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Question : The following table shows the marks obtained out of 100, by 5 students in 5 different subjects.
What are the total marks scored by Ayush in all the subjects?
Option 1: 435
Option 2: 465
Option 3: 445
Option 4: 425
Correct Answer: 425
Solution : The total marks scored by Ayush in all the subjects = 88 + 80 + 90 + 82 + 85 = 425 Hence, the correct answer is 425.
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.
Correct Answer: They solved questions on Ramanujan's graphs that had not been solved for a long time.
Solution : The correct choice is the fourth option.
As stated in the second paragraph of the passage, the prize winners, Marcus, Spielman, and Srivastava, solved longstanding questions on the Kadison-Singer problem
Question : Directions: Identify the diagram that best represents the relationship among the classes given. Whales, Fishes, Crocodiles
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Whales, fishes, and crocodiles are all different types of animals found in water bodies. They all are inherently different based on their size, eating habits, and the type of water body in which they live, so all three circles will be separate from each other.
The
Question : Select the most appropriate option that can substitute the underlined words in the following sentence.
The people who live here have had the same kind of lifestyle until hundreds of years.
Option 1: through hundreds of year
Option 2: for hundreds of years
Option 3: although hundreds of years
Option 4: since hundreds of year
Correct Answer: for hundreds of years
Solution : The correct choice is the second option.
This option correctly indicates the duration of time that the people have had the same lifestyle for hundreds of years denotes the length of time over which the lifestyle has remained unchanged.
The correct sentence
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at AB as shown.
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 : The pie chart given below shows the number of cars sold by 8 different companies. The total number of cars sold by all these 8 companies is 2,000. The number of cars sold by a particular company is shown as a percent of the total number of cars sold by all these 8 companies.
The average number of cars sold by C1 and C2 is how much percent less than the average number of cars sold by C7 and C8?
Option 1: 66.66%
Option 2: 33.33%
Option 3: 16.66%
Option 4: 25%
Correct Answer: 25%
Solution : The average number of cars sold by C1 and C2 = $\frac{8+22}{2}=15$%. The average number of cars sold by C7 and C8 = $\frac{10+30}{2}=20$%. The average number of cars sold by C1 and C2 is less than the average number of cars sold by C7
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the following set. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is NOT allowed) (4, 21, 33) (10, 111, 141)
Option 1: (13, 45, 97)
Option 2: (25, 53, 128)
Option 3: (65, 60, 244)
Option 4: (24, 52, 128)
Correct Answer: (25, 53, 128)
Solution : Given: (4, 21, 33); (10, 111, 141) ⇒ (4, 21, 33); 33 – 21 = 12; 12 ÷ 3 = 4 ⇒ (10, 111, 141); 141 – 111 = 30; 30 ÷ 3 = 10
Let's check the options – First option: (13,
Question : Directions: In the following question, four number pairs are, given. In each pair, the number on the left side of (–) is related to the number on the right side of (–) with some Logic/Rule /Relation. Three pairs are similar based on the same Logic/Rule/Relation. Select the odd one out from the given alternatives. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g.13 – operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
Option 1: 14 – 2762
Option 2: 16 – 4098
Option 3: 11 – 1333
Option 4: 13 – 2199
Correct Answer: 14 – 2762
Solution : Let's check each option –
First option: (14 – 2762); 143 + 2 = 2744 + 2 = 2746 ≠ 2762 Second option: (16 – 4098); 163 + 2 = 4096 + 2 = 4098 Third option: (11 – 1333); 11
Question : At how much percent above the cost price should a trader mark his goods so that after allowing a discount of 25%, he still gains 5%?
Option 1: 35
Option 2: 32
Option 3: 50
Option 4: 40
Correct Answer: 40
Solution : Let the cost price be Rs. $100$. So, the selling price is $100 + 5$ = Rs. $105$ Discount is $25$%. Let, the marked price be $x$. So, the selling price after the discount is $\frac{75}{100}×x=\frac{3x}{4}$ According to the question, $\frac{3x}{4} = 105$ $\therefore x
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: All teas are juices. All juices are cocktails. Conclusions: I. All teas are cocktails. II. All cocktails are definitely juices.
Option 1: Both conclusions I and II follow
Option 2: Only conclusion II follows
Option 3: Only conclusion I follows
Option 4: Neither conclusion I nor II follows
Correct Answer: Only conclusion I follows
Solution : The possible Venn diagram according to the given statements is as follows –
Let's analyse the conclusions – Conclusion (I): All teas are cocktails – From the Venn diagram, it is evident that the circle representing tea is completely inside the circle
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