List of top Questions asked in XAT

Consider the quadratic function \( f(x) = ax^2 + bx + a \) having two irrational roots, with \( a \) and \( b \) being two positive integers, such that \( a, b \leq 9 \). If all such permissible pairs \( (a, b) \) are equally likely, what is the probability that \( a + b \) is greater than 9?
A farmer has a quadrilateral parcel of land with a perimeter of 700 feet. Two opposite angles of that parcel of land are right angles, while the remaining two are not. The farmer wants to do organic farming on that parcel of land. The cost of organic farming on that parcel of land is Rs. 400 per square foot.
Consider the following two additional pieces of information:
1. The length of one of the sides of that parcel of land is 110 feet.
2. The distance between the two corner points where the non-perpendicular sides of that parcel of land intersect is 265 feet.
To determine the amount of money the farmer needs to spend to do organic farming on the entire parcel of land, which of the above additional pieces of information are MINIMALLY SUFFICIENT?
A straight line \( L_1 \) has the equation \( y = k(x - 1) \), where \( k \) is some real number. The straight line \( L_1 \) intersects another straight line \( L_2 \) at the point (5, 8). If \( L_2 \) has a slope of 1, which of the following is definitely FALSE?
For how many distinct real values of \( x \) does the equation below hold true? (Consider \( a>0 \)) \[ x^2 \log_a (16) - \log_a (64) \div \log_a (32) - x = 0 \]
In a computer game, each move requires pressing a button. When the button is pressed for the first time, as a move, the computer randomly chooses a cell from a 4x4 grid of sixteen cells and puts an "X" mark on that cell. When the button is pressed subsequently, the computer randomly chooses a cell from the remaining unmarked cells and puts an "X" mark on that cell. This goes on till the end of the game. The game ends when either all the cells in any one row, or all the cells in any one column, are marked with "X". What is the maximum possible number of times a player has to press the button to finish the game?
There are five dustbins along a circular path at different places. Ramesh takes multiple rounds of the path every morning, always at the same speed. He noticed that it took him a different number of steps to walk between any two consecutive dustbins. Ramesh also noticed that starting from any of the dustbins, it took a minimum 360 steps to reach every second dustbin, and a maximum 1260 steps to reach every third dustbin. If Ramesh's step size is 0.77 meter, and the width of the path is negligible, which of the following can be the radius of the circular path?
Eight employees of an organization have been rated on a scale of 1 to 50 for their performance. All ratings are integers. The overall average rating of the eight employees is 30. While the five employees with the highest ratings average 38, the five employees with the lowest ratings average 25. Which of the following, about the ratings obtained by the eight employees, is DEFINITELY FALSE?
Arun selected an integer \( x \) between 2 and 40, both inclusive. He noticed that the greatest common divisor of the selected integer \( x \) and any other integer between 2 and 40, both inclusive, is 1. How many different choices for such an \( x \) are possible?
An industrial robot manufacturing company is tasked to design humanoid robots to be used in warehouses where the robots need to pick items from a stack of shelves. The height of the topmost shelf from the ground is 7 feet. To operate, the robot has to move on a track, running parallel to the stack of shelves. The track is fixed 1 foot away from the base of the stack of shelves. Further, the robot cannot bend its arms by more than 60° from the horizontal plane. If the robot’s arms are attached to its shoulder, what should be the minimum height of the robot from the ground to the shoulder for its arms to reach the topmost shelf?
A solid trophy, consisting of two parts, has been designed in the following manner: the bottom part is a frustum of a cone with the bottom radius 30 cm, the top radius 20 cm, and height 40 cm, while the top part is a hemisphere with radius 20 cm. Moreover, the flat surface of the hemisphere is the same as the top surface of the frustum. If the entire trophy is to be gold-plated at the cost of Rs. 40 per square cm, what would the cost for gold-plating be closest to?
If \( a, b, c \) are all positive integers, with \( 4a>b \), then which of the following conditions is BOTH NECESSARY AND SUFFICIENT for the expression \[ \sqrt{(3)^a (21)^{3a-b} (49)^{2b+c}} \] to be a positive integer?
Read the following sentences carefully.
A. There are less cars on the road today.
B. She is nicer than her sister.
C. I have been here from Monday.
D. I know how to swim.
E. She is the girl that won the case competition.
F. The media are divided on the issue.
Which of the following options contains only grammatically CORRECT sentences?
Read the following sentences carefully.
A. The dean asked for additional funding.
B. The boss discussed about the new project with his team.
C. Radhika is good in data interpretation.
D. Neil is transitioning into a new phase of life.
E. Rajat emphasized on the need for consistency in XAT preparation.
F. This car is superior to the previous one in terms of efficiency.
Which of the following options contains only grammatically CORRECT sentences?
When each ...... generation grows up, it looks down on the next as if we all forget what it feels like to be ............ When most ............ think about their own youthful indiscretions they do so with a wink and a laugh. But when the same people think about those in today’s generation doing something similar, they .................. sound the alarm about a decline in morality in next generation.
From the options below, choose the one that meaningfully fills up the blanks.
Read the following statement carefully.
A. Whatever that might be on Europa—far from the Sun, and beneath kilometres of ice—it will not be sunlight.
B. The final ingredient for a habitable world is a source of energy for life to exploit.
C. On Earth almost every living thing ultimately depends on photosynthesis for its energy, including the rich ecosystems in the ocean depths, discovered in the 1980s and which helped the idea of life on Europa gain a foothold.
D. Their inhabitants do not benefit from sunlight directly, but their metabolisms are powered by chemicals created in the photosynthesising, oxygen-rich surface oceans far above.
E. That is a bit of a problem.
Fill in the blanks meaningfully, in the above statement, from the following options.
Employees complaining about mundane tasks are often ignored. There is a listlessness that settles around them. A bored employee may continue to produce good results, but that can also be because the tasks are repetitive, and the outcomes are expected.
Which of the following options can be BEST inferred from the passage?
No man knows how bad he is till he has tried very hard to be good. A silly idea is current that good people do not know what temptation means. This is an obvious lie. Only those who try to resist temptation know how strong it is. After all, you find out the strength of the German army by fighting against it, not by giving in. You find out the strength of a wind by trying to walk against it, not by lying down. A man who gives in to temptation after five minutes simply does not know what it would have been like an hour later. That is why bad people, in one sense, know very little about badness — they have lived a sheltered life by always giving in.
Which of the following options can be BEST concluded from the passage?
Read the following paragraph and answer the question that follows. A. The treaty tests of a budget deficit no bigger than 3% of the GDP and a public debt converging towards a ceiling of 60% of a GDP seemed impossible for Italy to pass by 1999.
B. That Belgium also had a public debt above 100 percent of GDP helped, as did a special euro tax Mr. Prodi introduced.
C. Into the uncompromising environment came the first of a series of external shocks. One of the earliest was entry into the European single currency, the euro, in 1999.
D. But when it became clear in 1997 that Spain was determined to join from the start, Romano Prodi, then Italian prime minister, decided that Italy, as a founder member of the bloc, must be there too.
E. Germany had more or less designed the 1992 Maastricht treaty’s convergence criteria to keep out a profligate, chronically indebted Italy.
Which of the following sequences is the MOST logically ordered?
Observe the cartoon below carefully and answer the question that follows. (Cartoon by Tom Toro, originally published in The New Yorker on November 18, 2024. Used for educational purpose.)
Which of the following options BEST explains the underlying message depicted in the cartoon?
Read the following passage and answer the question that follows. \textit{Passage:} The lovely thing about the unsayable is that it is unsaid. As soon as it is said, it is sayable and loses all its mystery and ambiguity. Art exists so that the unsayable can be said without having to actually say it. We cloud it in secrecy and obfuscation. The mind is free to roam and all things can be imagined, under the cover of darkness. How nice that is. The unsayable. How tired we are of having things explained to us. Having things said. How nice it is when people just shut ... up. Which of the following options can be BEST inferred from the passage?

The diagram below represents a road network connecting five towns, namely Meeren, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown in the diagram. The straight road that connects Meeren to Gulltown passes through Oldtown. Another straight road, running west to east, connecting Meeren to Winterfell, passes through Lannisport. Further, two straight roads, one from Lannisport to Oldtown and another from Winterfell to Gulltown, are perpendicular to the road joining Meeren to Winterfell, and run from south to north.

Consider a car always travelling at the maximum permissible speed, and always taking the shortest route. It takes 1 hour to reach Oldtown from Meeren, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown. (For this problem, always consider the shortest route in terms of distance.)

The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.

GadRev is a rm that reviews different latest gadgets through a team of four reviewers (R1, R2, R3, and R4). Recently the reviewers reviewed four different tech gadgets (A, B, C, and D) on a scale of 1 to 5 (all integer values) where 1 denotes poor and 5 denotes excellent. These review ratings were then tabulated. However, due to a technical glitch, some of these ratings got deleted. The average rating given by each reviewer, and the average rating given to each gadget were earlier communicated to the team management in a separate email and hence can be useful to retrieve the deleted ratings. The available ratings along with the average ratings are represented in the following table:

In an 8-week course, a professor administered a test at the end of each week. Each of the eight tests was scored out of 4 marks, and a student could only receive a non-negative integer score. Two students, Ravi and Sumana, took the eight tests. 
In the first test, Ravi and Sumana scored the same marks. From the second to eighth tests, Ravi scored the exact same non-zero marks. Sumana scored the same marks as Ravi from the fifth test onwards. Ravi’s total marks in the first three tests was the same as Sumana’s total marks in the first two tests. Also, Sumana’s marks in the first test, total marks of the first two tests, and total marks of the eight tests are in a geometric progression.

Sundaram Stores operated in a gated community, situated about 30 Kilometers away from the main town. The store owner Mr. Sundareswaran Pichaimuthu, or Sundaram as he was called by everyone, secured a space in the gated society through a competitive bidding process. The residents’ association, led by Mr. Thangamoorthy Selvaganapathy, selected Sundaram over three other bidders, based on his willingness to pay the highest rent. Desperate to augment his post-retirement income, Sundaram agreed to pay a very high rent, banking on the prospect of generating exceptional revenue from the gated community. 
Sundaram was awarded the contract to establish the store, with provisions for a review every three years. Feeling elated during the meeting with the residents’ association to finalize the contract, he enthusiastically committed to offering a 15% discount on all groceries and stationary, cementing goodwill and reinforcing the partnership established through the contract. The association was delightedly taken aback by his generous assurance. Sundaram hoped to make up the difference through volume.
Although his sales were strong during the initial months, he soon realized that the SUV-owning residents of the gated community primarily made their purchases at large, branded retail chains in the main town. These stores offered deeper discounts, which he could not afford to compete with. However, gradually, Sundaram store became their go-to store for daily essentials and occasional urgent big purchases such as replacing a broken mixer-grinder.