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Question : A train, 200 metres long, is running at a speed of 54 km/h. The time in seconds that will be taken by the train to cross a 175 metres long bridge is:
Option 1: 12.5
Option 2: 20
Option 3: 25
Option 4: 10
Correct Answer: 25
Solution : Given: Length of train = 200 m and length of bridge = 175 m. Its speed is 54 km/h. To convert km/h into m/s, multiply with $\frac{5}{18}$, we get $54 \times\frac{5}{18}=15$ m/s We know that $\text{time}=\frac{\text{Distance}}{\text{Speed}}=\frac{200+175}{15} = \frac{375}{15}=$ 25 seconds Hence, the correct answer is
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.
Correct Answer: The new connection they have discovered has inspired future theoretical computer scientists.
Solution : The correct choice is the third option.
As stated in the second paragraph, the NAS said they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that
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