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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
Correct Answer: every year to honour new thinking and research in a specific area of mathematics
Solution : The correct choice is the third option.
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 : Directions: Select the correct mirror image of the given figure when the mirror is placed at AB as shown below.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : As per the mirror image properties, closer things appear close to the mirror in the reflection. Here, according to the information provided, the mirror is placed on the right side of the figure (on Line AB). So, the left side of the reflected image will appear
Question : Ultraviolet radiation striking the earth is due to the depletion of
Option 1: Carbon monoxide
Option 2: Carbondioxide
Option 3: Ozone
Option 4: oxygen
Correct Answer: Ozone
Solution : The correct option is Ozone.
Some of the radiation is filtered and absorbed by the Earth's atmosphere, particularly in the UV spectrum. The ozone layer in the Earth's stratosphere absorbs and blocks a considerable amount of UV radiation. The ozone layer is being depleted as
Question : Improve the underlined part of the sentence. Choose 'No improvement' as an answer if the sentence is grammatically correct. Fishermen make their lives from the sea.
Option 1: there livings
Option 2: his living
Option 3: their live
Option 4: No improvement
Correct Answer: No improvement
Solution : The correct choice is the fourth option.
The given sentence is structured properly and grammatically correct.
Therefore, the given sentence is correct and requires no improvement.
Question : Directions: Two 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 follow(s) from the statements. Statements: No astronaut is tall. Some tall are blue. Conclusions: I. Some astronauts are blue. II. No tall is an astronaut.
Option 1: Only conclusion I follows.
Option 2: Both conclusions I and II follow.
Option 3: Neither conclusion I nor II follow.
Option 4: Only conclusion II follows.
Correct Answer: Only conclusion II follows.
Solution : According to the given statements, the Venn diagram is given below – Let's analyse the conclusions – Conclusion (I): Some astronauts are blue – As shown in the Venn diagram, the circles of the astronaut and blue are independent as no relation
Question : The compound interest accrued on a sum of INR 20,000 at the end of 2 years compounded annually is INR 2,050. Find the compound interest at the end of the 3rd year.
Option 1: INR 3,153.50
Option 2: INR 2852.50
Option 3: INR 3,152.50
Option 4: INR 3,154.50
Correct Answer: INR 3,152.50
Solution : Principal = INR 20000 Time = 2 years $\text{Compound interest}= \text{Total amount – Principal}$ $⇒\text{Compound interest}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$ $⇒2050=20000((1+\frac{\text{Rate}}{100})^2-20000$ $⇒22050=20000((1+\frac{\text{Rate}}{100})^2$ $⇒(1+\frac{\text{Rate}}{100})^2=\frac{22050}{20000}=\frac{441}{400}$ $⇒(1+\frac{\text{Rate}}{100})^2=(\frac{21}{20})^2$ $⇒1+\frac{\text{Rate}}{100}=\frac{21}{20}$ $\therefore \text{Rate}=5$% Now, the total amount after 3 years with a 5% compound interest on a sum of INR 20000 $=20000(1+\frac{5}{100})^3$ $=20000(\frac{21}{20})^3$ $=20000×\frac{441}{400}×\frac{21}{20}$
Question : Directions: Select the option in which the numbers are related in the same way as are the numbers in the given set. (7, 49, 343)
Option 1: (5, 25, 625)
Option 2: (11, 121, 1321)
Option 3: (13, 169, 2197)
Option 4: (3, 9, 29)
Correct Answer: (13, 169, 2197)
Solution : Given: (7, 49, 343)
Like, (7, 49, 343)→(7)2 = 49; (7)3 = 343
Let's check the options – First option: (5, 25, 625)→(5)2 = 25; (5)3 = 125 ≠ 625 Second option: (11, 121, 1321)→(11)2 = 121; (11)
Question : Directions: In the following question, select the word that cannot be formed using the letters of the given word. INSTRUCTOR
Option 1: RUST
Option 2: TORT
Option 3: STOP
Option 4: STINT
Correct Answer: STOP
Solution : Given: INSTRUCTOR
Now, let's compare all the option words with the word INSTRUCTOR – First option: RUST; All the letters of RUST are present in the word INSTRUCTOR. Second option: TORT; All the letters of TORT are present in the word INSTRUCTOR. Third option: STOP;
Question : Directions: Select the option that is related to the third letter cluster in the same way as the second letter cluster is related to the first letter cluster. OMP : QPT :: FOR : ?
Option 1: HSV
Option 2: HRU
Option 3: HRV
Option 4: HSU
Correct Answer: HRV
Solution : Given: OMP : QPT :: FOR : ?
Add the consecutive natural numbers (starting from 2) to the place value of the letters of OMP to get the related letter cluster. O + 2 = Q; M + 3 = P; P + 4 =
Question : Directions: In the following question a series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. 22, 31, 42, 55, ?, 87
Option 1: 64
Option 2: 70
Option 3: 72
Option 4: 68
Correct Answer: 70
Solution : Given: 22, 31, 42, 55, ?, 87
Add consecutive odd numbers in increasing order starting from 9 to the previous term to obtain the next term in the series – 22 + 9 = 31; 31 + 11 = 42; 42 + 13 = 55;
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