University of Madras, Chennai
Question : Direction: In the following question, select the one which is different from the other three alternatives.
Option 1: 41 - 72
Option 2: 12 - 30
Option 3: 51 - 42
Option 4: 11 - 20
Correct Answer: 41 - 72
Solution : Let's check the options —
First option: 41 - 72; 4 + 1 = 5; 7 + 2 = 9. The sum of the digits of the two numbers is not equal. This option is different from the other options.
Second option: 12
Question : Comprehension: Read the given passage and answer the questions that follow. It is not an exaggeration to say that the question of where and when the Black Death, the deadliest pandemic ever, originated is one of the biggest mysteries in human history. After all, the Black Death was the first wave of the second plague pandemic of the 14th to early 19th centuries. It killed some 50–60% of the population in Europe, the Middle East, and North Africa, and an unaccountable number of people in Central Asia. Different proposals, based on competing theories, have been put forward. But in 2017, I came across some records describing an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, which I suspected may hold the key. As part of a multidisciplinary team co-led by Maria Spyrou at the University of Tubingen, we have now investigated several specimens from individuals buried at that site and come up with an answer. The idea that the Black Death originated in the east—territories overlapping, roughly speaking, Central Asia, Mongolia, and China—dates back to the contemporaries of the pandemic in Europe and the Islamic world. The modern, academic Chinese origin theory dates back at least to 1756–8, and a publication about the history of Central Asia by French scholar Joseph de Guignes.
Which of the following may be the probable origin of the Black Death, according to the passage?
Option 1: Kyrgyzstan
Option 2: India
Option 3: Mongolia
Option 4: China
Correct Answer: Kyrgyzstan
Solution : The first option is correct.
The probable origin of the Black Death, according to the passage, is Kyrgyzstan. The passage mentions the discovery of an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, in 2017. The speaker suspected that this site may hold
Question : If $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$, then $(x+y+z)$ is:
Option 1: $a+b+c$
Option 2: $0$
Option 3: $a^2+b^2+c^2$
Option 4: $2$
Correct Answer: $0$
Solution : Given: $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}$ Let $\frac{x}{(b–c)(b+c–2a)}=\frac{y}{(c–a)(c+a–2b)}=\frac{z}{(a–b)(a+b–2c)}=k$. ${x}=k{(b–c)(b+c–2a)}$ (equation 1) ${y}=k{(c–a)(c+a–2b)}$ (equation 2) ${z}=k{(a–b)(a+b–2c)}$ (equation 3) Adding equations 1, 2, and 3 respectively, we get, $x+y+z=k{(b–c)(b+c–2a)}+k{(c–a)(c+a–2b)}+k{(a–b)(a+b–2c)}$ $x+y+z=k[(b–c)(b+c–2a)+(c–a)(c+a–2b)+(a–b)(a+b–2c)]$ $x+y+z= k[b^2+bc–2ab–bc–c^2+2ac+c^2+ac–2bc–ac–a^2+2ab+a^2+ab–2ac–ab–b^2+2bc)$ $x+y+z$ = 0 Hence, the correct answer is 0.
Question : Comprehension: Read the given passage and answer the questions that follow. It is not an exaggeration to say that the question of where and when the Black Death, the deadliest pandemic ever, originated is one of the biggest mysteries in human history. After all, the Black Death was the first wave of the second plague pandemic of the 14th to early 19th centuries. It killed some 50-60% of the population in Europe, the Middle East and North Africa and an unaccountable number of people in Central Asia. Different proposals, based on competing theories, have been put forward. But in 2017, I came across some records describing an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, which I suspected may hold the key. As part of a multidisciplinary team co-led by Maria Spyrou at the University of Tubingen, we have now investigated several specimens from individuals buried at that site – and come up with an answer. The idea that the Black Death originated in the east – territories overlapping, roughly speaking, Central Asia, Mongolia and China – dates back to the contemporaries of the pandemic in Europe and the Islamic world. The modern, academic Chinese origin theory dates back to at least 1756-8 and a publication about the history of Central Asia by French scholar Joseph de Guignes. Select the suitable word given in the passage which means ‘areas of land under the jurisdiction of a ruler or state’.
Option 1: Territories
Option 2: Contemporaries
Option 3: Population
Option 4: Mysteries
Correct Answer: Territories
Solution : The correct choice is the first option.
The passage mentions, "The idea that the Black Death originated in the east—territories overlapping, roughly speaking, Central Asia, Mongolia, and China." Here, territories refers to regions or areas under consideration.
The meanings of other options are as
Question : Comprehension:
Read the following passage and answer the questions that follow.
Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.
"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.
An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.
Question: How many mathematicians won the Michael Sheila Prize for 2021?
Option 1: Four
Option 2: Two
Option 3: Three
Option 4: One
Correct Answer: Three
Solution : The correct choice is the third option.
As stated in the first paragraph, the prize was won by Nikhil Srivastava, Adam W. Marcus, and Daniel Alan Spielman, which makes this a total of three prize winners.
Therefore, the correct answer is three.
Question : Comprehension: Read the given passage and answer the questions that follow. It is not an exaggeration to say that the question of where and when the Black Death, the deadliest pandemic ever, originated is one of the biggest mysteries in human history. After all, the Black Death was the first wave of the second plague pandemic of the 14th to early 19th centuries. It killed some 50-60% of the population in Europe, the Middle East and North Africa and an unaccountable number of people in Central Asia. Different proposals, based on competing theories, have been put forward. But in 2017, I came across some records describing an intriguing medieval cemetery in Kara-Djigach, Chüy Valley, northern Kyrgyzstan, which I suspected may hold the key. As part of a multidisciplinary team co-led by Maria Spyrou at the University of Tubingen, we have now investigated several specimens from individuals buried at that site – and come up with an answer. The idea that the Black Death originated in the east – territories overlapping, roughly speaking, Central Asia, Mongolia and China – dates back to the contemporaries of the pandemic in Europe and the Islamic world. The modern, academic Chinese origin theory dates back to at least 1756-8 and a publication about the history of Central Asia by French scholar Joseph de Guignes. What is the theme of the passage?
Option 1: Pitfall of Black Death
Option 2: Impact of Black Death
Option 3: Origin of Black Death
Option 4: History of Black Death
Correct Answer: Origin of Black Death
The passage primarily focuses on the mystery of the origin of the Black Death, discussing different proposals and theories, and introducing the findings of an investigation into a medieval cemetery in Kyrgyzstan that
Question: The Michael and Sheila Held Prize is presented:
Option 1: every two years to honour the best researchers in mathematics
Option 2: twice every year to honour young and influential researchers in mathematics
Option 3: every year to honour new thinking and research in a specific area of mathematics
Option 4: every year to honour those who solve longstanding problems in graph theory and linear algebra
Correct Answer: every year to honour new thinking and research in a specific area of mathematics
As stated in the last line of the passage, the Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential
Question : Comprehension: In the following passage, some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.
Can we see (1)________ the earth is a globe? Yes, we can, when we watch a ship that sails out to sea, if we watch closely, we see that the ship begins to (2)________. The bottom of the ship disappears first, and then the ship seems to sink lower and lower, (3)________ we can only see the top of the ship, and then we see nothing at all. What is hiding the ship from us? It is the earth. Stick a pin most of the way into an orange, and (4)________ turn the orange away from you. You will see the pin disappear, (5)________ a ship does on the earth.
Select the most appropriate option to fill in blank no. 2.
Option 1: being disappeared
Option 2: disappear
Option 3: have disappeared
Option 4: having disappeared
Correct Answer: disappear
Solution : The most appropriate choice is the second option.
Explanation: The word disappear is used in the simple present tense to describe the action of the ship gradually becoming hidden from view, which is the intended meaning in this context.
The other options do not
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