SRCC GBO 2023 Question Paper

Let's take a look at each option individually:

A: The author's main point is not to say that the parents are failing their children. Yes, they might not be taking care of their children and going to work, leaving them in the care of other people and foster homes, but the author does not blame the parents for this. He states those facts and tells us about the impact of these numbers; he does not say that it is the parent's fault for not planning their children's birth or not taking care of them. He simply states the facts and information about the serious condition the US is going through. 

B: This is exactly what the author tries to do throughout the passage. He tells us the statistics about the problem in the USA regarding unplanned parenthood, single parents, and an increase in the number of children in healthcare. He is not giving an opinion or blaming any single entity for the condition but simply informing his readers about it. 

C: This is again not true, as the author nowhere blames the state for the state of affairs. 

D: There has been little to no discussion about the lack of nutrition in the children (infants and toddlers), this is complete;y out of scope of the passage. 

Hence, Option B best represents the main point of the author's passage. 

Therefore, option B is the correct answer. 

The set of words that does NOT capture the main ideas expressed in the passage is Option B) America, progress, education

The passage primarily discusses the issues faced by infants and toddlers in the US, such as high infant mortality rate, low birth weight, low immunisation rates, and high rates of adolescent pregnancies. It also highlights the problems of unplanned parenthood, poverty, and single-parent families. 

The terms ‘progress’ and ‘education’ are not central to the issues discussed in the passage. 

Hence, option B does not capture the main ideas of the passage.

Option D is NOT an instance of the ‘quiet crisis’ referred to in the passage.

The passage mentions that women with unplanned pregnancies are less likely to seek pre-natal care.

Therefore, an increase in the number of young mothers seeking pre-natal care would not be part of the ‘quiet crisis’.

The other options A, B and C are all issues highlighted in the passage as part of the crisis.

The statement that cannot be inferred from the passage is Option D

The passage does not provide any information about the divorce rate among teenage couples or its impact on educators. 

While it does discuss the issues of unplanned pregnancies and single parenthood, it does not specifically mention divorce rates among teenagers. Therefore, option D cannot be inferred from the passage. The other options, A,B and C, can be inferred from the information provided in the passage.

The measure that would NOT be suggested by the task force, based on the passage, is Option C

The passage does not mention any suggestion about rewarding parents for looking after their children. While it does discuss the issues of poverty, abuse, and healthcare, it does not specifically mention a reward system for parents. Therefore, option C would not be a measure suggested by the task force. The other options, A, B and D, could be inferred as potential measures based on the issues highlighted in the passage.

The correct answer is option B. 

The author does not mention that big tech companies are firmly accountable to strict domestic regulations and laws and can be curtailed if they engage in criminal violation of data. The other options (a, c, d) are all arguments made by the author in the passage.

The passage does not suggest treating big tech companies as public utilities subject to laws that deter them from misusing data to cause actual harm. So, the correct answer is Option C.

The passage does discuss stricter laws and regulations, collective action by consumers, and regulation of access to data, but it does not mention treating tech companies as public utilities. It rather suggests that these companies are vital to the global economy and innovation and that they can be a line of defence against cyber threats. 

It also suggests that laws should focus on deterring the misuse of data to cause actual harm. However, it does not propose treating these companies as public utilities.

The other options are mentioned by the author in the passage.

The correct answer is Option D. 

In the first paragraph, the author notes various reasons for the erosion in privacy today, such as forwarding emails, capturing photos on cellphones, and tweeting opinions, which all leave a trail of data that can be collected without our knowledge. The author states that privacy no longer exists in an absolute sense in our networked world. 

The other options are not the main focus of the first paragraph.

The author makes all of the following observations regarding restricting data access except Option C

The passage does not mention or suggest that restricting data access hampers governmental efforts to formulate laws that tackle harmful data misuse. 

The other options, A, B and D, are discussed in the passage.

Option D is the correct answer.

The passage does not mention or suggest that big tech companies are a major contributor to the public exchequer through tax revenue.

Other options are mentioned in the passage.

Option A: The author suggests that big tech companies have a significant impact on global progress and growth. This is due to their role in job creation, economic activity, and innovation.

Option B:  The author points out that these companies are a crucial source of innovation, which is vital for our modern economies. They drive technological advancements and create new markets and opportunities.

Option C: The author argues that big tech companies can act as a defence against cyber threats. They have the resources and expertise to counter sophisticated cyber-attacks and surveillance.

The grammatically correct sentence from the given options is Option C.

This sentence correctly uses “notwithstanding” as a preposition meaning “in spite of” or "despite".

It indicates that despite his nervousness, the young man was able to look his employer directly in the eyes while asking for a raise. The other options have incorrect or awkward sentence structures.

Valuable means something of value. 

Option A: Invaluable means something too important to have a value or something indispensable. 

Option B: Priceless, similarly, means something beyond being priced. 

OptionD: Wothwhile means something that is worth the effort it takes. 

All of these options take a positive aspect on the value of the thing. The antonym of valuable would be something that is not valuable. 

Optoin C: Worthless means something which is not worth or have no real use or value. 

Therefore, Option C is the correct answer. 

Option A is the correct answer:
(a) had promised: This refers to a completed action in the past (promised) relevant to the current situation.
(b) am: This indicates the speaker's current state of belief ("I am sure").
(c) would have finished: This is a hypothetical situation—if she had continued marking through the weekend, she would have finished by Monday morning.
(d) is meeting: This refers to a scheduled meeting happening in the present ("by 9 a.m. in the morning").
(e) would reveal: This refers to a future action that is dependent on another action ("only when she meets").
(f) meets: This refers to her habit or usual action ("when she meets").
Option B: had been promising: This suggests repeated promises in the past, which isn't necessary here.
Option C: will have finished: This suggests the marking will be finished in the future, which contradicts the context of Monday morning.
Option D: has promised: This is grammatically correct but less specific than "had promised," which emphasizes a completed promise.

Therefore, Option A is the correct answer. 

The answer is Option A. It should be It can shoot out its tongue rather than shoot off.

Shoot off: This phrasal verb typically implies detachment or removal. For example, we might say, “He shot off an email” (meaning he sent an email quickly). However, in the context of the chameleon’s tongue, “shoot off” doesn’t convey the intended action accurately. It suggests detachment rather than extension.

Shoot out: This phrasal verb means rapidly extending or projecting something outward. When we say the chameleon can “shoot out its tongue,” we’re describing the quick, precise movement of its tongue as it catches prey. The emphasis here is on the action of extending the tongue.
Therefore, the correct phrase is “It can shoot out its tongue,” emphasizing the rapid extension of the chameleon’s tongue to catch insects.

The relationship between the first pair of words (STAR and CONSTELLATION) must be identified in this analogy. Then, we find a word that shares a similar relationship with CAT.

STAR is a component or part of a CONSTELLATION. A constellation is a group of stars forming a recognizable pattern in the sky.

Now let’s consider the options:

a) CLOWDER: A clowder is a group of cats that matches the relationship between a single cat and a group of cats.
b) TROOP: A troop typically refers to a group of soldiers or scouts. This doesn’t match the relationship between a single cat and a group of cats.
c) PARLIAMENT: A parliament is a group of owls. Again, this doesn’t match the relationship between a single cat and a group of cats.
d) PACK: A pack is a group of wolves.Again, this doesn’t match the relationship between a single cat and a group of cats.

Therefore, Option A is the correct answer.

The idiom “Give it a whirl” means to give something a try which is mentioned in Option D.

The correct answer is Option C.

The complete text would be: Corky’s uncle didn’t want him to be an artist. He didn’t think he had any talent in that direction. He was always urging him to chuck Art and go into the jute business and start at the bottom and work his way up. Jute had apparently become a sort of obsession with him. And what Corky said was that, while he didn’t know what they did at the bottom of the jute business, instinct told him that it was something too beastly for words. Corky, moreover, believed in his future as an artist. Someday, he said, he was going to make it big.

The other options are not grammatically correct or don't fit the passage's context.

Delightful: This word conveys a positive emotion or feeling. It is associated with joy, pleasure, and happiness. When something is delightful, it brings a sense of enjoyment or satisfaction.

Misery: In contrast, “Misery” represents a negative state or feeling. It signifies suffering, distress, or extreme unhappiness. When someone is in misery, they are experiencing great discomfort or pain.

Expectation: The word “Expectation” relates to anticipation or hope. It refers to what we anticipate or predict will happen in the future. Expectations can be positive or negative, depending on the context.

Failure: “Failure” signifies lack of success or achievement. It is associated with not meeting desired goals or outcomes. Failure can be disappointing and discouraging.

When comparing these words:

Delightful stands out because it is the only positive emotion among the options.

The other three words—Misery, Expectation, and Failure—all have negative connotations.

The most appropriate option to fill in the blank is:

He ran as fast as he could, with the angry shopkeeper hard on his heels.

So, the answer is Option D. This phrase is used to describe someone closely following or pursuing another. In this context, it means that the shopkeeper was chasing him closely.

Looking at the options, we can see that a carrot is a type of vegetable, and an apple is a type of fruit. Tubers are essentially plant parts that are enlarged to form storage containers that plants use to hold nutrients. This allows them to feed their offspring or survive through the winter. Potatoes are a form of stem tuber.

This leaves us with tomato. Tomatoes are used in making salads and are a part of salads, but they are not a type of salad.

Hence, the tomato is the odd one out among the given options. 

Therefore, option A is the correct answer.

Let's take a look at the tone and meaning of each option individually:
(A) Adoring: This word has a positive tone and means showing deep love and affection.

(B) Jealous: This word has a negative tone and means feeling or showing envy of someone or their achievements and advantages.

(C) Manic: This word has a somewhat negative tone. It means showing wild, deranged, or excited energy, often in a way that is overwhelming or uncontrollable.

(D) menacing: This word has a negative tone as well. It means suggesting the presence of danger or threat.

"Adoring" is the only word with a positive connotation and, hence, is the odd one out. 

Therefore, Option A is the correct answer. 

The most appropriate option to fill in the blanks is Option A.

So, the completed sentence is: “If you want to influence people in a positive way, then your attitude and how you are perceived using non-verbal communication is very important.” 

This option best captures the essence of the sentence, which is about positively influencing people through one’s attitude and non-verbal communication. The other options may not fully convey the positive aspect implied in the sentence.

Option B is not the best fit because the word “control” can have a negative connotation, implying manipulation rather than positive influence. The phrase “how you seem” is also less precise than “how you are perceived”. 

Option C, while positive, doesn’t quite fit the context. “Inspire” is more about motivating others through one’s actions or words, and “are apparent” suggests a clear, obvious presence, which doesn’t necessarily relate to non-verbal communication. 

Option D is not ideal because “impact” is a broader term that can be either positive or negative, and “are seen” is less specific about the perception of others compared to “are perceived”. Therefore, these options are not as suitable as option A for the given sentence.

The most appropriate phrases to fill in the blanks and complete the given text are from option c. 

Here’s the completed text:

“The global village that we live in brings with it (a) plentiful possibilities. Travel around the globe has (b) never been so easy. Movement of people from one nation to another has c) led to a mélange of cultures, language and customs. Let’s revel in this (d) newfound potpourri.”

The most appropriate option to fill in the blank Option B.

So, the sentence would read: “I didn’t have the heart to take the money from my poor nephew.” This phrase is used to express that someone couldn’t do something because it made them feel guilty or it seemed too cruel.

Options A,C and D doesn't fit into the blank in the given context.

Anomaly means something that deviates from what is standard, normal, or expected. The antonym is Conformity, which means compliance with standards, rules, or laws.

Chicanery: This means deception or trickery, especially by using language. The antonym is Honest, which means free of deceit; truthful and sincere.

Eulogy: This is a speech or piece of writing that praises someone or something highly, typically someone who has just died. The antonym is Censure, which means expressing severe disapproval of (someone or something), especially in a formal statement.

So, the correct match is:

a) Anomaly - 2. Conformity

b) Chicanery - 1. Honest

c) Eulogy - 3. Censure

Hence, Option B is the correct answer.

Option D is the correct answer. This choice conveys that despite the crisis shifting or changing direction, we remain anchored to a single plan or solution.

The phrase “even as” is a conjunction that indicates a contrast or concession. It is commonly used to introduce a clause that contrasts with the main idea. In this context, “even as” connects the idea of remaining anchored to a single plan or solution with the simultaneous occurrence of the crisis shifting or changing direction.

Option B is the correct answer. 'had been married' is a wrong phrase in the sentence.

The revised version should be:

“By the end of next year, my friend’s parents will have been married for 25 years.”

Going through the given options, we can see that Canoe, Helicopter and Submarine are all modes of transport in their respective modes of river, air and sea. 

Bicycles are also a mode of transport, but their relationship with wheels is not one of the environment, as it is in the case of the other three. Hence, this is the odd one out. 

Therefore, Option C is the correct answer. 

Option D is the correct choice. Saying “you are at a disadvantage” means that not being tech-savvy puts you in an unfavourable position. It’s a common expression to convey this idea.

Let's look at other options.

Option A: This choice doesn’t fit well in the context. Saying “you are in a disadvantage” doesn’t convey the intended meaning. We typically use “at a disadvantage” to express being in an unfavourable position.

Option B: While “with” can be used in other contexts, it doesn’t work here. Saying “you are with a disadvantage” sounds awkward and doesn’t convey the intended meaning.

Option C: Again, this choice doesn’t fit the context. Saying “you are of a disadvantage” doesn’t make sense. We don’t use “of” in this expression.

Therefore, the correct answer is Option D.

Sentence: Being tech-savvy is essential in today’s world, and not being so can indeed put you at a disadvantage.

Apropos - Pertinent: Both “Apropos” and “Pertinent” mean being relevant or appropriate in a particular situation. For instance, if someone makes a comment that is directly related to the ongoing discussion, you could say it’s “apropos” or “pertinent.”

Accost - Confront: “Accost” means to approach and address someone boldly or aggressively. Similarly, “confront” involves facing a situation head-on or challenging someone directly.

Appropriation - Allocation: Although not direct synonyms, both terms involve the utilization of resources. “Appropriation” refers to setting aside funds or resources for a specific purpose, while “allocation” involves distributing resources among different areas or needs.

Therefore, the correct answer is Option C.

The benefits associated with taking the help of the agencies listed in the passage include detecting vulnerabilities and ensuring national security. These agencies specialize in finding weaknesses and vulnerabilities, which contributes to safeguarding public safety and national interests. 

Therefore, the correct answer is option C.

Let's check other options.

Option A is not accurate. The passage does mention finding weaknesses, but the purpose is not to cause a backlash. Instead, it aims to enhance security.

Option B: While the passage discusses trade-offs, it doesn’t directly associate them with strengthening national security. The primary focus is on detecting vulnerabilities.

Option D: The passage doesn’t specifically mention “national interest” as a primary motivation. It emphasizes security and vulnerability detection.

We first need to understand what the passage is talking about, and then we can identify the one sentence that does not share the same concept as the other four.

The passage discusses the "inter-dependence" of the world and its people in changing times, and emphasises that, since the problems are now global, the solutions should also be international.

The first sentence appears to be an outlier because it is talking about how the thoughts of a single person will reach all corners of the world. But the passage is neither about thoughts nor about individuals.

Hence, option C is correct.

Option B makes the most grammatical sense and it is the correct answer.

Let's check other options.

Option A: The phrase “and it helps we differentiate ourselves” is grammatically incorrect. It should be “and it helps us differentiate ourselves.”

Option C: The phrase “with helping us understanding” is awkward and incorrect. It should be “by helping us understand.”

Option D: This option changes the focus from “us” to “others.” The original passage discusses how the ego-self helps us differentiate ourselves, not how it helps others understand us.

The correct answer is Option A. 

Reynolds told his aunt he would not mind standing and eating dinner as he was in a hurry to reach the bus station.

The phrase “standing and eat dinner” needs improvement. When using “mind,” we follow it with a gerund (the base form of the verb + “ing”).
So, we need to change “eat” to “eating.” To maintain a parallel structure, both gerunds should be in the same form. Therefore, we say “standing and eating.”

Although D looks similar to A, the issue with option D lies in the word “hurry.” 

In English, we use the phrase “in a hurry” to express that someone is rushing or has limited time. The correct form should be “in a hurry,” not just “in hurry.”

The correct option is indeed (d) In; to; of; for; from. 

Here’s the completed paragraph:

“In March, the Poles proposed sending old MiG-29 jets in Ukraine - a plan that caused much fuss but was then dropped. It was down to Beijing’s intervention - part of a secret China-US axis that is setting parameters for the Ukraine war and trying to ensure that Russia’s military would ignore any order from Vladimir Putin to use nukes.

Other options don't make grammatical sense to be filled in the blanks.

The sentence in question is: 

“It took about five seconds after Nancy Pelosi stepped aside for New York Rep. Hakeem Jeffries to combine support behind him in a bid to become the new House Democratic leader—he is on track to become the first Black party leader in congressional history.”

The verb “combine” means to unite or merge different elements into a single whole. It is synonymous with “coalesce,” which means coming together or uniting. Therefore, Option D is the correct answer.

Other options like “conjoin,” “collaborate,” and “conjugate” do not fit the context:

Option A: Conjoin means to join together, but it doesn’t capture the sense of merging or uniting support.
Option B: Collaborate implies working together on a project or task, which is not the intended meaning.
Option C: Conjugate refers to verb forms in grammar and is unrelated to the context.

The correct option is B:

The night is punctuated by brief awakenings. Typically, people return to sleep without realizing that they had ever been awake. But sometimes we might at least be aware of it - pulled entirely awake. Reasons range from the obvious to the medical.

All other options don't make grammatical sense in the given blanks.

The passage discusses how influencer marketing has shown better results than traditional marketing and what makes influencers connect more effectively with customers.

The first sentence, however, abruptly speaks of influencer history, which is not the context of the passage.

Therefore, the first sentence is an outlier.

The passage: "They talked passionately and knowledgeably not just about the subject but about knowledge as a vocation."
Then, the author mentions Teodor Shanin as an example of some of the good speeches he heard at the Delhi School of Economics, and not because of his passion for peasantry. His main takeaway from the speeches was the passion of the speakers for their subjects. 

Option A is completely alien to the passage. 
Option B and D focus on the example rather than the passage's main point. 

Option C accurately captures author's main takeaway from he speeches he heard. 

Therefore, Option C is the correct answer. 

Forming pairs can help us identify the odd sentence here.

Sentences one and five will form a pair because they talk about a scenario where the government needs to act, and sentence five talks about the challenges to the same scenario. Hence, these pairs are valid and a part of the paragraph.

Furthermore, sentences three and four can be a likely pair because they compare and contrast the impact of implementation on small and large firms. Therefore, they are also a pair.

The remaining sentence two shall be dropped because the others are forming more accurate pairs withing each other.

Ratio of Number of employees in A and B = 5:7 and total employees = 3600. This means that the number of employees in A and B = 1500 and 2100 respectively.
Males in A = 60% of 1500 = 900 and Females = 600. Ratio of males to females in B = 4:3 which means that males in B = 1200 and females in B = 900.
For Females in A, 30% work in Q i.e. 180, 20% of the remaining in R i.e. 84 and the remaining in P i.e. 336.
For males in A, 40% work in P i.e. 360, 2/9th of the remaining in Q i.e. 120 and the remaining in R i.e. 420.
For males in B, one third work in R i.e. 400, 1.25*400 i.e. 500 work in P and the remaining work in Q i.e. 300.
For females in B, 60% work in P i.e. 540, 135 work in R and 225 work in Q.

The difference between the number of female employees working in department R in company B and the number of male employees working in department Q in company A = 135 - 120 = 15.

Ratio of Number of employees in A and B = 5:7 and total employees = 3600. This means that the number of employees in A and B = 1500 and 2100 respectively.
Males in A = 60% of 1500 = 900 and Females = 600. Ratio of males to females in B = 4:3 which means that males in B = 1200 and females in B = 900.
For Females in A, 30% work in Q i.e. 180, 20% of the remaining in R i.e. 84 and the remaining in P i.e. 336.
For males in A, 40% work in P i.e. 360, 2/9th of the remaining in Q i.e. 120 and the remaining in R i.e. 420.
For males in B, one third work in R i.e. 400, 1.25*400 i.e. 500 work in P and the remaining work in Q i.e. 300.
For females in B, 60% work in P i.e. 540, 135 work in R and 225 work in Q.

The required percentage = $$\frac{360-225}{225}\times\ 100\ =\ 60\%$.

Ratio of Number of employees in A and B = 5:7 and total employees = 3600. This means that the number of employees in A and B = 1500 and 2100 respectively.
Males in A = 60% of 1500 = 900 and Females = 600. Ratio of males to females in B = 4:3 which means that males in B = 1200 and females in B = 900.
For Females in A, 30% work in Q i.e. 180, 20% of the remaining in R i.e. 84 and the remaining in P i.e. 336.
For males in A, 40% work in P i.e. 360, 2/9th of the remaining in Q i.e. 120 and the remaining in R i.e. 420.
For males in B, one third work in R i.e. 400, 1.25*400 i.e. 500 work in P and the remaining work in Q i.e. 300.
For females in B, 60% work in P i.e. 540, 135 work in R and 225 work in Q.

The required percentage = $$\frac{420}{800}\times\ 100\ =\ 52.5\%$$.

Ratio of Number of employees in A and B = 5:7 and total employees = 3600. This means that the number of employees in A and B = 1500 and 2100 respectively.
Males in A = 60% of 1500 = 900 and Females = 600. Ratio of males to females in B = 4:3 which means that males in B = 1200 and females in B = 900.
For Females in A, 30% work in Q i.e. 180, 20% of the remaining in R i.e. 84 and the remaining in P i.e. 336.
For males in A, 40% work in P i.e. 360, 2/9th of the remaining in Q i.e. 120 and the remaining in R i.e. 420.
For males in B, one third work in R i.e. 400, 1.25*400 i.e. 500 work in P and the remaining work in Q i.e. 300.
For females in B, 60% work in P i.e. 540, 135 work in R and 225 work in Q.

Value of X = 400+420 / 2 = 410 and value of Y = 336+540/2 = 438.
So, |X-Y| = 28 i.e. Option D.

The required figure is given below: 

Let the total number of students in 2019 be $$x$$. 

Number of Commerce students = $$15\%\ of\ x=225$$ (given)

$$x=1500$$

Number of students in 2021 increased by 20% as compared to 2019.

Total number of students in 2021 = $$1500\times\left(1+20\%\right)=1800$$

In 2019, 

Number of students in Computer Science = 21% of 1500 = 315

Number of students in Arts  = 10% of 1500 = 150

Number of students in Science = 18% of 1500 = 270

Number of students in Engineering = 20% of 1500 = 300

Number of students in Management = 16% of 1500 = 240

Number of students in Commerce = 225 (given)

In 2021, 

Number of students in Computer Science = 18% of 1800 = 324

Number of students in Arts = 12% of 1800 = 216

Number of students in Science = 15% of 1800 = 270

Number of students in Engineering = 25% of 1800 = 450

Number of students in Management = 20% of 1800 = 360

Number of students in Commerce = 10% of 1800 = 180

Total number of students studying Computer Science and Commerce in 2019 = 315 + 225 = 540

Let the number of students studying a particular subject in 2021 = $$x$$

Total number of students studying Computer Science and Commerce in 2019 is 50% more than the number of students studying a particular subject in 2021

Hence, $$x\times\left(1+50\%\right)=540$$

$$x=360$$

The required subject in 2021 is Management. 

Hence, total number of students studying Computer Science and Commerce in 2019 is 50% more than the number of students studying Management in 2021. 

$$\therefore\ $$ The required answer is D. 

The required figure is given below:

Let the total number of students in 2019 be $$x$$.

Number of Commerce students = $$15\%\ of\ x=225$$ (given)

$$x=1500$$

Number of students in 2021 increased by 20% as compared to 2019.

Total number of students in 2021 = $$1500\times\left(1+20\%\right)=1800$$

In 2019,

Number of students in Computer Science = 21% of 1500 = 315

Number of students in Arts = 10% of 1500 = 150

Number of students in Science = 18% of 1500 = 270

Number of students in Engineering = 20% of 1500 = 300

Number of students in Management = 16% of 1500 = 240

Number of students in Commerce = 225 (given)

In 2021,

Number of students in Computer Science = 18% of 1800 = 324

Number of students in Arts = 12% of 1800 = 216

Number of students in Science = 15% of 1800 = 270

Number of students in Engineering = 25% of 1800 = 450

Number of students in Management = 20% of 1800 = 360

Number of students in Commerce = 10% of 1800 = 180

Total number of students studying Engineering and Science in 2021 = (450 + 270) = 720

Total number of students studying Management and Arts in 2019 = (240+150) = 390

Difference = 720 - 390 = 330

Percentage = $$\ \dfrac{330}{390}\times100=84.61\%$$

Hence, the number of students studying Engineering and Science in 2021 is 84.61% more than the number of students studying Management and Arts in 2019.

$$\therefore\ $$ The required answer is A.

The required figure is given below:

Let the total number of students in 2019 be $$x$$.

Number of Commerce students = $$15\%\ of\ x=225$$ (given)

$$x=1500$$

Number of students in 2021 increased by 20% as compared to 2019.

Total number of students in 2021 = $$1500\times\left(1+20\%\right)=1800$$

In 2019,

Number of students in Computer Science = 21% of 1500 = 315

Number of students in Arts = 10% of 1500 = 150

Number of students in Science = 18% of 1500 = 270

Number of students in Engineering = 20% of 1500 = 300

Number of students in Management = 16% of 1500 = 240

Number of students in Commerce = 225 (given)

In 2021,

Number of students in Computer Science = 18% of 1800 = 324

Number of students in Arts = 12% of 1800 = 216

Number of students in Science = 15% of 1800 = 270

Number of students in Engineering = 25% of 1800 = 450

Number of students in Management = 20% of 1800 = 360

Number of students in Commerce = 10% of 1800 = 180

Average number of students studying Engineering, Commerce and Arts in 2019 = $$\ \dfrac{300+225+150}{3}=225$$

Average number of students studying Management, Computer Science and Science in 2021 = $$\ \dfrac{360+324+270}{3}=318$$

Difference in the number of students = 318 - 225 = 93

Percentage difference = $$\ \dfrac{93}{318}\times100=29.24\%$$

Hence, the average number of students studying Engineering, Commerce and Arts in 2019 is 29.24% less than the the average number of students studying Management, Computer Science and Science in 2021. 

$$\therefore\ $$ The required answer is C. 

The required figure is given below:

Let the total number of students in 2019 be $$x$$.

Number of Commerce students = $$15\%\ of\ x=225$$ (given)

$$x=1500$$

Number of students in 2021 increased by 20% as compared to 2019.

Total number of students in 2021 = $$1500\times\left(1+20\%\right)=1800$$

In 2019,

Number of students in Computer Science = 21% of 1500 = 315

Number of students in Arts = 10% of 1500 = 150

Number of students in Science = 18% of 1500 = 270

Number of students in Engineering = 20% of 1500 = 300

Number of students in Management = 16% of 1500 = 240

Number of students in Commerce = 225 (given)

In 2021,

Number of students in Computer Science = 18% of 1800 = 324

Number of students in Arts = 12% of 1800 = 216

Number of students in Science = 15% of 1800 = 270

Number of students in Engineering = 25% of 1800 = 450

Number of students in Management = 20% of 1800 = 360

Number of students in Commerce = 10% of 1800 = 180

Let the number of male and female students in Computer Science in 2019 be $$3x$$ and $$4x$$ respectively. 

Total number of students in Computer Science in 2019 = $$3x+4x=7x$$

Total number of students in Computer Science in 2019 = 315 (given)

$$7x=315$$

$$x=45$$

Number of male students in Computer Science in 2019 = $$\left(3\times x\right)=\left(3\times45\right)=135$$

Number of female students in Computer Science in 2019 = $$\left(4\times x\right)=\left(4\times45\right)=180$$

Let the number of male and female students in Management in 2019 be $$7x$$ and $$5x$$ respectively.

Total number of students in Management in 2019 = $$7x+5x=12x$$

Total number of students in Management in 2019 = 240 (given)

$$12x=240$$

$$x=20$$

Number of male students in Management in 2019 = $$\left(7\times x\right)=\left(7\times20\right)=140$$

Number of female students in Management in 2019 = $$\left(5\times x\right)=\left(5\times20\right)=100$$

Total number of students in Management in 2021 = 360

Number of female students = 30% of 360 = 108

Number of male students = 360 - 108 = 252

Number of male students in Management in 2021 = 252

Total number of female students in Computer Science and Management in 2019 = (180 + 100) = 280

Difference = 280 - 252 = 28 

Percentage = $$\ \dfrac{28}{280}\times100\ =\ 10\%$$

Hence, the number of male students in Management in 2021 is 10% less than the total number of female students in Computer Science and Management is 2019. 

$$\therefore\ $$ The required answer is C. 

Using the formula,
Income of company A in 2017 = 362.5 and Expenditures of Company B in 2019 = 250.
The required ratio = 362.5 : 250 = 29:20.

Profit Percentage of Company B in 2016 = 40%
$$\frac{420\ -\ E}{E}\times\ 100\ =\ 40$$ where E is the expenditure of Company B in 2016.
This gives E = 300 and Profit = Income - E ==> 420 - 300 = 120.

Profit percentage of B in 2018 is 45%, 
Using the given formula for profit percentage and the given expenditure, we can find the income of B in 2018
$$\frac{Income-300}{300}=\frac{45}{100}$$
$$Income\ =\ 135+300=435\ crores$$
The profit by B in 2018 is $$435-300=135\ crores$$

Profit percentage of A in 2015 is 30%
Using the given formula for profit percentage and the given income, we can find the expenditure of A in 2015
$$\frac{390-Expenditure}{Expenditure}=\frac{30}{100}$$
$$3900-10Expenditure\ =\ 3Expenditure$$
$$Expenditure=300$$
The profit by A in 2015 is $$390-300=90$$

The ratio of B's profit to A's profit is $$\frac{135}{90}=\frac{3}{2}$$
Which means that B's profit is 150% of A's profit or B's profit is 50% more than A's profit. 

Hence, Option B is the correct answer. 

Let the expenditure of A and B in 2020 be X and 2X respectively, where X is a constant. 
We can see that the profit percent of A in 2020 is 35%
using the formula given for the profit percentage, we get $$\frac{I_A-X}{X}=0.35$$  {$$I_A$$ is the investment made by A}
= $$100I_A-100X=35X$$
=$$I_A=1.35X$$

We can also see that the profit percent of B in 2020 is 55%
Using the formula given for the profit percentage, we get $$\frac{I_B-2X}{2X}=0.55$$  {$$I_B$$ is the investment made by B}
$$10I_B-20X=11X$$
= $$I_B=3.1X$$

Total investment by A and B is 4.45X, which we know is equal to 534 crores, through this we get the value of X to be 120.
Thus, the total investment is 3X, which is $$3\times\ 120=360$$ crores

Therefore, option D is the correct answer. 

We know that the ratio of the total number of Boys to Girls ratio is 7:5;
we also know that the total number of students is 2400.
Taking Boys and Girls to be 7x and 5x respectively, we get 12x = 2400, giving us x = 200
And hence, the total number of boys to be 1400 and the total number of girls to be 1000. 

Next we're given that 15% of the boys are in section A, $$\frac{15}{100}\times\ 1400=210$$
And 22% of the girls are in section B, $$\frac{22}{100}\times\ 1000=220$$

Next, $$\frac{2}{7}$$ of the boys are in section B, $$\frac{2}{7}\times\ 1400\ =\ 400$$

We are also given that 500 boys are split between D and E in the ratio of 2:3, which would mean that D has 200 boys and E has 300 boys. 
And the remaining boys are in Section C; the number of boys remaining are 290. 

Next, we are given that 26% of the girls are in section D, that would mean that section d has 260 girls. 
We are also given that section B has 120 girls. 

The remaining girls must be split between section C and E, of which we know that C has 100 girls more than section E. 
Taking the number of girls in section E to be x, we can calulculate these values as we know that 400 girls are yet to be place in any section, 
giving us the equation $$2x+100=400$$
or simply $$x=150$$
which means that section E has 150 girls and Section C has 250 girls. 

Our final data looks like this:
Section       Boys    Girls
A                 210      220
B                 400      120
C                 290      250
D                 200      260
E                 300      150

The difference between the boys enrolled in C and girls enrolled in Section E is
=$$290-150$$
= 140

Hence, Option B is the correct answer. 

We know that the ratio of the total number of Boys to Girls ratio is 7:5;
we also know that the total number of students is 2400.
Taking Boys and Girls to be 7x and 5x respectively, we get 12x = 2400, giving us x = 200
And hence, the total number of boys to be 1400 and the total number of girls to be 1000.

Next we're given that 15% of the boys are in section A, $$\frac{15}{100}\times\ 1400=210$$
And 22% of the girls are in section B, $$\frac{22}{100}\times\ 1000=220$$

Next, $$\frac{2}{7}$$ of the boys are in section B, $$\frac{2}{7}\times\ 1400\ =\ 400$$

We are also given that 500 boys are split between D and E in the ratio of 2:3, which would mean that D has 200 boys and E has 300 boys.
And the remaining boys are in Section C; the number of boys remaining are 290.

Next, we are given that 26% of the girls are in section D, that would mean that section d has 260 girls.
We are also given that section B has 120 girls.

The remaining girls must be split between section C and E, of which we know that C has 100 girls more than section E.
Taking the number of girls in section E to be x, we can calulculate these values as we know that 400 girls are yet to be place in any section,
giving us the equation $$2x+100=400$$
or simply $$x=150$$
which means that section E has 150 girls and Section C has 250 girls.

Our final data looks like this:
Section  Boys  Girls
A             210  220
B             400  120
C             290  250
D             200  260
E             300  150

Total number of Girls in B & E = $$120+150=270$$
Total number of Boys in A & C = $$210+290=500$$

Ratio of the C&E girls to A&C boys is $$\frac{270}{500}=\ 0.54$$
Which means that there are 46% less girls in C&E than the boys in A&C.

Therefore, Option B is the correct answer. 

We know that the ratio of the total number of Boys to Girls ratio is 7:5;
we also know that the total number of students is 2400.
Taking Boys and Girls to be 7x and 5x respectively, we get 12x = 2400, giving us x = 200
And hence, the total number of boys to be 1400 and the total number of girls to be 1000.

Next we're given that 15% of the boys are in section A, $$\frac{15}{100}\times\ 1400=210$$
And 22% of the girls are in section B, $$\frac{22}{100}\times\ 1000=220$$

Next, $$\frac{2}{7}$$ of the boys are in section B, $$\frac{2}{7}\times\ 1400\ =\ 400$$

We are also given that 500 boys are split between D and E in the ratio of 2:3, which would mean that D has 200 boys and E has 300 boys.
And the remaining boys are in Section C; the number of boys remaining are 290.

Next, we are given that 26% of the girls are in section D, that would mean that section d has 260 girls.
We are also given that section B has 120 girls.

The remaining girls must be split between section C and E, of which we know that C has 100 girls more than section E.
Taking the number of girls in section E to be x, we can calulculate these values as we know that 400 girls are yet to be place in any section,
giving us the equation $$2x+100=400$$
or simply $$x=150$$
which means that section E has 150 girls and Section C has 250 girls.

Our final data looks like this:
Section  Boys  Girls
A            210   220
B            400   120
C            290   250
D            200   260
E            300   150

Total number of boys and girls in section D is $$200+260=460$$
Total number of girls in A, C and E is $$220+250+150=620$$

The required percentage would be $$\frac{460}{620}\times\ 100=74.19$$%
Correcting this to one decimal place would give us 74.2%

Therefore, option A is the correct answer. 

We know that the ratio of the total number of Boys to Girls ratio is 7:5;
we also know that the total number of students is 2400.
Taking Boys and Girls to be 7x and 5x respectively, we get 12x = 2400, giving us x = 200
And hence, the total number of boys to be 1400 and the total number of girls to be 1000.

Next we're given that 15% of the boys are in section A, $$\frac{15}{100}\times\ 1400=210$$
And 22% of the girls are in section B, $$\frac{22}{100}\times\ 1000=220$$

Next, $$\frac{2}{7}$$ of the boys are in section B, $$\frac{2}{7}\times\ 1400\ =\ 400$$

We are also given that 500 boys are split between D and E in the ratio of 2:3, which would mean that D has 200 boys and E has 300 boys.
And the remaining boys are in Section C; the number of boys remaining are 290.

Next, we are given that 26% of the girls are in section D, that would mean that section d has 260 girls.
We are also given that section B has 120 girls.

The remaining girls must be split between section C and E, of which we know that C has 100 girls more than section E.
Taking the number of girls in section E to be x, we can calulculate these values as we know that 400 girls are yet to be place in any section,
giving us the equation $$2x+100=400$$
or simply $$x=150$$
which means that section E has 150 girls and Section C has 250 girls.

Our final data looks like this:
Section   Boys  Girls
A             210   220
B             400   120
C             290   250
D             200   260
E             300   150

Total number of boys in B&C = $$400+290=690$$
Total number of girls in A&D = $$220+260=480$$
The difference is x=$$690-480=210$$

Total number of boys and girls in E, y=$$300+150=450$$

The difference between x and y is $$450-210=240$$
This is $$\frac{240}{450}\times\ 100\ =\ 53.33\ \%\ $$ of y. 
Rounding it to the nearest integer gives us that x is 53% smaller than y. 

Therefore, Option D would be the correct answer. 

Export of A in 2015, 2016, 2019 are 
$$320\times\ 0.35=112$$
$$350\times\ 0.30=105$$
$$450\times\ 0.34=153$$
Total : 370

Export of B from 2016 to 2019:
$$200\times\ 0.42=84$$
$$350\times\ 0.34=119$$
$$320\times\ 0.30=96$$
$$300\times\ 0.27=81$$
Total : 308

Their ratio = $$\frac{370}{380}=37:38$$

Hence, Option A is the correct answer. 

B's average production in 2016, 2017 and 2018 is $$\frac{200+350+320}{3}=\frac{870}{3}=290$$
C's Domestic produce in 2015 and 2019 = $$350\times\ \frac{70}{100}(=245)$$ and $$325\times\ \frac{60}{100}(=195)$$
=$$440$$

The required percentage is $$\frac{290}{440}\times\ 100=65.9\%$$
The closest approximation go this would be 66% and hence, option c. 

A's export in 2017 = $$300\times\ \frac{40}{100}=120$$
A's export in 2018 = $$400\times\ \frac{45}{100}=180$$
A's total export in 2017 + 2018 = 300

B's domestic production in 2017 = $$350\times\ \frac{66}{100}=231$$
B's domestic production in 2019 = $$300\times\ \frac{73}{100}=219$$
B's total domestic produce in 2017 + 2019 = 450

A's export is 150 million tonnes less than the B's domestic produce. 
The percentage required  = $$\frac{150}{450}\times\ 100=33.33\%$$

Therefore, option C is the correct answer. 

The percentage increase in the production of foodgrain A in 2019 over 2018 will be $$\dfrac{450-400}{400}\times 100 = \dfrac{100}{8}\%$$

Therefore, the production of foodgrain A in 2020 over 2019 will be $$450\times \left(1+\dfrac{100}{800}\right)= 506.25$$

And the total Exports will be $$506.25\times \dfrac{40}{100} = 202.5$$

And the Domestic consumption will be $$506.25-202.5=303.75$$

The production of foodgrain C in 2020 will be $$325\times \left(1+\dfrac{35}{100}\right)= 438.75$$

And the total Exports will be $$438.75\times \dfrac{40}{100} = 175.5$$

And the Domestic consumption will be $$438.75-175.5= 263.25$$

Therefore, the total Domestic consumption for A and C in 2020 will be $$263.25+303.75 = 567$$

Out of the total Employees enrolled, E, F and G had total share of 8+12+16 = 36%
So the total number of employess enrolled from these three were, $$0.36\times\ 23550$$

Of all the employees who passed the exam, E, F, and G had a total share of 9+15+12 = 36%
So the total number of employees who passed from these three were, $$0.36\times\ 3700$$

Therefore the percentage of employees who passed from E, F and G were $$\frac{0.36\times\ 3700}{0.36\times\ 233550}\times\ 100=15.711\%$$

Number of employees who enrolled from E and C were, 8+10= 18% of 23550
Which is equal to 4,239

Number of employees who passed from D and A were, 16 + 18 = 34% of 3700
Which is equal to 1,258

The difference would be 4239-1258 = 2981
Therefore, Option A would be the correct answer. 

Since the values are given as percentages of the same numbers and we only have to find the highest and not the exact values, we can find the ratio between all of the options and see which is the highest value. 

C: 13% of passed/ 10% of enrolled
F: 15% of passed/ 12% of enrolled 
B: 17% of passed/ 16% of enrolled
E: 9% of passed/ 8% of enrolled

we can take passed/enrolled as constant K since they are same in all of the calculations, this would give us

C: 1.3 K
F: 1.25 K
B: 1.0625 K
E: 1.125 K

As we can see, C has the highest percentage of employees passed to enrolled ratio. 

The number of employees enrolled from A and E together are : 22+8 = 30% of 23550
The number of employees passed from A and G together are: 18+12 = 30% of 3700

The required ratio is $$\frac{23550}{3700}=\frac{471}{74}$$
Therefore, Option D is the correct answer. 

Average list price of the first four years: $$\frac{3+6+8+7}{4}=6$$
Average list price of the last four years: $$\frac{5+9+8+10}{4}=8$$
Increase = 2
percentage increase : $$\frac{2}{6}\times\ 100=\frac{100}{3}$$  {x}

Average net price of the first four years: $$\frac{2000+5000+7000+5000}{4}=\frac{19000}{4}$$
Average net price of the last four years: $$\frac{3000+6000+5000+8000}{4}=\frac{22000}{4}$$
Increase = $$\frac{3000}{4}$$
Percentage increase: $$\frac{3000}{4}\times\ \frac{4}{19000}\times\ 100=\frac{300}{19}$$  {y}

Putting these values in the given term we get:
$$\sqrt{\left(\ 3\times\ \frac{100}{3}\right)+\left(19\times\ \frac{300}{19}\right)}$$
$$\sqrt{\ 400}=20$$

Therefore, Option A is the correct answer. 

The question had an error in the original question paper, where the ratio $$\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$ was given as $$5\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$.

The sum of the product's net prices in 2015, 2016 and 2017 is $$7000+5000+3000=15000$$ million
The products list price in year 2017 is 5 billion, which is equivalent to 5000 million.
The ratio of the sum of net prices to the list price would be 15000:5000 = 3:1

Equating this with the ratio we are given, we get
$$\left(5+\frac{1}{p}+\frac{1}{p^2}\right)\ \frac{75}{131}:1\ =\ 3:1$$
$$\frac{\left(5p^2+p+1\right)}{p^2}\times\ \frac{75}{131}=3$$

131 is a prime number and in order to cancel it out from the denominator, we would require 131 in the numerator as well. 
At this point, we can try putting in the options to see if we can get 131 in the numberator.

putting p=5, we get $$\left(5(5)^2+(5)+1\right)$$ as 131
Using 5 as the value of p, we get:
$$\ \frac{131}{25}\times\ \frac{75}{131}=3$$

Therefore, Option C is the correct answer. 

(A) In 2020, The list price was 8000 Million or 8 Billion, which is more than the total list price in 2013.
Therefore, statement A is correct. 

(B) The highest net price was in year 2020 of 8000 Million or 8 Billion while the lowest list price was in year 2013 of 3 Billion. 
Therefore, statement B is correct. 

(C) Let's take the total market to be of 100 price units. 25 price units were from routers and 15 price units were from switches. After decreasing the router's price by 10% is comes down to 22.5 units and increasing the switches prices by 10% it come sup to 16.5%
The routers are still higher than the switches, therefore, statement C is incorrect. 

The average product net price would be: $$\frac{2000+5000+7000+5000+3000+6000+5000+8000}{8}=5125$$
The average of product prices less than this average price: 
$$\frac{2000+5000+5000+3000+5000}{5}=4000$$

The average product price greater than this average price would be:
$$\frac{7000+6000+8000}{3}=7000$$

The difference between these two averages would be 7000 - 4000 = 3000 million dollars. 
Hence, Option C is the correct answer. 

After reading the chart, we can get the data:

School   Total    Passed  Distinction  Without distinction     
A            800      640          300              340
B           1050     840          350              490
C           1200     920          450              470
D            750      600          260              340
E            900      750          330              420
F           1500     1000         450              550

Finding the percentage of students who passed without distinction to the total number of students who appeared we get:
A = $$\frac{340}{800}\times\ 100=42.5\%$$
B = $$\frac{490}{1050}\times\ 100=46.67\%$$
C = $$\frac{470}{1200}\times\ 100=39.1667\%$$
D = $$\frac{340}{750}\times\ 100=45.33\%$$
E = $$\frac{420}{900}\times\ 100=46.667\%$$
F = $$\frac{550}{1500}\times\ 100=36.67\%$$

We can see that B and E have the same percentage which aligns with option B. 
Therefore, Option B will be the correct answer. 

For this part, we will also have to calculate the number of students who failed in each school. 
adding that to our previous data table we get:

School    Total     Passed    Distinction     Without distinction    Failed
A              800          640            300                      340                   160
B             1050         840            350                      490                   210
C             1200         920            450                      470                   280
D              750          600            260                      340                   150
E              900          750            330                      420                   150
F             1500        1000           450                       550                   500


Calculating the students who passed with distinction as a percentage of students who failed for the given options we see, 
Option A: $$\frac{470}{280}\times\ 100\approx\ 170\%$$
Option B: $$\frac{420}{150}\times\ 100\approx\ 280\%$$
Option C: $$\frac{490}{210}\times\ 100\approx\ 230\%$$
Option D: $$\frac{550}{500}\times\ 100\approx\ 110\%$$

We can see that Option D or School F has the least percentage in this category. 
Therefore, Option D is the correct answer. 

School     Total      Passed      Distinction      Without distinction     Failed
A             800            640             300                       340                       160
B            1050           840              350                       490                      210
C            1200           920              450                       470                      280
D             750            600              260                       340                      150
E             900            750              330                        420                     150
F            1500          1000             450                        550                     500


Using our collected data, we can easily calculate the average number of students who failed in A, B, C and E to be $$(160+210+280+150)/4=800/4=200$$
The number of students who passed without distinction is 340.

Ratio of these two values is $$\frac{200}{340}=0.588$$
Which means that the average number of students who failed in A, B, C and E is 41.176% smaller than the number of students who passed without distinction in D. 
This is approximately 41%. 

Therefore, Option A is the correct answer. 

School   Total   Passed   Distinction    Without distinction      Failed
A             800          640          300                    340                         160
B            1050         840           350                    490                         210
C            1200         920           450                    470                         280
D              750         600           260                    340                         150
E              900         750           330                    420                          150
F             1500        1000         450                     550                         500


We are given that the 840 students who passed in B, the boy to girl ratio is 3:4, which gives us 360 boys and 480 girls in B.
Similarly, we are given that of the 920 students who passed in C, the boy to girl ratio is 11:12, which gives us 440 boys and 480 girls in C. 
And now we can calculate the total number of boys who passed from B and C, 800 boys. 

Next. the total number of students who passed with distinction from D, E and F are $$260+330+450=1040$$

the ratio of these students to the boys from B&C is $$\frac{1040}{800}=1.3$$
Which tells us that there are 30% more students who passed with distinction from D,E and F when compared to the number of boys from B&C. 

Therefore, Option B is the correct answer.  

Upon calculating the number of vacant seats on every day of the week, we get the data. 

The total number of seats vacant throughout the week would be 630. 

In making a pie chart, these 630 seats would encompass 360 degrees. So the number of degrees per seat would be $$\frac{360}{630}$$
Monday will have $$\frac{360}{630}\times\ 105\ =\ 60$$ degrees
Thursday will have $$\frac{360}{630}\times\ 140\ =\ 80$$ degrees

The difference between the angles covered by Monday and Thursday will be 20 degrees. 

Hence, Option D is the correct answer. 

Calculating the 2nd class non-Ac vacant seat data and Wednesday's  vacant seat data, we get 

Calculating the 2nd Non-AC vacant seats on Monday, Tuesday and Friday, we get, $$210+180+150=540$$

Vacant seats on Wednesday are, $$60+120+140+125+35=480$$

The percentage can be calculated as,

$$Percentage\ =\ \dfrac{\left(540\ -\ 480\right)}{540}\ \times\ 100\ =\ \dfrac{60}{540}\ \times\ 100\ =\ \dfrac{100}{9}\ =\ 11.1\%$$

Therefore, option A is correct. 

Calculating the vacant seats in AC Tier I class, gives us the data

Average number of reserved seats in 2nd Class Non-Ac on Wednesday and Saturday is $$\frac{\left(840+760\right)}{2}=800$$
Total number of vacant seats in AC I tier are $$50+30+35+25+20+12=172$$

The required percentage is $$\frac{172}{800}\times\ 100=21.5\%$$

Therefore, Option A is the correct answer. 

Calculating vacant seats on Thursday and AC III gives us the data, 

Total Vacant seats on Thursday are: $$100+40+80+140+25=385$$
Total vacant seats in AC III are: $$160+90+140+80+150+120=740$$
The difference between them; $$740-385=355$$

Total reserved seats in Non-Ac on Thursday and Saturday are; $$800+360+760+320=2240$$

The required percentage is $$\frac{355}{2240}\times\ 100\approx\ 15.8\%$$

Therefore, Option B is the correct answer. 

Checking the Export for all of the options we see:
Option A: 2017
Wheat Export - 40% of 180 = 72
Rice Export - 28% of 200 = 56
Total Export - 128

Option B: 2019
Wheat Export - 35% of 320 = 112
Rice Export - 48% of 300 = 144
Total Export - 256

Option C: 2020
Wheat Export - 30% of 360 = 108
Rice Export - 40% of 280 = 112
Total Export - 220

Option D: 2018
Wheat Export - 45% of 240 = 108
Rice Export - 32% of 250 = 80
Total Export - 188

As we can see, only option C satisfies our condition.
Therefore, Option C is the correct answer.

Total Domestic consumption of Rice in 2017: 72% of 200 = 144
Total Domestic consumption of Rice in 2019: 52% of 300 = 156
Adding them up we get,  300 million tonnes.

Exports of wheat in 2016, 2017 and 2020 are
$$\left(32\%\ of\ 250\right)+\left(40\%\ of\ 180\right)+\left(30\%\ of\ 360\right)$$
= $$80+72+108$$
= $$260\ $$ million tonnes

Calculating the domestic rice consumption to the wheat export we get, $$\frac{300}{260}=\ 1.1538$$
Which means the domestic consumption is 15.38% higher. 
Rounding it to one decimal place gives us, 15.4%
Hence, option C is the correct answer.  

Domestic consumption of rice in 2019: $$0.52\times\ 300\ =\ 156$$ million tonnes.

Average production of wheat in 2017, 2018 and 2020 is:
$$\frac{\left(180+240+360\right)}{3}=\ \frac{780}{3}=260$$ million tonnes.

Domestic consumption of rice in 2019 as a percentage of average production of wheat in 2017, 2018 and 2020 is $$\frac{156}{260}=0.6$$;
Which is equivalent to 60%

Therefore, Option D is the correct answer. 

Increase of Wheat production from 2019 to 2020: $$\frac{36-32}{32}\times\ 100=12.5\%$$
Wheat production in 2021: $$360\times\ 1.125$$ = 405
The domestic consumption would be $$60\%\ of\ 405$$

Rice production in 2021: $$280\times\ \frac{6}{5}=336$$
Domestic consumption would be $$60\%\ of\ 336$$

The difference between them would be :
= $$60\%\ of\ 405$$ - $$60\%\ of\ 336$$
=$$\frac{3}{5}\times\ \left(405-336\right)=\frac{3}{5}\times\ 69=\frac{207}{5}=41.4$$

Therefore, Option A is the correct answer. 

Taking X and Y as one pair, we can have 8 people on 8 seats. These 8 elements can be seated in 8! ways and X and Y can be seated in 2! ways. Therefore, the total number of ways X and Y can be seated together are 2!8!
Total number of ways 9 people can be seated is 9!

The probability that X and Y will be seated together is $$\frac{2!8!}{9!}=2\times\ \frac{8!}{9\times\ 8!}=\frac{2}{9}$$
Therefore, Option C is the correct answer.

The simplest way to solve this question would be through the options. 

Option A: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 3 becomes, 
$$3x^{2} — 7x + 3 = 0$$ and $$—7x^{2} + 3x + 3 = 0$$
Where we can not calculate the roots by factorisation. 

Option B: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 6 becomes, 
$$3x^{2} — 7x + 6 = 0$$ and $$—7x^{2} + 6x + 3 = 0$$
Where again,we can not calculate the roots by factorisation.

Option C: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k= 4 becomes, 
$$3x^{2} — 7x + 4 = 0$$ and $$—7x^{2} + 4x + 3 = 0$$
Where the first equation has roots 1 and 4/3 and the second equation has roots 1 and 3/7

Option D: $$3x^{2} — 7x + k = 0$$ and $$—7x^{2} + kx + 3 = 0$$ on putting k = 2 becomes, 
$$3x^{2} — 7x + 2 = 0$$ and $$—7x^{2} + 2x + 3 = 0$$
Where the first equation has roots 2 and 1/3 but for the second equation, we can not calculate the roots by factorisation.


We can see that option C gives us one common root, hence, that would be our answer. 

We can find the remainder on dividing by 9 and then find the negative remainder in order to find the reminder we would have gotten on dividing by -9. 
$$\left[\frac{8-5^{17}\times\ 2^{20}}{9}\right]_R$$
$$\left[\frac{8}{9}\right]_R-\left[\frac{5^{17}\times\ 2^{17}\times\ 2^3}{9}\right]_R$$
$$-1-\left[\frac{10^{17}}{9}\right]_R\times\ \left[\frac{8}{9}\right]_R$$
$$-1-1^{17}\times\ \left(-1\right)$$
$$-1+1\ =\ 0$$
Upon reversing the sign to calculate the remainder on dividing it by -9, we get 0 again. 
Hence, the remainder is 0.

When $$5x^4-3x^3+2x^2-1\ $$ is divided by $$x^2+4$$, the quotient is $$5x^2-3x-18$$ and the remainder is $$12x+71$$
Here we are asked to take the quotient as f(x);
f(x) = $$5x^2-3x-18$$

When $$2x^3-x+1$$ is divided by $$x^2+x+1$$ the quotient is $$2x-2$$ and the remainder is $$-x+3$$
Here we are asked to take the remainder as g(x);
g(x) = $$-x+3$$

We are to find the remainder when f(x) is divided by g(x)
Upon dividing we would get the quotient as -5x-12 and the remainder is 18. 

Hence, Option B is thee correct answer. 

Statement 1: 
Remainder of 3864335 when divided by 300 is a short calculation and gives us the remainder as 35. 
Remainder of 3864335 when divided by 382 is lengthy but after dividing the remainder would be 23.
Sum of these remainders is 58, this is twice of the remainder we get on dividing the unknown number by 32; 
This remainder would be 29
We now have to check the remainder when 1021 is divided by 32, 
1024 is $$32^2$$, so $$\left[\frac{1024}{32}\right]_R=-3=\ 29$$
And hence, we can confirm that statement 1 is correct. 

Statement 2: According to Wilson's theorem, 
$$\left[\frac{\left(p-2\right)!}{p}\right]_R=1$$ where P is a prime number. 
Taking P =47 we get, $$\left[\frac{45!}{47}\right]_R=1$$ and subtracting 1 from this would mean that 45!-1 is divisible by 47. 
Therefore, Statement II is incorrect. 

We need to first convert $$20_{\left(base-3\right)}$$ and $$202_{\left(base-3\right)}$$ into decimal system so as to get the values of a and b in the decimal system.
20 in 10 base system would be : $$\left(2\times\ 3^1\right)+\left(0\times\ 3^0\right)$$ = 6
202 in 10 base system would be : $$\left(2\times\ 3^2\right)+\left(0\times\ 3^1\right)+\left(2\times\ 3^0\right)=20$$

so a+b = 6 and $$a^2+b^2=20$$
From this we get, ab = 8
Trying out different values we can get the values of a and b to be 4 and 2 
converting these from decimal to 3 base system we get 2 as 2 only and 4 as $$\left(1\times\ 3^1\right)+\left(1\times\ 3^0\right)$$ = $$11_{\left(base-3\right)}$$

Therefore, Option A is the correct answer. 

David faces east and walks 70 steps in the east direction. 
After this, without turning his back, David walks 30 steps in reverse direction. Landing him 40 steps east of the starting point, facing eastwards. 
After this he reverses his back, and is now facing west towards his starting point. He then walk 20 steps in the direction he is facing i.e, 20 steps towards the starting point. Making his final position 20 steps east of the starting point. 
1 step measures 2 feet, so 20 steps would measure 40 meters. 
Therefore, David is 40 meters east of the starting point. 

Hence, Option C is the correct answer. 

Lateral surface area of a cube is $$4a^2$$, where a is the side length.
We are given that the lateral surface area is 2304, solving this for a, we get
$$a^2=576$$
$$a=24$$

Now we need to divide this cubic room which is of 24 m side length, in small 4m wide rooms which have the same length and height. 
For this we will be placing plywood parallel to the height of the room and a distance of 4 meters.

The room will be divided in 6 small rooms of 4 meter width and for this we would require 5 plywood sheets. 
The number of segments is 1 +  the number of cuts made. 

{Since, the length of the room is close is the the width section we want to divide the room in, we can count the number of plywood sheets we would need by drawing a rough sketch. But it is recommended to know such common logical reasoning solutions.}

Therefore, the correct answer would be Option D. 

Suppose we have two lines $$a_1x+b_1y+c_1=0$$ and $$a_2x+b_2y+c_2=0$$
The equation of pair of these two equations would be obtained by multiplying these two equations, 
Giving us, $$a_1a_2x^2+b_1b_2y^2+x\left(a_1c_2+a_2c_1\right)+y\left(b_1c_2+b_2c_1\right)+xy\left(a_1b_2+a_2b_1\right)+c_1c_2=0$$
Comparing this with the equation we have, we can start finding the values, 
$$a_1=a_2=1$$
From coefficient of x, we get $$c_1+c_2=-1$$
From the constant in the equation we get, $$c_1c_2=-2$$
The value of $$c_{1\ }and\ c_2$$ in some order must be -2 and 1 

From coefficient of xy, we get $$b_2=-b_1$$
And through coefficient of $$y^2$$, we get that $$b_{1\ }or\ b_2=\pm\ 2$$
Since the coefficients of x are equal in both the equations, b becomes the only differentiating point. 
The equations will therefore now be, 
$$x+2y+c_1=0$$ and $$x-2y+c_2=0$$
Where we can have two case:
Case 1: $$c_1=-2\ \&\ c_2=1$$
The required value would be : -6

Case 2: $$c_2=-2\ \&\ c_1=1$$
The required value would be : 6

The product of possible values therefore is -36

Upon finding the prime factors of 2835, we get $$7\times\ 5\times\ 3^4$$
Since we know that the HCF of x and y is 9, the $$3^4$$ must be split equally between x and y. 
Now the possible pair values of x and y are (315, 9) or (45,63) {This we get by distributing the remaining 5 and 7 between x and y}
of these pairs, we cannot we cannot find the exact values of x and y. 
So we will have to find the possible combinations for 2x+y and find those values. 
x=9 and y=315 gives us 333
x=63 and y=45 gives us 171
x=45 and y=63 gives us 153
x=315 and y=9 gives us 639

We can see that of all of these values, 333 and 153 are in the option C. 
Hence, Option C is the correct answer. 

The total number of pencils bought is $$20\times\ 12=240$$ and the price of each pencil is $$\frac{240}{12}=20$$ rs. 
Therefore, the total money invested is 4,800

Now, 2/3 rd of the pencils i.e, $$\frac{2}{3}\times240=160\ $$ pencils are sold at rs 25, earning back $$160\times\ 25=4,000$$
The remaining 80 pencils are sold at rs 22, earning back $$80\times\ 22=1,760$$
Giving us a net revenue of Rs 5,760 and a net profit of Rs 960

The profit percentage is $$\frac{960}{4800}\times\ 100=20\%$$
Therefore, Option A is the correct answer.

We are given that the highest common divisor of x and y is 2, which means that both of them are even. 
Next we are asked, for how many values of x can we have x+y=99
Now, 99 is an odd number, to get an odd number by addition of two numbers, one of those numbers must be odd and the other must be even. 
But we know that both x and y are even as they are both divisible by 2.
Therefore, no value of x and y is possible which satisfy both the conditions. 

Hence, Option C is the correct answer. 

Let's take the original work to be a multiple of the LCM of 24, 30 and 32; that would be 480x.

Now the efficiencies of Ajay, Bharat and Chandu are 20x, 16x and 15x units/day respectively. 

In the process defined in the question, we can add up the efficiencies of Ajay and Chandu, since they always work together, giving us an efficiency of 35x units/day. 
The next day, Bharat does 16x units/day.

In two days, these three do a total of 51x units/two-day.

So, in 9 days(18 days), all three can do a work of 51x*9 = 459x units.

Now, the remaining work is 480x-459x = 21x

The efficiencies of Ajay and Chandu, since they always work together, giving us an efficiency of 35x units/day.

They work together and complete the work in 21x/35x = 0.6 days

Option A is $$18\ \frac{21}{35}$$, this 21/35 is nothing but 0.6
So we can conclude that the answer would be Option A, without calculating the exact value.

Solving the given relation, 
$$\frac{157}{68}=2+\frac{1}{3+\frac{1}{4+\frac{1}{x}}}$$
$$\frac{21}{68}=\frac{1}{3+\frac{1}{4+\frac{1}{x}}}$$
$$3+\frac{1}{4+\frac{1}{x}}=\frac{68}{21}$$
$$\frac{1}{4+\frac{1}{x}}=\frac{5}{21}$$
$$\frac{21}{5}=4+\frac{1}{x}$$
$$\frac{1}{5}=\frac{1}{x}$$

Giving the value of x to be 5, 
Using this we can find the value of polynomial to be 
$$5^3+3\left(5\right)^2-9\left(5\right)+5$$
$$125+75-45+5$$
= 160

Therefore, Option A is the correct answer. 

The distance between the 1st position and 2nd position would be 2 meters. 
The distance between the 2nd position and 3rd position would be 3 meters.
The distance between the 3rd position and the 4th position would be 4 meters. 
we can see a pattern emerging here, 
.....
The distance between the 49th position and the 50th position would be 50 meters. 

So the total distance between the 1st position and the 50th position would be 2+3+4+......+50
We can easily calculate this as the sum of an AP and it turns out to be $$\frac{49}{2}\left[2\left(2\right)+\left(48\times\ 1\right)\right]$$
Which is equal to 1274

Hence, Option A is the correct answer. 

Let's take the original marked price to be MP.
2/3rd of the original 300 pumpkins were sold at the marked price, so the sales from this part is 200 MP.
75% of the remaining 100 pumpkins, which is 75 pumpkins were sold at a 20% discount, the sales from this part would be
 $$75\times\ \frac{4}{5}MP\ =\ 60MP$$
The remaining 25 pumpkins are sold at 40% discount, the sales from this part would be $$25\times\ \frac{3}{5}MP=15MP$$.

This gives us a total sales of $$200MP+60MP+15MP=275MP$$
We are given that this is equal to 2750, which gives us the value of MP to be 10.

Thus, Option B is the correct answer. 

In cases of question asking the probability of an event happening at least one time, it is usually easier to calculating the probability of the event not happening at all and subtracting it from 1.
In this case, we can find the probability of both dices rolling any number but 4, so each dice will have 5 available options. 
The probability of this happening on one dice is $$\frac{5}{6}$$ and the probability of this happening on both the dices simultaneously is $$\frac{5}{6}\times\frac{5}{6}=\frac{25}{36}$$

Now subtracting this from 1 gives us the required probability, $$1-\frac{25}{36}=\frac{11}{36}$$

Hence, Option B is the correct answer. 

Although option C might seem like a good choice,we have to remember that the given function is not algebraic is nature. 
Upon simplifying g(x) we get, 
$$g(x) = \sin (x + \pi) + \sin (2x + \pi) + \cos (3x + \pi)$$
$$g(x) = -\sin (x) - \sin (2x) - \cos (3x)$$
This is because $$\pi\ +x\ $$ lies in the third quadrant, where both sine and cosine functions are negative. 
We can get g(x) upon reflection of f(x) along the x-axis, but it is not possible using the operations given in option A, B and C. 
Therefore, Option D is the correct answer. 

Volume of the semi-sphere = $$\frac{1}{2}\times\ \frac{4}{3}\pi\ r^3$$
Diameter of the Semi-sphere = 2r

Volume of the Cone = $$\frac{1}{3}\times\ \pi\ r^2h$$
Diameter of the base of the cone = 2r

We are given that the diameter of the sphere is 4 inch. 
2r = 4
giving us, r = 2 inches

We are also given that the volume of the cone and volume of the semi-sphere are equal. 
using r =2 gives us,
$$\frac{1}{2}\times\ \frac{4}{3}\pi\ r^3$$ = $$\frac{1}{3}\times\ \pi\ r^2h$$
$$\frac{1}{2}\times\ \frac{4}{3}\pi\ 8$$ = $$\frac{1}{3}\times\ \pi\ 4h$$
this gives us h=4

Now we are to find the volume of the upper half of the toy. 
The total height of the toy is 2 inches of the semi-sphere + 4 inches of the cone = 6 inches
So the upper half of this toy would be the upper 3 inches of the cone. 

We will have to find the radius of base of this section of cone. 
Using the tan of the semi-angle of the cone we get, $$\tan\ \theta\ =\frac{perpendicular}{base}=\frac{2}{4}=\frac{required\ base}{3}$$
This gives the required base radius as $$\frac{3}{2}$$ inches. 

Finding the volume of this section of the cone, $$\frac{1}{3}\pi\ \left(\frac{3}{2}\right)^23\ =\ \frac{9\pi}{4}$$
Hence, Option D is the correct answer. 

Let the efficiency of a single man and single woman by M units/day and W units/day respectively. 

The first statement is : Total work = 18(M + W)                       {Work = Time x efficiency}
The second statement is: Total work = 5(4M  + 3w)

Since, the total work is same in both the equations, we can equate them to get;
$$18M+18W=20M+15W$$
$$3W=2M$$
$$M=\frac{3}{2}W$$

With this relation, we can find the total work in terms of W or M; Using equation 1 to find the total work in terms of W we get, 
$$18\left(\frac{3}{2}W\right)+18W=45W$$
Now the time taken by 2 men and 3 women to do this work will be 
Time x($$2\left(\frac{3}{2}W\right)+3W\ =\ 45W$$
Time = $$\frac{45}{6}=\frac{15}{2}=7\ \frac{1}{2}$$

Therefore, Option B is the correct answer. 

We want the function to be odd i.e, f(-x) = - f(x)
Now we know that sin(-x) = - sin (x) as sine is an odd function 
But cos (-x) = cos (x) as cosine is an even function

So if we put the input as -x in our defined function, we get, 
= $$\sum_{j=1}^k a_{j} \cos(-jx) + \sin (-x) + 2 \sin (-3x) + 4 \sin (-8x)$$
= $$\sum_{j=1}^k a_{j} \cos(jx) - \sin x - 2 \sin 3x - 4 \sin 8x$$
I we want both of these terms to be equal, we would have to remove the cosine term 
Option B does just that, by putting the coefficient of the cosine function as zero for all values of j. And the range given in option B is the same as the range of j in the given function.
This would give us the value of function to be  $$\sin (x) + 2 \sin (3x) + 4 \sin (8x)$$, which is an odd function. 
So option B is the correct answer.

The question asks us the integer values of x for which, the inequality
$$\left|\left|x+3\left|-\right|x-3\right|\right|<6$$ is satisfied. 
We can also interpret the given inequality as, 
$$-6<\left|x+3\left|-\right|x-3\right|<6$$

Now we see that there are two key points to take note of, where the modulus shows it's effects. Those are at x=-3 and x=3
We need to check the value of the middle term for the three cases of x<-3, -3<x<3 and 3<x

For x< -3, 
We see that the first and second modulus terms will have negative values inside them, and will thus reverse the sign. 
We can take a value as an example to see the result. Let's take x= -10
$$\left|-10+3\right|-\left|-10-3\right|$$
$$\left|-7\right|-\left|-13\right|$$
$$7-13\ =\ -6$$
For any negative value of x < -3, the answer will be -6. 
This does not satisfy our condition as we need the resulting values bigger than -6.

For x> 3,
We see that both the terms in the modulus will be positive and hence the modulus will not change any signs.
$$\left(x+3\right)-\left(x-3\right)$$
$$x+3-x+3\ =\ 6$$
For any value of x> 3, the answer would be 6. 
This again does not satisfy our condition and thus is not valid. 

For -3< x< 3, 
For this range, the first modulus term will have positive value inside while the second modulus modulus will have a negative value inside. 
$$\left(x+3\right)-\left(-\left(x-3\right)\right)$$
$$\left(x+3\right)-\left(-x+3\right)$$
$$\left(x+3\right)+x-3$$
$$2x$$
And since the values of x lies between -3 and 3, the values of 2x lies between -6 and 6. 
And thus this range satisfies the inequality.

The integers that lie in this range are -2, -1, 0, 1 and 2.
So a total of 5 integers satisfy this inequality.

Since we know that b is a cube, we should try to express b in terms of its prime factors to get a clear idea on how to proceed. 
$$b=8^8=\left(2^3\right)^8=2^{3\times\ 8}=2^{24}$$
Now, $$b=a^3=2^{24}$$
$$a=\sqrt[\ 3]{2^{24}}=2^{\frac{24}{3}}=2^8$$
Which is equal to 256

Therefore, Option A is the correct answer. 

Let P and Q's income be 16x and 9x respectively, and P and Q's expenditure be 8y and 5y respectively, where x and y are constants. 

P's savings = 16x - 8y
Q's savings = 9x - 5y

We are given that P's savings are 220% more or 320% of Q's savings. Using this we get, 
$$16x-8y=\frac{32}{10}\left(9y-5x\right)$$
$$160x-80y=288x-160y$$
$$80y=128x$$
$$\frac{y}{x}=\frac{8}{5}$$

we are given that R's earning are 25% less than P's earnings, using this we get R's earnings to be $$\frac{3}{4}\times\ 16x=12x$$
We are also given that R's expenses are 20% more than Q, using this we get R's expenditure to be $$\frac{6}{5}\times\ 5y=6y$$

This gives R's savings to be 12x - 6y, using the relation between y and x, we can convert this in terms of x, 
$$12x-6\left(\frac{8}{5}x\right)=12x-\frac{48}{5}x=\frac{12}{5}x$$

The ratio of P's income to R's savings would be $$\frac{16x\times\ 5}{12x}$$
=$$\frac{20}{3}$$

Therefore, Option B is the correct answer. 

Option A: 
$$4a^{2} — 3ab + b^{2} \geq 9$$
= $$4a^{2} — 4ab + b^{2} + ab \geq 9$$
= $$\left(2a\ -\ b\right)^2+ab\ \ge\ 9$$

From this we cannot necessarily say that $$ab\ \ge\ 9$$, because we don't know the value of $$\left(2a-b\right)^2$$

If we look at option D which is very similar, 
It says that we have $$ab\ \ge\ 9$$ and we have to prove $$4a^{2} — 3ab + b^{2} \geq 9$$. 
From the inequality we derived above, $$\left(2a\ -\ b\right)^2+ab\ \ge\ 9$$, 
from the option we know that$$ab\ge\ 9$$ , therefore, this term would absolutely be $$\ge\ 9$$ since the minimum value $$\left(2a-b\right)^2$$ can have is zero and even that satisfies the condition. 

Option B is simple calculations, where upon squaring the original statement, we get $$9a^{2} — 12ab + 4b^{2} > 0$$ which is opposite to what are are supposed to check. 

Option C is different, Upon taking a common from the given equation, we get:
$$a\left(9a-12b+4b^2\right)=0$$
Since it's given that a and b are non-zero, the second term must be zero.
Solving this for b we would reach an irrational equation where we cannot solve for b anymore and not reach the value of b= 2a/3
That is, we cannot reach the conclusion that b=2a/3 from the initial equation. 

Therefore, Option D is the correct answer. 

Thinking about this through a number line would make the solution a lot simpler. 

We can eliminate option B and C because we are talking about the distance between two numbers, that would be an absolute value and thus never less than zero. 
Option A comes close but miss out on the case of zero. The distance between zero and double of zero, which would be zero again is also zero. 
That is why Option D would be the correct answer. 
It covers all the cases as the distance between a number and double of that number, for negative numbers, positive numbers and zero. 

After seeing that the initial quadratic equation cannot be easily factorised, we should be looking at the sum and product of the roots, 
Sum of the roots: $$x_1+x_2=2$$
Product of roots: $$x_1x_2=\frac{5}{2}$$

Now for the new equation we need, we can again calculate the sum and product of roots. 
Sum of roots: $$x_1\ +x_2\ +\frac{1}{x1}+\frac{1}{x2}$$
                     =$$\left(x_1+x_2\right)+\left(\frac{x_1+x_2}{x_1x_2}\right)$$
                     =$$\left(x_1+x_2\right)\left(1+\frac{1}{x_1x_2}\right)$$  
Putting in the values, we get: $$2\left(1+\frac{2}{5}\right)=\frac{14}{5}$$

Product of roots: $$\left(x_1+\frac{1}{x_1}\right)\left(x_2+\frac{1}{x_2}\right)$$
                          =$$x_1x_2+\frac{x_1}{x_2}+\frac{x_2}{x_1}+\frac{1}{x_1x_2}$$
                          =$$x_1x_2+\frac{1}{x_1x_2}+\frac{\left(x_1^2+x_2^2\right)}{x_1x_2}$$
                          =$$x_1x_2+\frac{1}{x_1x_2}+\frac{\left(x_1+x_2\right)^2-2x_1x_2}{x_1x_2}$$
Putting in the values, we get $$\frac{5}{2}+\frac{2}{5}+\frac{2\left(\left(2\right)^2-\left(2\times\ \frac{5}{2}\right)\right)}{5}$$
                          =$$\frac{5}{2}+\frac{2}{5}-\frac{2}{5}$$
                          =$$\frac{5}{2}$$

Checking the options for these conditions of sum and product of roots, we see that only option A satisfies all of our criterion.
Therefore, Option A is the correct answer. 

We can rewrite the series as 
$$2+0.12+1+0.0012+0.000012+\ ...$$ and so on
=$$2+1+0.12+0.0012+0.000012+0.00000012+.....$$
=$$3+\frac{12}{100}+\frac{12}{100^2}+\frac{12}{100^3}+\frac{12}{100^4}+.....$$
=$$3+12\left(\frac{1}{100}+\frac{1}{100^2}+\frac{1}{100^3}+.....\right)$$
Using the formula for the sum of an infinite series we get, 
$$3+\frac{12\left(\frac{1}{100}\right)}{\left(1-\frac{1}{100}\right)}$$
=$$3+\frac{12}{99}$$
$$\frac{309}{99}=\frac{103}{33}$$

And hence, Option A is the correct answer. 

$$\sqrt{\ 3-2\sqrt{\ 2}}$$ is the same as $$\sqrt{\ 2}-1$$
So we can rewrite the equation as, $$\sqrt{\ 10+4\sqrt{\ \left(\sqrt{\ 2}-1\right)^2}}=\sqrt{\ 10+4\left(\sqrt{\ 2}-1\right)}$$
$$\sqrt{\ 6+4\sqrt{\ 2}}=a+\sqrt{\ 2}b$$
Squaring on both side, we get
$$6+4\sqrt{\ 2}=a^2+2b^2+2\sqrt{\ 2}ab$$
Equating the rational and irrational parts on both side, we get
$$a^2+2b^2=6$$  and
$$2ab\ =\ 4$$

Trying different values, we can reach that a=2 and b=1

Putting these values in the given formula we get, 
$$\sqrt{\ a^3+b^3+4a^2b}$$
$$\sqrt{\ 8+1+16}\ $$ 
=$$\sqrt{\ 25}=5$$

Therefore, option B is the correct answer. 

In still water, the boat can cover a distance of 10 km with a speed of 5 km/hr in $$\frac{10}{5}=2$$ hours.

In two hours, the boat travels 8 km upstream. 
Therefore, the speed of boat upstream is $$\frac{8}{2}=4$$km/hr.

We know the speed of the boat is 5 km/hr and thus we can find the speed of the stream.

In upstream, effective speed = boat's speed - stream's speed
4 = 5 - stream's speed
Stream's speed = 1 km/hr

Hence, Option C is the correct answer. 

We can take the hollow cylinder to be made of two concentric cylinders, with the inner cylinder carved out of the outer cylinder. 
Taking the radius of the outer cylinder to be R, we know that the thickness of the cylinder is 2 cm; therefore, the radius of the inner cylinder will be R-2 cm.
We know that the volume of this hollow cylinder would be $$100\pi\ $$
$$\pi\ R^2h-\pi\ \left(R-2\right)^2h=100\pi\ $$
Putting h=20 and solving the left-hand side, we get
$$4R\ -4=5$$
$$R=\frac{9}{4}$$

The inner radius would be $$\frac{9}{4}-2=\frac{1}{4}$$ cm
The capacity of this hollow cylinder would be $$\pi\ \left(\frac{1}{4}\right)^220=\pi\ \frac{20}{16}=\frac{5\pi}{4}\ cm\ $$

Therefore, Option C is the correct answer. 

We should choose a number which is a factor of all of these numbers so that when they are grouped among themselves, there are no leftovers. 
The count in the boxes have HCF 32, so we can distribute the bulbs in groups of 32 so that each box has 32 bulbs and each box has only one type of bulb. 

The bulb with 64 count would require 2 boxes.
The bulb with 192 count would require 6 boxes.
The bulb with 128 count would require 4 boxes.
The bulb with 384 count would require 12 boxes.
The bulb with 256 count would require 8 boxes.
The bulb with 32 count would require 1 boxes.
The bulb with 96 count would require 3 boxes.
The bulb with 288 count would require 9 boxes.

Adding all of them up, we would get that a total of 45 boxes are required. 
Therefore, Option B is the correct answer. 

This question did not require detailed analysis and making the venn-diagram. 
The questions asks the difference between the number of players involved in only swimming and the number of players involved in all three activities. 

We are given both of these exact values in the question. 
Players involved in only swimming: 290
Number of players involved in all three activities: 150

There are 140 less players doing all three activities than players doing only swimming. 
Hence, Option C is the correct answer, 

The number of newly trained people after the first three day period is 3.
Including the initial member who trained them, the total number of trained people would be 1+3

The number of newly trained people after the second trained people is 9.
Including the number of people who are already trained, we get the total number of trained people to be 1+3+9

We can follow through with this reasoning and see that the total number of trained people make the sum of a GP with the common ratio 3 and the number of terms equal to the number of three day periods required. 
We want the total number of trained people to be 1093. 
Using the formula for the sum of an GP with n terms we get, $$\frac{a\left(r^n-1\right)}{r-1}=\frac{1\left(3^n-1\right)}{3-1}=1093$$
$$3^n-1=2186$$
$$3^n=2187$$
from here, we can keep checking the value of n and we find that n=7 satisfies the equation. 

So there are a total of 7 three day periods required, hence, a total of 21 days required for 1093 people to be trained. 

The profit and loss difference in this question is a misdirection. 
The profit on A is equal to the loss on B simply means that the exact values of these are equal. Them being a profit or loss would not make any difference. 

we are given, 
$$10\%\ of\ A\ =\ 20\%\ of\ B\ =\ 15\%\ of\ C$$
= $$2A\ = 4B = 3C$$

From this we can get, A:B = 2:1 and B:C = 3:4
giving us, A:B:C to be 6:3:4

Option A is the correct answer. 

Using the sum and product of roots formula, we get $$\frac{c}{a}=uv$$, and hence, $$c=auv$$
And $$-\frac{b}{a}=u+v$$, and hence, $$-b=a\left(u+v\right)$$

Putting values of c and b in the equation we get, 
$$\sqrt{\ \frac{2\sqrt{\ ac}-b}{c}}=\sqrt{\ \frac{2\sqrt{\ a\left(auv\right)}+a\left(u+v\right)}{auv}}$$
=$$\sqrt{\ \frac{2\sqrt{\ a^2uv}+a\left(u+v\right)}{uav}}=\sqrt{\ \frac{2\sqrt{\ uv}+\left(u+v\right)}{uv}}$$
=$$\sqrt{\ \frac{\left(\sqrt{\ u}+\sqrt{\ v}\right)^2}{uv}}=\sqrt{\ \frac{\left(\sqrt{\ u}+\sqrt{\ v}\right)^2}{\sqrt{\ uv}^2}}=\sqrt{\ \left(\frac{\sqrt{\ u}+\sqrt{\ v}}{\sqrt{\ uv}}\right)^2}$$
=$$\frac{1}{\sqrt{\ u}}+\frac{1}{\sqrt{\ v}}$$

Therefore, Option A is the correct answer. 

This is a series of prime numbers. The prime number next to 71 is 73. 

X can do 60% of the total work in 9 days, this gives us that X can complete the total work in 15 days. 
X and Y can together complete 10% of the work in 1 day, this gives us that X and Y can complete the work in 10 days. 

We can take the total work to be a multiple of the LCM of these values, let it be 30U. 
Now X has an efficiency of 2U units/day.
And X and Y together have an efficiency of 3U units/day. 

This gives us that the efficiency of Y to be 1U units/day.
In order for Y to 5% of the total work, that is 3/2 U units of work, Y would require, $$\frac{3}{2\ }=\ 1\ \frac{1}{2}$$ days. 

Hence, Option A is the correct answer. 

The question had an error in the original questions paper the fraction $$\frac{81}{16}$$ was given as $$\frac{18}{16}$$.

Taking the multiplication factor of this compound interest to be X and the principal amount be P.
We are given that 
$$P\left(X\right)^2=\frac{3}{2}P$$
which would give us, $$X=\ \left(\frac{3}{2}\right)^{\frac{1}{2}}$$

Using this for the second condition we had, 
we can get 
$$P\left(X\right)^N\ =\ \frac{81}{16}P$$
$$\left(\frac{3}{2}\right)^{N\times\ \frac{1}{2}}\ =\ \frac{81}{16}$$
$$\left(\frac{3}{2}\right)^{N\times\ \frac{1}{2}}\ =\ \left(\frac{3}{2}\right)^4$$
Giving us N=8.

Therefore, Option B is the correct answer. 

We can solve this by simply solving for the value under the root, 
$$\sqrt{\ 1600+80\times\ 50+225+30\times\ 35+1225}$$
=$$\sqrt{\ 1600+4000+225+1050+1225}$$
=$$\sqrt{\ 8100}=90$$

Hence, Option B is the correct answer. 

Conclusion 1 does not follow as some reptiles are snakes and no snake is a flying animal.
Conclusion 2 "can be" a possibility.
Conclusion 3 is also a possibility.
Conclusion 4 "can be" a possibility but Conclusion 2 and Conclusion 4 are mutually exclusive and collectively exhaustive which means that exactly one of them has to be the case.
Thus, the correct answer is Option D.

It is given that certain code is written as

'Best of Luck' is written as 'Jan Feb Mar'

'All The Best' is written as 'May Mar Jun'

'The Noble Man' is written as 'Jun Jan Dec'

If you observe the first 2 sentences, "Best" is common in both, so the common term in both in code form is Mar

Best = Mar

If you observe the last 2 sentences, "The" is common in both, so the common term in both in code form is Jun

The = Jun

Thus, the code 'Honesty is the Best Policy' will definitely have Mar and Jun (Mar for Best and Jun for The)

Only option C have Mar and Jun.

The correct option regarding the Assertion (A) and Reason (R) statements is:

Option B: Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Assertion (A) states that "Nutritional support of probiotics is prebiotics," which means that prebiotics provide the necessary nutrition to support the growth and activity of probiotics. Reason (R) states that "Prebiotics is described as indigestible fiber supporting growth and multiplication of probiotics," which is a correct definition of prebiotics. Furthermore, Reason (R) explains why Assertion (A) is true, as it clarifies that prebiotics, being indigestible fiber, indeed support the growth and multiplication of probiotics. Therefore, both the Assertion and the Reason are true, and the Reason correctly explains the Assertion.

From the given information in the question, The 2 males that can be selected with David are

(John, David), (Paul, David) and (David, Sam)

The teams of females possible are

(Gita, Mita) and (Sita, Rita) [Gita and Mita are always selected together in a team]

Now, total possible combinations are 3*2 = 6, but we need to exclude this case [(Paul, David), (Sita, Rita)]

=> Total combinations are 6 - 1 = 5.

Assertion (A) correctly states that the central dogma of life applies universally to all living beings, which is true. This dogma describes the fundamental process by which genetic information flows from DNA to RNA to protein.

Reason (R) accurately identifies the direction of this flow of genetic information as a key aspect of the central dogma. However, while this directionality is indeed crucial, it does not fully elucidate why the central dogma applies to all living organisms. The central dogma's universality extends beyond its directional flow; it encompasses the fundamental mechanism by which genetic information is expressed across all forms of life.

Therefore, both Assertion (A) and Reason (R) are true, but Reason (R) does not serve as the complete explanation for Assertion (A).

Option A is the correct answer.

Let us assume the position of A => B is opposite to A and C sits on the side adjacent to A and B.

Now given that F is to the immediate left of D => D is to the immediate left of B (all other possibilities give a contradiction)

=> The final arrangement looks like follows:

=> Required answer is E and A.

In Option A)

One point is connected with 4 points at max and other 4 points are connected with 3 points.

In Option B) C) and D)

Each point is either connected with 2 or 3 points in the figure. But, no point is added with 4 points.

So, B, C and D are similar.

From the given statements, p is false, q is true, and r is true.

=> Option A => p or q is true and true => true is true => correct.

Option B => false or true is true => Wrong.

Option C => true => false is false => Wrong.

Option D => false => true is true => Wrong.

We are given that there are 9 people between Rajeev and Heena. 
R _ _ _ _ _ _ _ _ _ H

Next, we are given that Prachi is exactly between Rajeev and Heena. 
R _ _ _ _ P _ _ _ _ H

We are given that Tushar is 3rd from the start 
T 2 1

We are given that there are five people between Rushar and Heena. 
Now, Tushar cannot be to the left of Heena because that would mean that the arrangement:
R _ _ _ T P _ _ _ _ H

In which case, he cannot be the third from the start
Therefore, he must be standing to the right of Heena

R _ _ _ _ P _ _ _ _ H _ _ _ _ _ T _ _

Making Heena's position from the start to 9th and Prachi's position to be 14th

Since there are 23 people in the line, Prachi's position from the back would be 23-14+1 = 10th

Therefore, Option C is the correct answer. 

T is to the right of R and R is facing V. Also, R is facing North which means that V is facing South. From these statements, we could get a general idea of their positions:

V       
R     T

Now, M is to the left of V and M is facing T. This gives:

V    M
R    T

Option B gives the correct position of M wrt R.

First start with the absolute data:

=> Yash is to the immediate left of Ram and right of Gita and Sheela is seated to the immediate right of Ram, opposite Pinki and to the left of Sohan

and we can use this information "Tom is just adjacent to Sohan and Meena" to make the final arrangement.

=> 

Required answer is 

Pinki and Gita.

Let us assume that Harish started walking towards A and then took 3 left turns and 1 right turn to reach T.
Now, AP = BC = 170 m.
We need to find the value of HP. 
We will draw a perpendicular from H on DT. Length of this perpendicular = PD = 120 m and Hypotenuese is HT i.e. 150m.
This gives the length of base i.e. TQ = 90m. 
Thus QD = 200 - 90 = 110m.
HP = QD = 110m.
AH i.e. the initial distance covered = HP + PA = 110 + 170 = 280m.

Option 1) L is the daughter-in-law of E

Option 2) L is the grand daughter-in-law of E

Option 3) There is no L in the relation.

Option 4) L is grand daughter of E

Statement i and iv are two opposite statements. So, one of those two has to be true.

We know that all Bowls are Glasses, and some Bowls are Pans. So, some Pans are Glasses.

Statement ii is always true.

Option D: Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).

Assertion (A) states that bad breath odour experienced regularly can indicate an underlying health issue. This is true because chronic bad breath, also known as halitosis, can be a sign of various health problems such as gum disease, dry mouth, or even gastrointestinal issues.

Reason (R) mentions that stomach acid reflux is associated with bad breath, which is also true. Stomach acid reflux, particularly when it reaches the mouth, can lead to an unpleasant odour contributing to bad breath. This occurs because the acid can cause irritation and bacterial growth in the mouth, leading to halitosis.

Therefore, Reason (R) provides a valid explanation for Assertion (A), making both statements true and Reason (R) the correct explanation for Assertion (A).

Let's consider the statement:
The girl wants her passport to be verified, and the police officer is asking for a bribe to do so. 

Let's look at the options:
(1) Complaining to another officer present is a logical and ethical way to proceed in the situation, as the new officer would get the corrupt officer under criticism and also make sure your verification process goes through. 

(2) refusing to bribe in order to get the verification process done is a logical and ethical decision. Unless there is something wrong with the documentation, the process should go through smoothly, and the police officer would have no reason to stop your verification. 

(3) Agreeing to give the bribe not only makes the girl indulge in corruption but also brings her verified passport under scrutiny if the knowledge of her bribery ever goes out. 

Hence, only 1 and 2 are logical and ethically correct decisions. 

Therefore, Option B is the correct answer. 

The series  contains two series according to separate patterns for odd and even terms:

1. Odd terms: 5, 6, 7, 8, 9,... This appears to be a simple increment by 1 series.
2. Even terms: 7, 10, 15,..., 31 The difference between consecutive terms seems to be increasing by 3, 5, 7, 9,...

So, let's continue this pattern:

1. Odd terms: 5, 6, 7, 8, 9,...
2. Even terms: 7, 10, 15, 22, 31,...

So, the next even term is 22. Therefore, the missing number is 22.

Option C is correct answer.