with right angles at vertex A and P, respectively, having the common vertex O, The lengths of some of the sides are indicated in the figure. (Note that the figure is not drawn to scale.) AB and OP are parallel.
What is ∠QOB?

A, B, C, D and E are five employees working in a company. In two successive years, each of them got hikes in his salary as follows:
A : p% and (p+1)%,
B : (p+2)% and (p-1)%,
C : (p+3)% and (p-2)%,
D : (p+4)% and (p-3)%,
E : (p+5)% and (p-4)%.
If all of them have the same salary at the end of two years, who got the least hike in his salary?

If \(\sqrt[3]{7^a\times35^{b+1}\times20^{c+2}} \) is a whole number then which one of the statements below is consistent with it?

A computer is sold either for Rs.19200 cash or for Rs.4800 cash down payment together with five equal monthly installments. If the rate of interest charged is 12% per annum, then the amount of each installment (nearest to a rupee) is:

In the picture below, EFGH, ABCD are squares, and ABE, BCF, CDG, DAH are equilateral triangles. What is the ratio of the area of the square EFGH to that of ABCD?

What is the maximum number of points that can be placed on a circular disk of radius 1 metre (some of the points could be placed on the bounding circle of the disk) such that no two points are at a distance of less than 1 metre from each other?

Study the first sentence and then identify from among the options given the closest antonym of the highlighted word in the second sentence:
It’s conventional wisdom that procreation between first cousins is unhealthy. But what are the actual genetic risks?

Which option does not reflect the relationship implicit in ‘Emendation : Editor’?

Choose the option that would fill in the blanks meaningfully in the sentence(s) below:
______ the importance of ‘horizontal stratification’ ______ higher education is widely acknowledged, ______ attention has been applied to horizontal stratification ______ compulsory schooling.

Carefully read the following paragraph:
Who could resist the idea of remembering everything they wanted to, without trying? Learning would be made easy, exams a ______ and you would never forget where you left your keys. And memory-related disorders like Alzheimer’s would have met their match. So, it is of little surprise that scientists have turned their attention to ways of ______ human memory using techniques that ______, supplement or even mimic parts of the brain. The immediate goal is to treat memory disorders, but the idea of a memory ______ for everyday life is gaining ground.
Fill in the blanks in the above paragraph, with the best option from among the following:

Please study the paragraph given below:
In 1942, the French writer Albert Camus composed an essay, ‘The Myth of Sisyphus’. It draws on the Greek fable of a man condemned to roll a rock up a mountain only to have it roll back down under its own weight, a ______ that lasts for eternity. Camus argues that this image ______ the human condition in a world where we can no longer make sense of events; but instead of committing suicide, we should ______ ourselves to this ‘elusive feeling of absurdity’ and bear it as best we can. In this sense, Sisyphus is the ideal hero.
Consider the following words:
1. surrender
2. choice
3. symbolises
4. quandary
5. attune
6. option
7. reconcile
8. depicts
Which of the following options is the most appropriate sequence that best fits the blanks in the above paragraph?

Read the following statements and answer the question that follows:
1. They subjected the residues from sherds of the rhyta- vessels to radiocarbon dating to determine their ages and chromatography - mass spectrometry (GC-MS) - to identify their structure and isotopic composition and found that the vessels were used to store cheese.
2. In many Neolithic sites near the Adriatic Sea, researchers unearthed cone-shaped clay vessels, known as rhyta, with four legs on the bottom and a round opening on the side.
3. Fresh milk couldn’t be kept for long without going bad; cheese, on the other hand, could be stored for months at a time, providing much-needed calories to early farmers between harvests.
4. Archaeologists who used to assume animals such as cows and goats were mainly used for meat early in their domestication history are thus forced to admit that humans might have been using animals for dairy quite early in their domestication history.
5. “If you kill one cow, you eat meat for about a week until it goes off; but by milking the animals, the farmer would be spreading the food gain from that animal over several months rather than just one week”
Rank the above five statements so as to make it a logical sequence:

Read the following statements and answer the question that follows:
1. An in-depth exploration of the Indian case and case studies of early adopters of mobile technology will provide spectrum managers a pragmatic and modern approach whereby they could utilize their resources efficiently and optimally.
2. Even as spectrum management regimes are moving from a command and control regime to a flexible use regime, new technological developments are suggesting that there are significant opportunities in managing large swathes of spectrum as a common property resource, in addition to flexible use.
3. Political legacies and market realities in different regimes pose unique challenges for spectrum managers who must negotiate a tricky path to the land promised by technological possibility.
4. On the other hand, supply of spectrum is restricted due to competing nature of uses and vested interests of incumbent holders.
5. The demand for spectrum has never been so acute as today's communication services extend beyond simple voice to complex data and video, augmented by evolving technologies such as peer-to-peer sharing, social networking, Fourth and Fifth Generation networks, Big Data, and cloud computing.
Rank the above five statements so as to make it a logical sequence:

Given below is the time table for a trans-continental train that cuts across several time zones. All timings are in local time in the respective cities. The average speed of the train between any two cities is the same in both directions.

The break-up of the students in a university by subject major is given in the polar pie-chart.The bar chart shows the number of students who major in physics by geographic location.

Read the following caselet and answer the questions that follow:
Due to increased competition, Electro Automobiles, the Indian subsidiary of Robert Automobile Company (RAC) reported lower sales and profits. RAC expects its new model Limo, developed especially for value conscious customers of India and China, would revive its fortunes. In order to prevent customers from buying competing products, RAC announced the launch of Limo six months ahead of schedule. Unrest in its Indian supplier resulted in delayed delivery of essential components to its main plant. Hence, Limo was launched on schedule only in China. Within a short span, Limo captured 30% of the Chinese market , which was 200% higher than expectation. Indian customers were becoming increasingly restless because they couldn't get a Limo in India. Electro’s dealers were worried, customers might switch to other cars.

Read the following caselet and answer questions that follow:
Divya grew up in a business family in Hyderabad. As a Systems engineer she travelled extensively on business deals and later settled in her in-law’s place in Warangal. Once during her visit to Thailand she got to taste some roll over ice cream. Interestingly, a few weeks later, she came across an advertisement from a reputed Bangalore based Rollover Handcrafted Ice Cream Company calling for expression of interest from potential franchises.
Warangal did not have any quality ice cream parlour. The company wanted the potential franchisees to invest Rs. 20 lacs and 700 square feet space. Profits were to be shared in 3:7 ratio between the company and the franchisee. Divya was excited, but was wondering if Rs. 20 lacs was too much to invest. Further, she did not have the entire amount and was thinking of taking a loan. She enquired with the Rollover franchisees and found that a franchisee in Hyderabad had sales revenue varying between 5 and 6 lacs rupees per month with a profit margin between 25-30%. Divya decided to go ahead.
Warangal had three main areas -Kazipet, Jangaon and Warangal. All areas were linked by good roads. Kazipet was a business area where most high end retail formats were located. It was also the education hub of the city. Jangaon, on the other hand, was a growing lower middle class business area and Warangal was mostly residential.
Divya favoured Kazipet. However, she soon encountered problems. Not only was it difficult to obtain space in Kazipet but property rentals touched 30-40 rupees per square feet per month as against Jangaon and Warangal where it was 15-20 rupees per square feet per month. Divya’s friend, who lived in Jangaon, told her that a few branded outlets were opening in Jangaon and it appeared to be the fastest growing market in Warangal with the highest percentage of teenagers. But, Divya was not in favour of Jangaon. She hoped to target college going crowd of Kazipet. High real estate prices in Kazipet and lower profitability estimate in Jangaon market confused Divya.

Read the following caselet and answer the questions that follow:
Mrs. Bhalla is the principal of ‘Happy Public School’. While it is a private school, the trust is socially sensitive and as part of their “Spread Happiness Policy” provides quality education to many needy students from low income neighborhood for free. She received a strange complaint from some of the affluent parents regarding their discomfort with allowing poor children to study along with their kids. They were concerned more about their manners, habits and language than about schooling. They wanted the trust to either start a separate shift for such children or remove them from the school since they are supporting them. On the other hand, the parents of the poor children complained of bullying and teasing and shared their concern regarding the mental trauma their children undergo. While Mrs. Bhalla, by no means wants to yield to the demands of the affluent parents, she also cannot ignore them since some of them have been making substantial donations to the school.

Read the following caselet and answer the questions that follow:
Thakur Raja, a young cabinet minister, glanced through the notes of his secretary regarding the recent controversies on ‘Racket’, the most popular game of the country. While International Racket Association (IRA) has agreed to implement Drug Testing Code (DTC), the Racket Club which controls the entire Racket related activities had some reservations regarding the initiative. A majority of the citizens eagerly awaited their country's participation and performance at the international competitions during the Champions Trophy. Due to the popularity of the game, 70% of the total revenue associated with the game originates from the country. Hence, the Racket Club has earned high bargaining power with the IRA and can influence decisions not aligned with its interests. Three of the most popular and senior players of the Club, including the captain, are against the imposition of DTC citing security reasons. A decision against the interests of these players might result in law and order problems throughout the country. Other players support the decision of their senior colleagues and if the Racket Club refuses, players may support the rebel Counter Racket Club, a new national level initiative. The Counter Racket Club can challenge the monopoly of the Racket Club, if it succeeds in attracting some popular players.
Raja was a great soccer player and has major reservations against racket. According to him, racket has negative influence on the country’s youth and distracts them from productive work. He also considers drug testing as an essential feature of any sports and games across the world. As the new cabinet minister for Youth and Sports, he needs to take some important decisions on this contentious issue.

Read the following caselet and answer questions that follow:
Sanchit group of Hospitals seeks to improve the success rate and patient satisfaction rate by 100% in the next year. However, the management can't afford to send doctors for professional development outside the country nor afford purchasing more equipment. As an in-house measure, the managing board thought of having doctors with high patient satisfaction to mentor those with less. Most of the doctors found it an interference by the management, judgmental and an expression of distrust. There were, however, some isolated few who found it a novel way of learning from each other. The doctors felt the management should instead increase consultancy fees and spend more on recruiting more paramedics who could spend time with patients, rather than blame doctors and decided to call it quits. For the management, this would mean loss of patients.