CAT preparatory questions, Exams of Information Technology

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• CAT 2022 Question Paper Slot

CAT Quants (Slot 2) Question 1- In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠BAC=45∘ and ∠ABC=θ, then ADBE equals A. 2√sinθ B. 2√cosθ C. (sinθ+cosθ)/2√ D. 1 Question 2- Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is Question 3- Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals Question 4- If a and b are non-negative real numbers such that a+2b=6, then the average of the maximum and minimum possible values of (a+b) is A. 4 B. 4. C. 3. D. 3 Question 5- Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be A. 4200 B. 4400 C. 4300 D. 4350 Question 6- There are two containers of the same volume, first container half-filled with sugar syrup and the second container half-filled with milk. Half the content of the first container is transferred to the second container, and then the half of this mixture is transferred back to the first container. Next, half the content of the first container is transferred back to the second container. Then the ratio of sugar syrup and milk in the second container is A. 5 : 6 B. 5 : 4 C. 6 : 5

A. 5

B. 7

C. 4

D. 6

Question 14- The number of distinct integer values of n satisfying 4−log2n/3−log4n<0, is Question 15- In an examination, there were 75 questions. 3 marks were awarded for each correct answer, 1 mark was deducted for each wrong answer and 1 mark was awarded for each unattempted question. Rayan scored a total of 97 marks in the examination. If the number of unattempted questions was higher than the number of attempted questions, then the maximum number of correct answers that Rayan could have given in the examination is Question 16- Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is A. 21 B. 24 C. 20 D. 22 Question 17- The number of integer solutions of the equation (x2−10)(x2−3x−10)= is Question 18- Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is Question 19- Consider the arithmetic progression 3,7,11,…and let An denote the sum of the first n terms of this progression. Then the value of 125∑25n=1An is A. 404 B. 442 C. 455 D. 415 Question 20- Let f(x) be a quadratic polynomial in x such that f(x)≥0 for all real numbers x. If f(2)=0 and f(4)=6, then f(−2) is equal to A. 12 B. 36 C. 24

D. 6

Question 21- The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in cm, is A. √ B. √ C. √ D. √ Question 22- Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is A. 12 B. 18 C. 20 D. 24

A few salesmen are employed to sell a product called TRICCEK among households in various housing complexes. On each day, a salesman is assigned to visit one housing complex. Once a salesman enters a housing complex, he can meet any number of households in the time available. However, if a household makes a complaint against the salesman, then he must leave the housing complex immediately and cannot meet any other household on that day. A household may buy any number of TRICCEK items or may not buy any item. The salesman needs to record the total number of TRICCEK items sold as well as the number of households met in each day. The success rate of a salesman for a day is defined as the ratio of the number of items sold to the number of households met on that day. Some details about the performances of three salesmen - Tohri, Hokli and Lahur, on two particular days are given below.

1. Over the two days, all three of them met the same total number of households, and each of them sold a total of 100 items.
2. On both days, Lahur met the same number of households and sold the same number of items.
3. Hokli could not sell any item on the second day because the first household he met on that day complained against him.
4. Tohri met 30 more households on the second day than on the first day.
5. Tohri's success rate was twice that of Lahur's on the first day, and it was 75% of Lahur's on the second day. Question 1- What was the total number of households met by Tohri, Hokli and Lahur on the first day? Question 2- How many TRICCEK items were sold by Tohri on the first day? Question 3- How many households did Lahur meet on the second day? A. 20 or less B. between 21 and 29 C. between 30 and 35 D. more than 35 Question 4- How many households did Tohri meet on the first day? A. more than 40 B. 10 or less C. between 11 and 20 D. between 21 and 40 Question 5- Which of the following statements is FALSE? A. Among the three, Tohri had the highest success rate on the first day. B. Tohri had a higher success rate on the first day compared to the second day. C. Among the three, Lahur had the lowest success rate on the first day. D. Among the three, Tohri had the highest success rate on the second day.

Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long. Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance. Question 6- If the last location visited is Ahmednagar, then what is the total distance covered in the route (in km)? Question 7- If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)? Question 8- What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore? A. 10.80% B. 33.33% C. 7.56%

C. At least 10 and at most 80 D. At least 20 and at most 70 Question 14- If 70 cosmetic products did not have EU approval, then how many nutrition products had both the approvals? A. 10 B. 30 C. 50 D. 20 Question 15- If 50 nutrition products did not have EU approval, then how many domestic cosmetic products did not have EU approval? The two plots below show data for four companies code-named A, B, C, and D over three years - 2019, 2020, and 2021. The first plot shows the revenues and costs incurred by the companies during these years. For example, in 2021, company C earned Rs.100 crores in revenue and spent Rs.30 crores. The profit of a company is defined as its revenue minus its costs. The second plot shows the number of employees employed by the company (employee strength) at the start of each of these three years, as well as the number of new employees hired each year (new hires). For example, Company B had 250 employees at the start of 2021, and 30 new employees joined the company during the year.

Question 16- Considering all three years, which company had the highest annual profit? A. Company C B. Company B C. Company A D. Company D Question 17- Which of the four companies experienced the highest annual loss in any of the years? A. Company D B. Company C C. Company A D. Company B Question 18- The ratio of a company's annual profit to its annual costs is a measure of its performance. Which of the four companies had the lowest value of this ratio in 2019? A. Company A B. Company B C. Company C D. Company D Question 19- The total number of employees lost in 2019 and 2020 was the least for: A. Company A B. Company C C. Company B

CAT VARC (Slot 2)

The passage below is accompanied by a set of questions. Choose the best answer to each question. [Octopuses are] misfits in their own extended families... They belong to the Mollusca class Cephalopoda. But they don't look like their cousins at all. Other molluscs include sea snails, sea slugs, bivalves - most are shelled invertebrates with a dorsal foot. Cephalopods are all arms, and can be as tiny as 1 centimetre and as large at 30 feet. Some of them have brains the size of a walnut, which is large for an invertebrate.... It makes sense for these molluscs to have added protection in the form of a higher cognition; they don't have a shell covering them, and pretty much everything feeds on cephalopods, including humans. But how did cephalopods manage to secure their own invisibility cloak? Cephalopods fire from multiple cylinders to achieve this in varying degrees from species to species. There are four main catalysts - chromatophores, iridophores, papillae and leucophores.... [Chromatophores] are organs on their bodies that contain pigment sacs, which have red, yellow and brown pigment granules. These sacs have a network of radial muscles, meaning muscles arranged in a circle radiating outwards. These are connected to the brain by a nerve. When the cephalopod wants to change colour, the brain carries an electrical impulse through the nerve to the muscles that expand outwards, pulling open the sacs to display the colours on the skin. Why these three colours? Because these are the colours the light reflects at the depths they live in (the rest is absorbed before it reaches those depths).... Well, what about other colours? Cue the iridophores. Think of a second level of skin that has thin stacks of cells. These can reflect light back at different wavelengths.... It's using the same properties that we've seen in hologram stickers, or rainbows on puddles of oil. You move your head and you see a different colour. The sticker isn't doing anything but reflecting light - it's your movement that's changing the appearance of the colour. This property of holograms, oil and other such surfaces is called "iridescence".... Papillae are sections of the skin that can be deformed to make a texture bumpy. Even humans possess them (goosebumps) but cannot use them in the manner that cephalopods can. For instance, the use of these cells is how an octopus can wrap itself over a rock and appear jagged or how a squid or cuttlefish can imitate the look of a coral reef by growing miniature towers on its skin. It actually matches the texture of the substrate it chooses. Finally, the leucophores: According to a paper, published in Nature, cuttlefish and octopuses possess an additional type of reflector cell called a leucophore. They are cells that scatter full spectrum light so that they appear white in a similar way that a polar bear's fur appears white. Leucophores will also reflect any filtered light shown on them... If the water appears blue at a certain depth, the octopuses and cuttlefish can appear blue; if the water appears green, they appear green, and so on and so forth.

mould and plan them. We have family law, established and disestablished churches, constitutions and laws, including those governing the economy and the military. Institutions deriving from statute, like joint-stock companies are formal by contrast with informal ones such as friendships. There are some institutions that come in both informal and formal variants, as well as in mixed ones. Consider the fact that the stock exchange and the black market are both market institutions, one formal one not. Consider further that there are many features of the work of the stock exchange that rely on informal, noncodifiable agreements, not least the language used for communication. To be precise, mixtures are the norm... From constitutions at the top to by-laws near the bottom we are always adding to, or tinkering with, earlier institutions, the grown and the designed are intertwined. It is usual in social thought to treat culture and tradition as different from, although alongside, institutions. The view taken here is different. Culture and tradition are sub-sets of institutions analytically isolated for explanatory or expository purposes. Some social scientists have taken all institutions, even purely local ones, to be entities that satisfy basic human needs - under local conditions... Others differed and declared any structure of reciprocal roles and norms an institution. Most of these differences are differences of emphasis rather than disagreements. Let us straddle all these versions and present institutions very generally... as structures that serve to coordinate the actions of individuals.... Institutions themselves then have no aims or purpose other than those given to them by actors or used by actors to explain them.. . Language is the formative institution for social life and for science... Both formal and informal language is involved, naturally grown or designed. (Language is all of these to varying degrees.) Languages are paradigms of institutions or, from another perspective, nested sets of institutions. Syntax, semantics, lexicon and alphabet/character-set are all institutions within the larger institutional framework of a written language. Natural languages are typical examples of what Ferguson called 'the result of human action, but not the execution of any human design'[;] reformed natural languages and artificial languages introduce design into their modifications or refinements of natural language. Above all, languages are paradigms of institutional tools that function to coordinate. Question 5- "Consider the fact that the stock exchange and the black market are both market institutions, one formal one not." Which one of the following statements best explains this quote, in the context of the passage? A. The stock exchange and the black market are both organised to function by rules. B. Market instruments can be formally traded in the stock exchange and informally traded in the black market. C. The stock exchange and the black market are both dependent on the market to survive. D. The stock exchange and the black market are examples of how, even within the same domain, different kinds of institutions can co-exist. Question 6- All of the following inferences from the passage are false, EXCEPT:

A. "natural language" refers to that stage of language development where no conscious human intent is evident in the formation of language. B. the institution of friendship cannot be found in the institution of joint-stock companies because the first is an informal institution, while the second is a formal one. C. as concepts, "culture" and "tradition" have no analytical, explanatory or expository power, especially when they are treated in isolation. D. institutions like the family, rituals, governance, economy, and the military are natural and cannot be consciously modified. Question 7- Which of the following statements best represents the essence of the passage? A. Institutions are structures that serve to coordinate the actions of individuals. B. It is usual in social thought to treat culture and tradition as different from institutions. C. Language is the fundamental formal institution for social life and for science. D. The stock exchange and the black market are both market institutions. Question 8- In the first paragraph of the passage, what are the two "characterisations" that are seen as overlapping but not congruent? A. "the philosophy of the social sciences" and "a set of social institutions". B. "academic disciplines" and "institutions". C. "an arena of thought" and "academic disciplines". D. "individuals" and "social structures". The passage below is accompanied by a set of questions. Choose the best answer to each question. When we teach engineering problems now, we ask students to come to a single "best" solution defined by technical ideals like low cost, speed to build, and ability to scale. This way of teaching primes students to believe that their decision-making is purely objective, as it is grounded in math and science. This is known as technical-social dualism, the idea that the technical and social dimensions of engineering problems are readily separable and remain distinct throughout the problem-definition and solution process. Nontechnical parameters such as access to a technology, cultural relevancy or potential harms are deemed political and invalid in this way of learning. But those technical ideals are at their core social and political choices determined by a dominant culture focused on economic growth for the most privileged segments of society. By choosing to downplay public welfare as a critical parameter for engineering design, we risk creating a culture of disengagement from societal concerns amongst engineers that is antithetical to the ethical code of engineering. In my field of medical devices, ignoring social dimensions has real consequences.... Most FDA-approved drugs are incorrectly dosed for people assigned female at birth, leading to unexpected adverse reactions. This is because they have been inadequately represented in clinical trials.

A. "And we hardly question whether devices are built sustainably, which has led to a crisis of medical waste and health care accounting for 10 percent of U.S. greenhouse gas emissions." B. "These racially based adjustments are derived from research done by eugenicists who thought these racial differences were biologically determined and who considered nonwhite people as inferior." C. "Beyond physical failings, subjective beliefs treated as facts by those in decision-making roles can encode social inequities." D. "But those technical ideals are at their core social and political choices determined by a dominant culture focused on economic growth for the most privileged segments of society." Question 11- All of the following are examples of the negative outcomes of focusing on technical ideals in the medical sphere EXCEPT the: A. incorrect assignment of people as female at birth which has resulted in faulty drug interventions. B. exclusion of non-privileged groups in clinical trials which leads to incorrect drug dosages. C. neglect of research and development of medical technologies for the diagnosis and treatment of diseases that typically afflict marginalised communities. D. continuing calibration of medical devices based on past racial biases that have remained unadjusted for changes. Question 12- We can infer that the author would approve of a more evolved engineering pedagogy that includes all of the following EXCEPT: A. moving towards technical-social dualism where social community needs are incorporated in problem-definition and solutions. B. making considerations of environmental sustainability intrinsic to the development of technological solutions. C. design that is based on the needs of communities using local knowledge and responding to local priorities. D. a more responsible approach to technical design and problem-solving than a focus on speed in developing and bringing to scale. The passage below is accompanied by a set of questions. Choose the best answer to each question. Humans today make music. Think beyond all the qualifications that might trail after this bald statement: that only certain humans make music, that extensive training is involved, that many societies distinguish musical specialists from nonmusicians, that in today's societies most listen to music rather than making it, and so forth. These qualifications, whatever their local merit, are moot in the face of the overarching truth that making music, considered from a cognitive and psychological vantage, is the province of all those who perceive and experience what is made. We are, almost all of us, musicians - everyone who can entrain (not necessarily dance) to a beat, who can recognize a repeated tune (not necessarily sing it), who can distinguish one

instrument or one singing voice from another. I will often use an antique word, recently revived, to name this broader musical experience. Humans are musicking creatures.... The set of capacities that enables musicking is a principal marker of modern humanity. There is nothing polemical in this assertion except a certain insistence, which will figure often in what follows, that musicking be included in our thinking about fundamental human commonalities. Capacities involved in musicking are many and take shape in complicated ways, arising from innate dispositions... Most of these capacities overlap with nonmusical ones, though a few may be distinct and dedicated to musical perception and production. In the area of overlap, linguistic capacities seem to be particularly important, and humans are (in principle) language-makers in addition to music-makers - speaking creatures as well as musicking ones. Humans are symbol-makers too, a feature tightly bound up with language, not so tightly with music. The species Cassirer dubbed Homo symbolicus cannot help but tangle musicking in webs of symbolic thought and expression, habitually making it a component of behavioral complexes that form such expression. But in fundamental features musicking is neither language-like nor symbol-like, and from these differences come many clues to its ancient emergence. If musicking is a primary, shared trait of modern humans, then to describe its emergence must be to detail the coalescing of that modernity. This took place, archaeologists are clear, over a very long durée: at least 50,000 years or so, more likely something closer to 200,000, depending in part on what that coalescence is taken to comprise. If we look back 20,000 years, a small portion of this long period, we reach the lives of humans whose musical capacities were probably little different from our own. As we look farther back we reach horizons where this similarity can no longer hold - perhaps 40,000 years ago, perhaps 70,000, perhaps 100,000. But we never cross a line before which all the cognitive capacities recruited in modern musicking abruptly disappear. Unless we embrace the incredible notion that music sprang forth in full-blown glory, its emergence will have to be tracked in gradualist terms across a long period. This is one general feature of a history of music's emergence... The history was at once sociocultural and biological... The capacities recruited in musicking are many, so describing its emergence involves following several or many separate strands. Question 13- Which one of the following sets of terms best serves as keywords to the passage? A. Musicking; Cognitive psychology; Antique; Symbol-makers; Modernity. B. Humans; Psychological vantage; Musicking; Cassirer; Emergence of music. C. Humans; Capacities; Language; Symbols; Modernity. D. Humans; Musicking; Linguistic capacities; Symbol-making; Modern humanity.