Question : Directions: In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements
Statements:
I. No dean is a teacher.
II. All teachers are professors.
III. No professor is a lecturer.
Conclusions:
I. Some deans are lecturers.
II. Some teachers are lecturers.

Option 1: Only conclusion II follows

Option 2: Only conclusion I follows

Option 3: Both conclusions I and II follow

Option 4: Neither conclusion I nor II follows

Question : Read the passage given below and answer the question that follows:
Once upon a time, a psychology professor walked around on a stage while teaching stress management principles to an auditorium filled with students. As she raised a glass of water, everyone expected they'd be asked the typical "glass half empty or glass half full" question. Instead, with a smile on her face, the professor asked, "How heavy is this glass of water I'm holding?" Students shouted out answers ranging from eight ounces to a couple of pounds. She replied, "From my perspective, the absolute weight of this glass doesn't matter. It all depends on how long I hold it.

If I hold it for a minute or two, it's fairly light. If I hold it for an hour straight, its weight might make my arm ache a little. If I hold it for a day straight, my arm will likely cramp up and feel completely numb and paralyzed, forcing me to drop the glass to the floor. In each case, the weight of the glass doesn't change, but the longer I hold it, the heavier it feels to me." As the class shook their heads in agreement, she continued, "Your stresses and worries in life are very much like this glass of water. Think about them for a while and nothing happens. Think about them a bit longer and you begin to ache a little. Think about them all day long, and you will feel completely numb and paralyzed incapable of doing anything else until you drop them."

Question:
What is the moral of the passage?
 

Option 1: On days when you're stressed out and feeling overwhelmed, learn to embrace the inevitable and let go
 

Option 2: Friends come in all shapes and sizes
 

Option 3: Don't condemn someone for not doing something that you yourself are unable to do
 

Option 4: True friends do not distinguish between rich and poor

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

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:
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

Question :  Read the passage given below and answer the question that follows:
Once upon a time, a psychology professor walked around on a stage while teaching stress management principles to an auditorium filled with students. As she raised a glass of water, everyone expected they'd be asked the typical "glass half empty or glass half full" question. Instead, with a smile on her face, the professor asked, "How heavy is this glass of water I'm holding?" Students shouted out answers ranging from eight ounces to a couple of pounds. She replied, "From my perspective, the absolute weight of this glass doesn't matter. It all depends on how long I hold it.

If I hold it for a minute or two, it's fairly light. If I hold it for an hour straight, its weight might make my arm ache a little. If I hold it for a day straight, my arm will likely cramp up and feel completely numb and paralyzed, forcing me to drop the glass to the floor. In each case, the weight of the glass doesn't change, but the longer I hold it, the heavier it feels to me." As the class shook their heads in agreement, she continued, "Your stresses and worries in life are very much like this glass of water. Think about them for a while and nothing happens. Think about them a bit longer and you begin to ache a little. Think about them all day long, and you will feel completely numb and paralyzed incapable of doing anything else until you drop them."

Question:
Which of the following words could replace the word 'perspective' as used in the passage?
 

Option 1: pattern

Option 2: viewpoint
 

Option 3: yank
 

Option 4: obedience

Question : Directions: Five professors A, B, C, D, and E are sitting in a row facing the North (not necessarily in the same order). A is second to the left of D. Only two professors are sitting between C and E. No professor is sitting to the right of E. How many professors are sitting to the left of D?

Option 1: 3

Option 2: 0

Option 3: 2

Option 4: 1

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:
In what way have the prize winners helped future theoretical computer scientists?

Option 1: They have found connections between algebra, geometry and computer science.

Option 2: They solved new problems in graph theory used in theoretical computer science.

Option 3: The new connection they have discovered has inspired future theoretical computer scientists.

Option 4: They have done innovative research on Ramanujan graphs and geometry of polynomials.