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:
What is the connection between the prize winners and the famous Indian mathematical genius Ramanujan?

Option 1: They explained Ramanujan's graphs in solving the Kadison-Singer problem.

Option 2: The prize winners were all admirers of Ramanujan's great contribution.

Option 3: The prize winners were all students of Ramanujan.

Option 4: They solved questions on Ramanujan's graphs that had not been solved for a long time.

Question : Comprehension:
Read the given passage and answer the questions that follow.
Plato is the earliest important educational thinker, and education is an essential element in 'The Republic' (his most important work on philosophy and political theory, written around 360 B.C.). In it, he advocates some rather extreme methods: removing children from their mothers' care and raising them as wards of the state, and differentiating children suitable to the various castes, the highest receiving the most education, so that they could act as guardians of the city and care for the less able. He believed that education should be holistic, including facts, skills, physical discipline, music, and art. Plato believed that talent and intelligence are not distributed genetically and thus can be found in children born to all classes, although his proposed system of selective public education for an educated minority of the population does not really follow a democratic model.

Aristotle considered human nature, habit, and reason to be equally important forces to be cultivated in education, the ultimate aim of which should be to produce good and virtuous citizens. He proposed that teachers lead their students systematically, and that repetition be used as a key tool to develop good habits, unlike Socrates' emphasis on questioning his listeners to bring out their own ideas. He emphasized the balancing of the theoretical and practical aspects of subjects taught, among which he explicitly mentions reading, writing, mathematics, music, physical education, literature, history, and a wide range of sciences, as well as play, which he also considered important.

Question:
What tool does Aristotle advocate to teachers to develop good habits in students?

Option 1: Writing

Option 2: Reading

Option 3: Questioning

Option 4: Repetition

Question : Comprehension:
Read the given passage and answer the questions that follow.
Plato is the earliest important educational thinker, and education is an essential element in 'The Republic' (his most important work on philosophy and political theory, written around 360 B.C.). In it, he advocates some rather extreme methods: removing children from their mothers' care and raising them as wards of the state, and differentiating children suitable to the various castes, the highest receiving the most education, so that they could act as guardians of the city and care for the less able. He believed that education should be holistic, including facts, skills, physical discipline, music, and art. Plato believed that talent and intelligence are not distributed genetically and thus can be found in children born to all classes, although his proposed system of selective public education for an educated minority of the population does not really follow a democratic model.

Aristotle considered human nature, habit, and reason to be equally important forces to be cultivated in education, the ultimate aim of which should be to produce good and virtuous citizens. He proposed that teachers lead their students systematically, and that repetition be used as a key tool to develop good habits, unlike Socrates' emphasis on questioning his listeners to bring out their own ideas. He emphasized the balancing of the theoretical and practical aspects of subjects taught, among which he explicitly mentions reading, writing, mathematics, music, physical education, literature, history, and a wide range of sciences, as well as play, which he also considered important.

Question:
Which of these methods is NOT advocated in 'The Republic'?

Option 1: Differentiating children based on castes

Option 2: Imparting similar education to all children

Option 3: Bringing up children under state guardianship

Option 4: Keeping children away from mothers

Question : Study the following table and answer the question that follows. A school has four sections A, B, C, and D of Class IX students. The results of the Science and Mathematics examinations are shown in the following table.

What is the ratio of the number of students who failed in Science but passed in Mathematics of section B and section D together to the number of students of section A that passed in both subjects?

Option 1: 9 : 17

Option 2: 3 : 7

Option 3: 4 : 9

Option 4: 5 : 11

Question : Directions: Five books of History, Mathematics, English, Hindi, and Science are kept on top of each other. English is kept between History and Mathematics. Hindi and Science are kept together. Science is kept above Mathematics. Which book is kept in the middle? 

Option 1: Mathematics

Option 2: English 

Option 3: Science 

Option 4: Mathematics or English

Question : Directions: Six books Hindi, Biology, Mathematics, Economics, Physics, and Chemistry are placed in two racks facing each other with three books in each rack. Hindi and Chemistry are in the same rack but are not neighbours. Biology is placed exactly opposite to Economics. Biology is just left of Hindi facing the South direction. Physics is exactly opposite to Chemistry. Which of the following is placed exactly opposite to Hindi?

Option 1: Chemistry

Option 2: Economics

Option 3: Biology

Option 4: Mathematics

Question : Who among the following persons of Indian origin was in the news in December 2021 for solving the Kadison-Singer 1959 problem in the field of mathematics?

Option 1: Nikhil Srivastava

Option 2: Nikhil Sachdev

Option 3: Satya Nadella

Option 4: Pratap Bhanu Mehta