CAT Mock Test- 1 - CAT MCQ

Option A is a distortion. At the end of the second paragraph, the author states, "So the fact that they’re rational but still capable of inhuman acts shows that moral sensibility can’t be grounded in reason alone." The author points out that moral sensibility is not grounded in reason alone. However, reason is still relevant and cannot be discounted.

" Like psychopaths, we can dial our empathy up and down;" Option B can be inferred from this line.

"But you might have noticed that psychopaths don’t experience fear as often, and in the same situations, as do ordinary people. Last time I looked, fear was an emotion." From this option C can be inferred.

"There’s no major ability that psychopaths lack altogether, and their deficits are often small and circumscribed... They usually attend almost exclusively to the task at hand, and ignore relevant contextual information - although when context doesn’t play a role, they do very well."  Option D can be inferred from these lines.

The author quotes several examples where both rational and emotional responses of psychopaths deviate from normal - For rational, the author quotes "Psychopaths struggle with what philosophers call ‘reasons for actions’: considerations that underlie our decisions to act, such as the likelihood that what we’ll do will satisfy our goals and won’t come into conflict with other projects or aims. Psychopaths appear to be poor at integrating all the various factors that go into making good choices, and often have poor reasons for their actions". And for emotional, "Psychopaths respond normally to direct threats, such as an image of the gaping jaw of a shark or a striking snake, but not to social threats, such as people in pain or distress.". Hence, we can say that both responses show deviation from normal. Hence, the author will not agree with option A.

"Psychopaths struggle with what philosophers call ‘reasons for actions’: considerations that underlie our decisions to act, such as the likelihood that what we’ll do will satisfy our goals and won’t come into conflict with other projects or aims." So, the psychopath is not capable of factoring in how his actions affect his other plans/aims, i.e., the action is devoid of contextual consideration and does not factor in the derivative effects. The author would agree with option B.

" Psychopaths respond normally to direct threats, such as an image of the gaping jaw of a shark or a striking snake, but not to social threats, such as people in pain or distress." Hence, option C is likely to receive approval as well.

"The claim that psychopaths don't show rationalism is plain wrong. Psychopaths are as logical as you and me - in fact, they outsmart us all the time, hence their everyday depiction as connivers and con artists. So the fact that they’re rational but still capable of inhuman acts shows that moral sensibility can’t be grounded in reason alone."-  Using these lines, the author implies that psychopaths are rational because their logical reasoning skills as good as anybody else's. So, their moral decision-making abilities are not dependant on their reasoning ability alone. Option D captures this accurately. The author would agree with option D.

Hence, Option A is the correct choice.

In the passage, the author pitches two competing moral theories against one another. One approach, known as rationalism, links moral sensibility to reason, and towards the end, a second approach links morality to emotion. Also, the author points out that the people promulgating the second approach typically focus on empathy. Hence, the next line of discussion should ideally be centred on the idea of empathy/empathetic concern and how it fares as a basis for explaining moral sensibility.  

Comparing the options, option C captures this theme correctly. Option C is the answer.

The author establishes that psychopaths experience empathy in the first paragraph. (" Like psychopaths, we can dial our empathy up and down; "). Hence, option A does not add much value to the overall discussion.

The author does not expand upon the role of fear in the passage and does not provide hints that suggest fear might have a dual role, as stated in option B. Hence, option B can be eliminated.

Option D is too narrow. The second camp typically focuses on empathy. Moreover, the author does not explicitly highlight the importance of personal distress anywhere in the passage. Hence, option D can be eliminated as well.

"and for all the praise we heap on empathy, a closer look at this emotion suggests that it’s nearer to a kind of self-preservation instinct than any ‘warm and fuzzy’ fellow-feeling." The author posits that empathy is more of an instinct to protect oneself from harm rather than a feeling of genuine concern for others. 

Option A is wrong. The person is concerned about his/her own safety and not relieved. 

Option B cannot be inferred. Based on the information presented in the passage, it cannot be established that empathy is absent when someone else's misfortune has no bearing on us. 

Option C captures the author's view correctly. Option C is the answer.

Option D is extreme. Empathy generates concern for one's own safety, but that concern need not necessarily trigger an adaptive response that prepares the self for similar adversity. The cognitive adaption has not been implied in the passage. Hence, option D can be eliminated.

In the opening line of the paragraph, the author states that the history of sport is full of suffering. And then to validate this statement, the author quotes several examples, including that of Micheal Jordan and Mohammed Ali. The author, hence, provides examples to validate his claim that sports are full of suffering. Only option C captures this and hence is the right answer.

Options A and B can be easily eliminated because it has not been implied in the first paragraph that these sports persons were victorious or successful in their endeavour.

Option D is out of scope. The author does not talk about the fear of defeat in the first paragraph.

Option A: The author mentions how inviting and turning up the intensity of pain confers a competitive advantage. Tolerating pain a little longer than your competitor could make all the difference {...And of course, if you’re suffering, the chances are that your opponent is, too. Indifference to pain confers a tactical advantage...} He quotes an Olympic athlete in this regard-  "If nothing is going wrong and there are no mechanical problems during the race then sometimes you can just turn the volume up a little higher and then a little higher, and other people suffer, and you almost enjoy it, even though you are in pain." Option A coincides with this idea and hence, is a valid inference. 

Option B: While the author states that "Japanese trainers have gone so far as to enshrine this marriage of pain and athletic discipline in the concept of taibatsu", he quotes Whiting and calls it 'savage'. There is no comparison undertaken in the passage concerning the opinion around 'taibatsu' being acceptable then or now. Hence, Option B is invalid. 

Option C: "We are always ruled by pain, and those capable of breaking its hold for a few moments become our heroes, role models, and victors." The statement in C aligns with the point made towards the end of the discussion, wherein the author emphasises that tolerating pain a little longer raises us to the levels of those we idolise. Thus, Option C is a valid inference. 

Option D: The statement in D correlates to the following lines from the passage: "Training can’t make athletes numb to pain, but it can condition them to tolerate it."

Hence, Option B is the correct choice.

In the penultimate paragraph, the author discusses the 'taibatsu' concept, which found popular acceptance in Japan as a form of training in the late 1920s. The taibatsu training is an extreme example of pain being tied with athletic discipline and being made an overt part of athletic training. The example of taibatsu is given to highlight the thinking that pain is an integral part of sports and sports training - it is in fact reflective of the athlete's discipline. Kuroda's example is given to show that this thinking continues to exist to this day.

Option D conveys the author's view correctly, as elucidated above. Option D is the answer.

Option A is far-fetched. The author does not present sufficient examples for us to conclude that the concept has produced several successful athletes.

Option B is not incorrect but is not the reason why the author mentions the Japanese pitcher.

Option C gives the reason behind why taibatsu is mentioned. But not why Kuroda is mentioned. Hence, D is the right answer.

The author starts off by saying that pain and suffering are common in sports. He goes on to add that learning to tolerate pain is crucial to excelling in sports. Those who can tolerate pain better, gain a tactical advantage. Pain is almost seen as a positive - and is thus tied to the idea of sports discipline. The author concludes by saying that we have a complicated relationship with pain - on one hand, we try to minimize it and on the other, we idolize those who learn to tolerate it. Hence, the central idea of the passage is that tolerating pain is an integral part of sports and those who learn to do this gain a tactical advantage and rise above others.

Comparing the options, option A comes closest to the view given above. Option A is the answer.

The passage revolves around the role of pain in sports. While the author does extend this to broader life in the last paragraph, the focus remains on sports throughout the passage. Thus, options B and C, which miss the context of sports, can be eliminated.

Option D contains two distortions - enjoy pain and emerge as victors. The author states that putting one's competitors through greater pain is enjoyable to sportspersons. However, it does not state that learning to enjoy pain offers one any specific advantage. Secondly, the author does not state that those who tolerate pain better emerge as victors. The ability to tolerate pain is an advantage but not the sole advantage needed to succeed. Hence, D is incorrect.

The statement in Option A has not been presented in the passage. The author, in no manner, portrays that fantasy politics enables previously "unheard voices" to be heard/noticed. He indicates that people feel significant and powerful. And this feeling especially draws those who feel neglected or unheard. But this does not mean that those people are actually neglected and then heard after coming together. Hence, option A cannot be inferred.

"Fantasy politics is also much more inherently satisfying than real politics....and has an immediate psychic pay off". Therefore, Option B can be inferred from this excerpt.

"It should also be mentioned that fantasy politics is everywhere these days because fantasy itself is so popular." Hence, Option C can be inferred from this line.

"Why is fantasy politics so popular these days? One reason is that it is so much easier than real politics...Real politics is a difficult and time-consuming activity that usually requires dissatisfactory compromise with reality and what other people want." Thus, Option D aligns with the ideas that the author discusses. 

In the entire passage, the author attempts to bring out the fallacies of fantasy politics and make a case for real politics. Also, in the antepenultimate paragraph, the author states, "In the mid-term, the failure of populist fantasies like Brexit will no doubt reinforce their followers' cynicism and alienation." Hence, in the long-term, there is no other bona fide alternative except real politics. The author would agree with statement A.

Option B is a distortion. "..so long as large numbers of our fellow citizens are disinterested in outcomes and prefer wallowing in fantasy, populist politicians will make hay." The author argues that the citizens are disinterested, not unaware. Hence, the author is likely to disagree with the statement in option B.

"Real politics is a difficult and time-consuming activity that usually requires dissatisfactory compromise with reality and what other people want. It is much easier to make-believe our way to our favoured outcomes". Option C can be inferred.

"In the mid-term, the failure of populist fantasies like Brexit will no doubt reinforce their followers' cynicism and alienation." The author would agree with the statement in option D as well.

Option B is the answer.

Option A cannot be inferred. The author is wary of the popularity of fantasy politics and its impractical promises. But the author does not refer to these populist theories as evil anywhere in the passage. 

Option B has not implied in the passage. Though the failure results in followers relapsing into a state of scepticism and alienation, it cannot be inferred whether the leaders were expecting such outcomes. 

The author begins the discussion by stating the following: "Fantasy politics starts from the expectation that wishes should come true, that the best outcome imaginable is not just possible but overwhelmingly likely. The great appeal of fantasy politics is that it puts you in complete control. Using the power of your imagination, you get to control not only what you will do but also how everyone else will react..." Note the author's tone in the passage - he does not appear to be a big fan of fantasy politics. In this introductory part, the author highlights the underlying elements that contribute to the appeal of fantasy politics. There is a subtle tinge of sarcasm wherein the author emphasises the way individuals feel when they engage in fantasy politics - it makes you feel in control; are you truly in control? Not so much! Subsequently, the author delves into the reason behind the appeal of fantasy politics and highlights how quotidian/everyday situations are elevated to the level of decisive moral battles. Thus, given the points underlined in the passage, the false sense of control imparted by indulgence in fantasy politics adds to its appeal. Option C aligns with this idea.

Option D is incorrect. The author does not make such an assertion. 

Hence, Option C is the correct choice.

The author ridicules the popularity of fantasy politics using sarcastic and ironic examples in the passage. Here is one such example- "The psychic benefits of fantasy politics seem especially attractive to those who feel neglected and unheard by the political system, such as the white working class in towns left behind by the modern economy. For these losers, animated by grievance, fantasy politics offers their only way to feel politically significant."

In the third paragraph, the author ridicules those endorsing fantasy politics, claiming that they express their political views while not really making an impact on a personal level. Additionally, in the penultimate paragraph, the author further ridicules fantasy politics, citing the eccentricity of the American gun rights movement.

Hence, Option D is the answer.

The author is not explicitly critical. Option A can be eliminated.

The author is not ambivalent. He is unilaterally in favour of real politics.

The author does not plead for action. Hence, option C can be eliminated.

On referring to the following excerpt from the first paragraph, we can see that Options A and B are examples of racism of the first degree: {...The most well-understood dimension of racism involves taking actions that people of colour view as overtly prejudiced—policing black citizens much differently than whites, calling the police on a black bird-watcher in Central Park who is asking you to obey the law, calling somebody the N-word to show them who is boss. This is racism in the first degree...}

{...The final, most pernicious category undergirds the everyday black experience. When employers, educational institutions, and governmental entities do not unwind practices that disadvantage people of colour in the competition with whites for economic and career mobility...}.These lines highlight the disadvantages that people of colour face at their workplaces, often labelled as third-degree racism. Option D serves as an example of the same. 

The author describes second-degree racism as follows: {...Then there is opposing or turning one’s back on anti-racism efforts, often justified by the demonization of the people courageously tackling racist behaviour. I call this racism in the second degree, akin to aiding and abetting...} Option C is an example reflective of second-degree racism - punishing those who support anti-racism efforts.

Hence, Option C is the correct choice. 

Through the passage, the author first introduces us to the three forms of racism. She then puts forward ideas to tackle third-degree racism. Finally, in the last paragraph, the author highlights what is at stake - not fighting third-degree racism could cost us many lives. Of the options, only option A highlights the purpose of the example - showing the impact of third-degree racism with the help of an example. 

The example of pandemic response is used to make a larger point of how we need to tackle third-degree racism. As options B and C focus on the example instead of the larger point, they are incorrect. Moreover, option B is an extreme statement.

Option D is in line with the passage - and it is a valid conclusion that can derived from the last paragraph. However, it does not answer "why" the example is given. The purpose behind the example is captured by option A and hence is the right answer.

"If officers anticipated that they would be held fully accountable for bad policing, they would do more good policing and we could begin healing the wounds they’ve inflicted on black people for centuries."

"If the people who designed that process knew upfront that they would be exposed as racist, fired, and ostracized if their approach put minorities at a greater health risk than white people, they would have designed it differently and saved black lives."

The above examples suggest that the author blames the apparent impunity for the pervasiveness of racism. Hence, option A is likely to receive the author's approval.

" For example, the majority of white executives operate as if there is a tension between increasing racial diversity and maintaining the excellence-based “meritocracies” that have made their organizations successful."

The above line from the passage means that to a lot of white executives, hiring people of colour is akin to compromising of merit. This has been condemned by the author in the passage. The author, through the passage, means to say that efforts to increase racial diversity and maintain meritocracy are not contrary to each other. Option B is incorrect.

On reading the last para of the passage, we can understand that the author wants the government to make the process of getting vaccinated easier so that the minorities do not face as many difficulties as they actually had to. He does not ask the government to give them more priority over others. Option C is incorrect.

Option D is close but incorrect. The author argues that companies that do not implement basic diversity practices will be shunned by good talent and thus suffer. The author proposes an indirect punishment and not government intervention. As the option goes against the author's proposed policy, we can say that the author is less likely to agree with it.

In the second paragraph, the author states the following-

"For example, the majority of white executives operate as if there is a tension between increasing racial diversity and maintaining the excellence-based “meritocracies” that have made their organizations successful."

However, this does not lead to the conclusion those who do operate to increase racial diversity do so because they understand the excellence-based meritocracy system is flawed. Some might feel, like the author, that there is no trade-off involved between promoting diversity and meritocracy.

" When employers, educational institutions, and governmental entities do not unwind practices that disadvantage people of colour in the competition with whites for economic and career mobility, that is fundamentally racist."

The employers and institutions do not put in the effort required to curb racist practices. Hence, they are not necessarily unwitting participants in the system. Statement II is wrong.

The degrees of racism are classified by whether they are direct / indirect / institutional. The author does not classify them according to severity of impact. In fact, as shown by the example of pandemic response, even third-degree racism can have severe impact. Hence, III is incorrect.

"Then more people of colour will become economically mobile, organizations will become more diverse and competitive, and there will be a critical mass of black leaders whose institutional influence leads to more racially equitable behaviour."

"Just having a critical mass of minorities in decision-making roles regarding that test-qualification process would have also saved many lives."

From the above lines, Statement IV can be inferred.

So, statements I, II, and III are not inferrable. Option B is the answer.

Sentence 2 is the opening sentence, as it sets the context, describing the situation that ensues when believers and non-believers discuss a seemingly miraculous event. 4 has to follow 2 because the 'radically different attitudes' that 4 refers to the difference in attitudes of believers and non-believers, discussed in 2. 1 follows 4, as it expands on the idea described in 4, i.e., the different views of the world. Finally, 3 concludes the paragraph, presenting an alternate possibility (despite the differing views, there might be some common ground). Hence, 2413 is the answer. 

324 is a unit. 3 presents a vulnerability associated with Antarctica, and sentences 2 and 4 expand on it, describing how human activities exacerbate the situation. 1 talks about the 'battle for knowledge', which is a reference to people watching penguins, to study their behaviour, outlined in 2. Hence, the correct order is 3241.

We notice that statements 5 and 2 form a pair. Statement 5 talks about an expectation ('change in attitude'), and statement 2 refutes this belief ('not the case'). Statement 4 appears to be the introductory sentence - we can eliminate the remaining statements due to markers such as "also" (for Statement 1), and "these" (for Statement 3). Statement 1 seems to logically fit after statement 4 as it adds to the context for the paragraph. Sentences 4-1 followed by 5-2 forms a coherent paragraph. Statement 3 does not fit in the above arrangement due to its emphasis on biological routes. Hence, Statement 3 is the odd-one-out.

Statements 5 and 3 forms a logical pair. Statement 3 talks about "this judgement", which alludes to the "subjective judgment" mentioned in statement 5. Additionally, "it" in statement 1 also describes the subject judgement which is not binary and not quantifiable. So, 531 forms a group. The author talks about the difference in diagnosis: he begins by citing how diagnosing diabetes is based on the objective interpretation of a number from a blood test. He tags this as something that is "binary and quantifiable". This is in contrast to the diagnosis of dementia, which according to the author, is based on his "subjective judgement" - something that is not "binary and quantifiable". Hence, we notice that the arrangement 4-5-3-1 forms a coherent paragraph. At the same time, Statement 2 is the odd-one-out: it talks about the early stages of mental disorders and the disagreement between clinicians concerning the same. We notice that the focus here varies and hence our decision to label statement 2 as being out of context.

While arranging the parts of the paragraph, we should find some grammatical or contextual connections between them -

• 3 is the first sentenceas it serves as the foundation for the remaining sentences. It is talking about the countries with abundant oil and gas resources and how they are being developed to a large extent. Based on this statement, the rest of the statements refer to a country that lacks these oil and gas resources.
• 2 is the second sentence as it is talking about Japan as a country that lacks these oil and gas resources, and it states that in order to meet the country's energy needs, Japan has put into place some alternative forms of energy.
• 4 is the third sentence as it describes Japan's position in the world in terms of energy consumption and production by implementing some alternative forms of energy.
• 1 is the last sentence as it begins with the conjunction 'because' which is used to refer to the demand for energy that has been mentioned in statement 4.

Thus, the correct order is 3241:

• 3: In countries where oil and gas resources are plentiful, they are being developed to a great extent because of the economic benefits that can be gained. 
• 2: In the case of Japan, which lacks any significant fossil fuel reserves, some alternative forms of energy production have been implemented. 
• 4: Japan is the fifth largest consumer of energy and the third-largest producer and consumer of electricity in the world. 
• 1: Because of this demand for energy and energy security, Japan has implemented alternative energy options such as nuclear power, photovoltaic power, hydroelectric power, and other various energy alternatives and renewable resources.

The given paragraph is talking about  understanding how the memory system works and the biological mechanisms of memory formation. 

• Option 1 gets eliminated  since the passage implies that they didn't obtain insights about the memories.
• Option 3 gets eliminated  as the paragraph didn't mention anything about understanding the occurrence of neurodevelopmental disorders.
• Option 4 gets eliminated  as the main focus of the paragraph isn't just to understand rodent memory systems.
• In the passage, it is given that  "It became clear to me that we couldn’t understand how memory systems work if we did not understand how they develop. It’s a question that, at the mechanistic level, has been largely overlooked."  and  "very few investigations have been done to address the nature of the biology of learning and memory in normal development."
• From these lines, we can understand that the passage is emphasizing that if we do not understand  how the memory system develops or the nature of biology,  we cannot understand how memory systems work.
• From the given explanation we can conclude that  statement 2 best summarizes the given paragraph  as it says that "understanding the nature of biology is important for understanding how memories work throughout life and gaining new insights into biological mechanisms of memory."

Therefore,  option 2  is the correct answer.

• To answer such questions, we need to find the central idea of the passage.
• The passage talks about how according to the author Brutus is the real hero of the play Julius Caesar
• Brutus has more screen time and helps the viewers to feel the spirit of Rome
• Just like Shakespeare's other works like Othello, Brutus meets a tragic end and hence is the tragic hero of the play

To answer such questions, we need to find the central idea of the passage.

• The passage talks about how the author thinks a "classic" should be defined
• According to the author, classical work is revolutionary and different from the contemporaries
• Hence given its novelty and revolutionary nature, a classical work appeals to the masses and stirs the human consciousness over any period of time.

Clearly, we need to bifurcate the employees into males and females to proceed. 

> The number of women who like at least 2 out of 3 preferences are 65

>  55 Women only like Italian

> Overall 25 employees like only Chinese out of which 40% are male. Thus 10 male and 15 female employees only like Chinese

> The number of Employees liking only Continental is the same as the number of women liking only Italian = 55. Thus 25 are female and 30 are male

Let the total number of females be F. Then the number of females who do not like any of the 3 options = 0.2F.

Total number of Female = Females who like none + Females who like exactly one+ Female who like atleast 2

F = 0.2F + 15+25+55+65 or 0.8F = 160. Thus F = 200. Females who like none of the option = 0.2F = 40

Thus number of male employees who did not like any of the 3 options = 20 which is also equal to a number of females liking all 3 options.

> 175 of the employees like exactly one of the 3 options. Thus number of males liking only Italian = 175-(10+30+15+25+55) = 40

> Total number of male employees = 7 times the number of males liking only continental = 210

> Number of male employees like only Italian is same the number of male liking Chinese and Continental but not Italian = 40

Number of male employees not liking Italian = 10+40+30+20 = 100

Clearly, we need to bifurcate the employees into males and females to proceed. 

> The number of women who like at least 2 out of 3 preferences are 65

>  55 Women only like Italian

> Overall 25 employees like only Chinese out of which 40% are male. Thus 10 male and 15 female employees only like Chinese

> Number of Employees liking only Continental is the same as the number of women liking only Italian = 55. Thus 25 are female and 30 are male

Let the total number of females be F. Then the number of females who do not like any of the 3 options = 0.2F.

Total number of Female = Females who like none + Females who like exactly one+ Female who like atleast 2

F = 0.2F + 15+25+55+65 or 0.8F = 160. Thus F = 200. Females who like none of the option = 0.2F = 40

Thus  number of male employees who did not like any of the 3 option = 20 which is also equal to number of females liking all 3 options.

>175 of the employees like exactly one of the 3 options. Thus number of males liking only Italian = 175-(10+30+15+25+55) = 40

> Total number of male employees = 7 times the number of males liking only continental = 210

> Number of male employees like only Italian is same the number of male liking Chinese and Continental but not Italian = 40

We see only 40 men like Continental and Chinese.

For Women, 65 people like at least 2 options. Out of which 20 like all three. Therefore maximum possible of females liking only Continental and Chinese = 65-20=45

Maximum possible = 40+45 = 85

Clearly, we need to bifurcate the employees into males and females to proceed. 

> The number of women who like at least 2 out of 3 preferences are 65

>  55 Women only like Italian

> Overall 25 employees like only Chinese out of which 40% are male. Thus 10 male and 15 female employees only like Chinese

> Number of Employees liking only Continental is the same as the number of women liking only Italian = 55. Thus 25 are female and 30 are male

Let the total number of females be F. Then the number of females who do not like any of the 3 options = 0.2F.

Total number of Female = Females who like none + Females who like exactly one+ Female who like atleast 2

F = 0.2F + 15+25+55+65 or 0.8F = 160. Thus F = 200. Females who like none of the option = 0.2F = 40

Thus  number of male employees who did not like any of the 3 option = 20 which is also equal to number of females liking all 3 options.

> 175 of the employees like exactly one of the 3 options. Thus number of males liking only Italian = 175-(10+30+15+25+55) = 40

> Total number of male employees = 7 times the number of males liking only continental = 210

> Number of male employees like only Italian is same the number of male liking Chinese and Continental but not Italian = 40

Given that 100 male employees like Chinese. Number of male liking both  continental and Italian and not Chinese = 210-(100+30+40+20) = 20

The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.

Then a+b+c = 6 ....(I)

Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.

when c= 1, then b=3 and a = 2

when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.

Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.

Let us start by filling in the known information.

> Painting was taught on Wednesday C slot

>Slot D of Monday was a free slot

> Week starts with teaching English

> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot

>On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects

Thus Dance is not a subject of Optional Category.

The slot is made for 5 days with 4 slots each. Thus the total number of fields to be filled = 5\times4 = 205×4=20
We know each day there is 1 free slot. Let a,ba,b and cc be the number of Compulsory, Optional, and Necessary subjects be there.

Then a+b+c = 6 ....(I)

Then 5+4a+2b+c = 20 or 4a+2b+c = 15....(II) It is clear that c has to be odd.

when c= 1, then b=3 and a = 2

when c= 3, then b=0 and a= 3 which is rejected as we know there is one subject of each category.

Thus Number of Compulsory classes = 2, Number of Optional classes = 3, and Number of Necessary subject = 1.

Let us start by filling in the known information.

> Painting was taught on Wednesday C slot

>Slot D of Monday was a free slot

> Week starts with teaching English

> Physical Education happens only on A slot. Thus we know that it is the subject in the Necessary Category. We know that none of the optional category classes was conducted on Friday. Thus only the Compulsory and Necessary category subject happened on Friday. Thus Physical Education happened on Friday A slot

> On one particular day, Physical Education, Dance, and English were taught in that order. Slot C was a free slot that day. Thus Dance and English are the Compulsory category subjects

> Overall 3 classes each happened in the B and C slots throughout the week. Implies overall 2 free slots were there in B and C slot each.

> There were 2 instances that the free period was in the same slot as that of the preceding day.

From above we can say that Thursday and Friday had C as free slots and Tuesday and Wednesday had B as their free slot.

Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English

Since English is a Compulsory category. 4 classes have to happen. All in different slots. From the above table, the only possibility is when Thursday B and Tuesday C are English

We are also given that Dance does not happen on Thursday, which implies it needs to happen on all 4 other days. For Monday it is possible only when it happens in C slot.

>On a particular day, singing happened after a free slot. It is only possible when Singing is taught on Thursday D slot

Since Counting was taught on Monday, it has to be in B slot.

Singing class did not happen on Tuesday, it implies that one of the two singing classes has to happen on Wednesday. The only possibility is A slot. This will imply that the Wednesday D slot is Dance and thus Tuesday A slot is Dance

Exactly one of the optional subjects was not taught on consecutive days Thus counting has to be taught on Thursday. And Painting has to be taught on Tuesday

There is only 1 Possiblilty.