Official XAT 2021 Paper – Questions, Answers, and Detailed Solutions

XAT 2021 Questions and Answers – Quantitative Aptitude

Q.1 Mohan has some money (₹M) that he divides in the ratio of 1:2. He then deposits the smaller amount in a savings scheme that offers a certain rate of interest, and the larger amount in another savings scheme that offers half of that rate of interest. Both interests compound yearly. At the end of two years, the total interest earned from the two savings schemes is ₹830. It is known that one of the interest rates is 10% and that Mohan deposited more than ₹1000 in each saving scheme at the start. What is the value of M?
Q.2 Mr. Jose buys some eggs. After bringing the eggs home, he finds two to be rotten and throws them away. Of the remaining eggs, he puts five-ninth in his fridge, and brings the rest to his mother’s house. She cooks two eggs and puts the rest in her fridge. If her fridge cannot hold more than five eggs, what is the maximum possible number of eggs bought by Mr. Jose?
Q.3 At any point of time, let x be the smaller of the two angles made by the hour hand with the minute hand on an analogue clock (in degrees). During the time interval from 2:30 p.m. to 3:00 p.m., what is the minimum possible value of x?
Q.4 One third of the buses from City A to City B stop at City C, while the rest go non-stop to City B. One third of the passengers, in the buses stopping at City C, continue to City B, while the rest alight at City C. All the buses have equal capacity and always start full from City A. What proportion of the passengers going to City B from City A travel by a bus stopping at City C?
Q.5 If log(base 4)m + log(base 4)n = log(base 2)(m+n), where m and n are positive real numbers, then which of the following must be true?
Q.6 A small store has five units of a new phone model in stock: two white, two black, and one red. Three customers arrive at the shop to buy a unit each. Each one has a predetermined choice of the colour and will not buy a unit of any other colour. All the three customers are equally likely to have chosen any of the three colours. What is the probability that the store will be able to satisfy all the three customers?
Q.7 Two circles P and Q, each of radius 2 cm, pass through each other’s centres. They intersect at points A and B. A circle R is drawn with diameter AB. What is the area of overlap (in square cm) between the circles R and P?
Q.8 Swati can row a boat on still water at a speed of 5 km/hr. However, on a given river, it takes her 1 hour more to row the boat 12 km upstream than downstream. One day, Swati rows the boat on this river from X to Y, which is N km upstream from X. Then she rows back to X immediately. If she takes at least 2 hours to complete this round trip, what is the minimum possible value of N?
Q.9 The six faces of a wooden cube of side 6 cm are labelled A, B, C, D, E and F respectively. Three of these faces A, B, and C are each adjacent to the other two, and are painted red. The other three faces are not painted. Then, the wooden cube is neatly cut into 216 little cubes of equal size. How many of the little cubes have no sides painted?
Q.10 Rajesh, a courier delivery agent, starts at point A and makes a delivery each at points B, C and D, in that order. He travels in a straight line between any two consecutive points. The following are known……
Q.11 On the bank of the pristine Tunga river, a deer and a tiger are joyfully playing with each other. The deer notices that it is 40 steps away from the tiger and starts running towards it. At the same time, the tiger starts running away from the deer. Both run on the same straight line. For every five steps the deer takes, the tiger takes six. However, the deer takes only two steps to cover the distance that the tiger covers in three. In how many steps can the deer catch the tiger?
Q.12 An encryption system operates as follows:
Step 1. Fix a number k (k≤26).
Step 2. For each word, swap the first k letters from the front with the last k letters from the end in reverse order. If a word contains less than 2k letters, write the entire word in reverse order….

Q.13 Let f(x) = x^2+1/x^2-1 if x ≠ 1, -1, and 1 if x = 1, -1. Let g(x) = x+1/x-1 if x ≠ 1, and 3 if x=1. What is the minimum possible value of f(x)/g(x) ?
Q.14 The following plot describes the height (in cm), weight (in kg), age (in years) and gender (F for female, M for male) of 20 patients visiting a hospital….
Q.15 ABC is a triangle with integer-valued sides AB = 1, BC >1, and CA >1. If D is the midpoint of AB, then, which of the following options is the closest to the maximum possible value of the angle ACD (in degrees)?
Q.16 Four friends, Ashish, Brian, Chaitra, and Dorothy, decide to jog for 30 minutes inside a stadium with a circular running track that is200 metres long. The friends run at different speeds. Ashish completes a lap exactly every 60 seconds. Likewise, Brian, Chaitra and Dorothy complete a lap exactly every 1 minute 30 seconds, 40 seconds and 1 minute 20 seconds respectively. The friends begin together at the start line exactly at 4 p.m. What is the total of the numbers of laps the friends would have completed when they next cross the start line together ?
Q.17 Zahir and Raman are at the entrance of a dark cave. To enter this cave, they need to open a number lock. Raman sees a note on a rock: “ … chest of pure diamonds kept for the smart one … number has six digits … second last digit is 2, third last is 4 … divisible by all prime numbers less than 15 …”. Excited, Zahir and Raman seek your help: which of these can be the first digit of the six-digit number that will help them open the lock?
Q.18 A company awards incentives to its employees for successful project performances. It rates successful project performance in categories A*, A, B, and C. Employees, in solo projects rated A*, A, B, and C, are awarded incentives ₹6 lakh, ₹5 lakh, ₹3 lakh, and ₹1 lakh respectively. When a project has multiple team members, the following scheme is used to award the incentives…
Q.19 Rahul has just made a 3 x 3 magic square, in which, the sum of the cells along any row, column or diagonal, is the same number N. the entries in the cells are given as expressions in x, y, and z. find N.
Q.20 Find z, if it is known that:
a. -y^2 + x^2 = 20,
b. y^3 – 2x^2 – 4z ≥ -12 and

Q.21 The topmost point of a perfectly vertical pole is marked A. The pole stands on a flat ground at point D. The points B and C are somewhere between A and D on the pole. From a point E, located on the ground at a certain distance from D, the points A, B and C are at angles of 60, 45 and 30 degrees respectively. What is AB : BC : CD?
Q.22 A quick survey at the end of a purchase at asks the following three questions to each shopper:
1. Are you shopping at the website for the first time? (YES or NO)
2. Specify your gender: (MALE or FEMALE)

XAT 2021 Questions and Answers – English

Q.1 Behavioral models in finance most often critique the efficient market hypothesis, which states that if investors behave rationally then prices should reflect all available information about the financial asset in consideration.
Q.2 While start-ups have__________ reach, _____ they introduce ________ products, they open-up ________ markets.
Q.3 1. Some countries are, at least, trying to curb emissions.
2. Morocco is building a colossal solar-power plant in the desert……

Q.4 Which of the following sentences uses a WRONG tag-question.
Q.5 Sit, drink your coffee here; your work can wait awhile.
You’re twenty-six, and still have some of life ahead.

Q.6 And that has to do with the question of uncertainty and doubt. A scientist is never certain. We all know that. We know that all our statements are approximate statements with different degrees of certainty; that when a statement is made,…..
Q.7 Most of recorded human history is one big data gap. Starting with the theory of Man the Hunter, the chroniclers of the past have left little space for women’s role in the evolution of humanity, whether cultural or biological. …
Q.8 In my opinion, Tom Jones is a picaresque novel….
Q.9 We can think of the history of life on earth as a vast, long-term experiment in pure competition. Every living organism is competing with all other living organisms for resources (nutrients, sunlight, water, territory, etc.)…..
Q.10 Twitter is not on the masthead of a newspaper. But Twitter has become its ultimate editor…..
Q.11 We are going to a restaurant but we haven’t decided which one……
Q.12 Considering the multitude of situations in which we humans use numerical information, life without numbers is inconceivable. But what was the benefit of numerical competence for our ancestors, before they became Homo sapiens? …..
Q.13 The painting, which is in poor condition, suggests that a highly advanced artistic culture existed some 44,000 years ago, punctuated by folklore, religious myths and spiritual belief……
Q.14 Para 1: We plan to right-size our manufacturing operations to align to the new strategy and take advantage of integration opportunities. We expect to focus phone production mainly in Hanoi,……
Q.15 We stand before this great world. The truth of our life depends upon our attitude of mind towards it – an attitude which is formed by our habit of dealing with it according to the special circumstance of our surroundings and our temperaments…….
Q.16 Multitasking has been found to increase the production of the stress hormone cortisol as well as the fight-or-flight hormone adrenaline, which can overstimulate your brain and cause mental fog or scrambled thinking……..
Q.17 Multitasking has been found to increase the production of the stress hormone cortisol as well as the fight-or-flight hormone adrenaline, which can overstimulate your brain and cause mental fog or scrambled thinking……..

XAT 2021 Questions and Answers – Decision Making

Q.1 Ashraf has been working at a cybersecurity company called NuTech Pvt. Ltd. for seven years. Having missed a promotion in the previous appraisal cycle, Ashraf is anxious about it in the upcoming cycle. Ashraf is aware that the HR head is meeting….
Q.2 Saradeep was the proprietor of Saradeep & Sons Pvt. Ltd., an auto parts manufacturing company. He had three children–Taapsi, Kesar and Sandeep. His wife passed away when Sandeep, the youngest kid of the family, was only eight years old. Taapsi, being the eldest sibling, was more of a mother to Kesar and Sandeep…
Q.3 Himaja was among the top ten students of her Business Management batch. She got placed in a reputed strategy consulting firm during campus placements. She was delighted to work under Nirmal, her superior, who was known for grooming many stars in the organisation….
Q.4 Rohini is one of the most popular faculty members in the finance department, known for her in-class engagement with students. Every year, she offers an elective Financial Risk and Derivatives Management…
Q.5 Churna is a peaceful village, surrounded by thickly forested high hills that isolate it from the rest of the world. Agriculture is the main occupation of the Churna villagers. Moreover, the forests provide seasonal fruits…
Q.6 The occasion was a hyper publicised switch-on ceremony of solar power facilities on an island, with many villages, in the Bay of Bengal. PK was the brand ambassador of a Multinational Company (MNC) that was banking heavily on this CSR…
Q.7 Amish is the marketing head of an e-commerce firm named FillInCart (FICT). Recently, FICT signed a contract with a top celebrity to endorse their firm. A few months later, the celebrity was signed as the ambassador to promote tourism in a small country..
Q.8 Amish is the marketing head of an e-commerce firm named FillInCart (FICT). Recently, FICT signed a contract with a top celebrity to endorse their firm. A few months later, the celebrity was signed as the ambassador to promote tourism in a small country..

XAT 2021 Questions and Answers – General Knowledge

Q.1 Which of the following will be a debut event in the Summer Olympics of 2024?
Q.2 Which of the following mountain ranges houses the famous pilgrimage Amarkantak?
Q.3 Who was the first woman chief minister in Independent India?
Q.4 Who is the chief minister of Jharkhand as of 31st December 2020?
Q.5 Match the following wild animal species with the national parks/wildlife sanctuaries where they naturally occur in India:…
Q.6 Vijay Prashad’s discussion event at the online Tata Literature Live!,2020, was cancelled. Who was to feature in the discussion with Vijay Prashad?
Q.7 Who was recently appointed as the CEO of Cafe Coffee Day?
Q.8 Which of the following is not an online learning application?
Q.9 The first woman to lead a listed Indian Information Technology (IT) company is?
Q.10 Which of the following is a Danish dependency?
Q.11 From which organisation was Timnit Gebru terminated recently?
Q.12 Which is the first GI tagged product in India?
Q.13 What is Hayabusa2?
Q.14 Who authored the famous book Economy of Permanence?
Q.15 Which Indian business group built the British Royal Navy ship, HMS Minden, on which the lyrics of the national anthem of the United States of America was supposedly written?
Q.16 Arecibo telescope, known for its stellar contributions in the field of astronomy, collapsed recently. Where was it located?
Q.17 In India, where did Mahatma Gandhi stage his first major Satyagraha in 1917?
Q.18 Who was the first Indian to win the Global Teacher Prize?
Q.19 15-year old Gitanjali Rao was recently in the news. Which of the following best describes her?
Q.20 Which Wildlife Sanctuary/National Park is identified and prepared to translocate Asiatic Lions from Gir National Park, Gujarat?
Q.21 Dries Mertens, recently became the highest goal-scorer for the football club Napoli by surpassing the tally of 115 goals across all competitions. Whose goal scoring record did he surpass?
Q.22 Which of the following is not an OECD (Organization for Economic Cooperation and Development) member?
Q.23 The table below lists countries and capital cities
Countries Capital Cities P. Jamaica 1. Port Of Spain Q. Cuba 2. Havana R. Guyana 3. Kingston S. Trinidad and Tobago 4. Georgetown

Q.24 Tedros Adhanom has been in the news for the last one year for being?
Q.25 What is the Nagorno-Karabakh conflict?