Description

This mock test of CAT Mock Test - 1 for CAT helps you for every CAT entrance exam.
This contains 100 Multiple Choice Questions for CAT CAT Mock Test - 1 (mcq) to study with solutions a complete question bank.
The solved questions answers in this CAT Mock Test - 1 quiz give you a good mix of easy questions and tough questions. CAT
students definitely take this CAT Mock Test - 1 exercise for a better result in the exam. You can find other CAT Mock Test - 1 extra questions,
long questions & short questions for CAT on EduRev as well by searching above.

*Answer can only contain numeric values

QUESTION: 1

Arrange statements 1-5 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 23514.

1. Even knowing how to start can be difficult.

2. Is colour to be understood as an objective part of reality, a property of objects with a status similar to shape and size?

3. The central role colour plays in our lives, in visual experience, in art, as a metaphor for emotions, has made it an obvious candidate for philosophical reflection.

4. Philosophy has long struggled to understand the nature of colour.

5. Understanding the nature of colour, however, has proved a daunting task, despite the numerous fields that contribute to the project.

Solution:

Statement 4 is the obvious introductory statement since it introduces the theme of the paragraph which is the “nature of colour.” 4- 3 is a pair, the commonality being “Philosophy” and “philosophical reflection” about colour. 5- 1 is a pair. Statement 5 mentions the “daunting task” of understanding the nature of colour, so daunting that “even knowing how to start can be difficult.” Statement 2 will follow statement 1 since 2 poses a question as to how colour is to be understood.

Hence, the correct answer is 43512.

*Answer can only contain numeric values

QUESTION: 2

Arrange statements 1-6 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 235146.

1. Enrollment in computer-related degrees in the U.S has dropped recently due to lack of general interests in science and mathematics and also out of an apparent fear that programming will be subject to the same pressures as manufacturing and agriculture careers.

2. Large companies claim there is a skills shortage with regard to programming talent.

3. Technology and software jobs were supposed to be the replacement for factory and agriculture jobs lost to cheaper foreign labor, but if those are subject to free trade losses, then the nature of the next generation of replacement careers is not clear at this point.

4. This situation has resulted in confusion about whether the U.S economy is entering a “postinformation age” and the nature of U.S comparative advantages.

5. However, U.S programmers and unions counter that large companies are exaggerating their case in order to obtain cheaper programmers from developing countries and to avoid paying for training in very specific technologies.

6. Objective studies on this debate that both sides accept have been hard to come by and a distrust has formed between large companies and programming trade groups.

Solution:

Statement 2 should precede statement 1 since 2 introduces the topic, “skills shortage” while statement 1 mentions the reason for the shortage in US programming talent.

Statement 5 should logically follow statement 2 since 2 talks about companies complaining about skills shortages while statement 5 starts with “however” and introduces a contrasting idea put forward by the unions about the skills shortages.

Statement 6 will follow 5 since statement 5 introduces the divergence of views between companies and unions and 6 follows up with the “debate and distrust” between the two groups.

There is a clear 1-4 link since statement 1 introduces the topic of falling enrolment in US colleges and 4 follows up with “this situation” and explains the consequences of this falling enrolment.

Statement 3 does not link with any statement very well and can only be the concluding statement.

Hence, the correct sequence is 256143.

*Answer can only contain numeric values

QUESTION: 3

Arrange statements 1-5 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 23514.

1. One of the hypothesis proposes that warming may be the result of variations in solar activity.

2. The detailed causes of the recent warming remain an active field of research, but the scientific consensus identifies elevated levels of greenhouse gases due to human activity as the main influence.

3. The Earth's climate changes in response to external forces, including variations in its orbit around the Sun (orbital forcing), volcanic eruptions, and atmospheric greenhouse gas concentrations.

4. This attribution is clearest for the most recent 50 years, for which the most detailed data are available.

5. Some other hypotheses departing from the consensus view have been suggested to explain the observed increase in mean global temperature.

Solution:

The strongest link in this paragraph is that of 2-4.

Statement 2 talks about the human activity as the main reason for elevated levels of greenhouse gas and statement 4 refers to this attribution (by humans) of emission of gases, being clear for last 50 years.

Statement 3 is a good introduction to the paragraph - this is because it states the fact that earth's climate changes in response to certain factors. It can be followed by 2 which talks about one such factor. These three statements are followed by statements 5 and 1, as 5 talks about "other hypotheses" and 1 mentions one particular hypothesis. Hence, the correct answer is 32451.

*Answer can only contain numeric values

QUESTION: 4

Arrange statements 1-5 given below in a logical sequence in order to form a coherent paragraph. Your answer will be the order of statement numbers that forms this logical sequence e.g. 23514.

1. Often it was found on its knees when the rider would expect it the least.

2. As the horse that was borrowed by Mr Adams from his clerk had a violent tendency to kneel without giving any notice of his intention to do so.

3. However, this eccentricity was of little consequence to Mr Adams as he was well acquainted with it.

4. No sooner did the coach stop at the inn, Mr. Adams, according to his custom, threw himself into the kitchen and found Joe sitting by the fireplace, and the host attending to his bruised leg.

5. Since his legs nearly touched the land when he rode the horse, he had fewer chances to fall and pushed himself forward during such occasions so brilliantly that he by no means suffered any accident.

Solution:

Statement 4 is the first sentence. It describes Adam’s custom of alighting from his horse. The other sentences provide reasons for this custom.

Statement 2 follows statement 4 as it describes the horse as well as Mr. Adams.

Statement 1 follows statement 2 because the pronoun “it” used in statement 1 indicates the horse in statement 2.

Statement 3 follows statement 1 because “this eccentricity” in statement 3 refers to “often it was found on its knees” in statement 1. “Such occasions” in statement 5 refer to “This eccentricity that Adams is acquainted with...” in statement 3. So statement 5 comes last. At the same time the pronoun “he” indicates Adams in statement 3.

Hence, the correct answer is 42135.

QUESTION: 5

The passage given below is followed by a set of questions. Choose the most appropriate answer to each question.

Pieces of music, or performances of them, are usually said to be happy, sad, and so on. Music's emotional expressivity is a philosophical problem since the paradigm expressers of emotions are psychological agents, who have emotions to express. Neither pieces of music, nor performances of them, are psychological agents, thus it is puzzling that such things could be said to express emotions. One immediately helpful distinction is that between expression and expressivity, or expressiveness. Expression is something persons do, namely, the outward manifestation of their emotional states. Expressivity is something artworks, and possibly other things, possess. It is presumably related in some way to expression, and yet cannot simply be expression for the reason just given. Most theorists also distinguish between expressivity and representation, claiming that music is expressive of emotions, rather than representing them. To give a non-musical example, one might paint a person crying, yet do so in a clinical style such that the painting represents the person's sadness, yet is itself not a sad painting, that is, expressive of sadness, but rather a cool, detached one. The emotions in a piece of music are thus, more closely tied to it than mere descriptions of emotional states.

An obvious way to connect expressivity with expression is to argue that pieces of music or performances of them are expressions of emotion - not the piece's or performance's emotions, but rather those of the composer or performer. There are two major problems with this ‘expression theory’. The first is that neither composers nor performers often experience the emotions their music is expressive of as it is produced. Nor does it seem unlikely that a composer could create, or a performer perform, a piece expressive of an emotion that she had never experienced. This is not to deny that a composer could write a piece expressive of her emotional state, but two things must be observed. The first is that for the expression theory to be an account of musical expressivity, at least all central cases of expressivity must follow this model, which is not the case. The second is that if a composer is to express her sadness, say, by writing a sad piece, she must write the right kind of piece. In other words, if she is a bad composer she might fail to express her emotion. This brings us to the second major problem for the expression theory. If a composer can fail to express her emotions in a piece, then the music she writes is expressive independently of the emotion she is experiencing. Thus, music's expressivity cannot be explained in terms of direct expression.

*Q. *In the context of this passage, **“musical expressivity” **describes to all of the following except

Solution:

Option 1 does ascribe to “musical expressivity” as can be inferred from, “...if a composer is to express her sadness, say, by writing a sad piece, she must write the right kind of piece.” Similarly option 2 is also vindicated by, “If a composer can fail to express her emotions in a piece, then the music she writes is expressive independently of the emotion she is experiencing.”. According to the passage, “Expression is something persons do, namely, the outward manifestation of their emotional states. Expressivity is something artworks, and possibly other things, possess.”. This validates option 4 as something that “musical expressivity” would ascribe to.

The passage makes a case for how expressivity in music can be independent from direct expression and the emotions of music composers. Option 3 contradicts this by establishing a relationship of dependency between these two entities. Thus, option 3 highlights what “musical expressivity” cannot ascribe to. Though the passage does mention the exception of a musician being accurately able to portray the emotions she is going through, through her work, as a whole the passage would not support the stance made in option 3.

Hence, the correct answer is option 3.

QUESTION: 6

Pieces of music, or performances of them, are usually said to be happy, sad, and so on. Music's emotional expressivity is a philosophical problem since the paradigm expressers of emotions are psychological agents, who have emotions to express. Neither pieces of music, nor performances of them, are psychological agents, thus it is puzzling that such things could be said to express emotions. One immediately helpful distinction is that between expression and expressivity, or expressiveness. Expression is something persons do, namely, the outward manifestation of their emotional states. Expressivity is something artworks, and possibly other things, possess. It is presumably related in some way to expression, and yet cannot simply be expression for the reason just given. Most theorists also distinguish between expressivity and representation, claiming that music is expressive of emotions, rather than representing them. To give a non-musical example, one might paint a person crying, yet do so in a clinical style such that the painting represents the person's sadness, yet is itself not a sad painting, that is, expressive of sadness, but rather a cool, detached one. The emotions in a piece of music are thus, more closely tied to it than mere descriptions of emotional states.

An obvious way to connect expressivity with expression is to argue that pieces of music or performances of them are expressions of emotion - not the piece's or performance's emotions, but rather those of the composer or performer. There are two major problems with this ‘expression theory’. The first is that neither composers nor performers often experience the emotions their music is expressive of as it is produced. Nor does it seem unlikely that a composer could create, or a performer perform, a piece expressive of an emotion that she had never experienced. This is not to deny that a composer could write a piece expressive of her emotional state, but two things must be observed. The first is that for the expression theory to be an account of musical expressivity, at least all central cases of expressivity must follow this model, which is not the case. The second is that if a composer is to express her sadness, say, by writing a sad piece, she must write the right kind of piece. In other words, if she is a bad composer she might fail to express her emotion. This brings us to the second major problem for the expression theory. If a composer can fail to express her emotions in a piece, then the music she writes is expressive independently of the emotion she is experiencing. Thus, music's expressivity cannot be explained in terms of direct expression.

*Q. *Which of the following examples represents emotions instead of expressing them?

Solution:

In context of representing emotions instead of expressing them, the passage gives the example of a detached and clinical painting depicting a person crying. Though the painting represents sadness, on its own it is not sad. This is similar to what has been said about the satire on a totalitarian regime in option 4. This piece of work represents a totalitarian regime but is not factual in its approach. Rather it is humorous. The artist adopts the technique of satire to portray his/her political purpose.

Though option 3 seems extremely tempting as well, it is not the correct answer. Option 3 highlights a contradiction between what is portrayed and what is actually meant. Option 4 on the other hand does not represent a contradiction, rather it represents treatment. Eliminate option 3.

A dark painting is likely to be disturbing and hence, will be expressive. Eliminate option 1.

An artist moving from regular to abstract art as his schizophrenia progress is expressing the experience of his mind. Eliminate option 2.

Hence, the correct answer is option 4.

QUESTION: 7

Pieces of music, or performances of them, are usually said to be happy, sad, and so on. Music's emotional expressivity is a philosophical problem since the paradigm expressers of emotions are psychological agents, who have emotions to express. Neither pieces of music, nor performances of them, are psychological agents, thus it is puzzling that such things could be said to express emotions. One immediately helpful distinction is that between expression and expressivity, or expressiveness. Expression is something persons do, namely, the outward manifestation of their emotional states. Expressivity is something artworks, and possibly other things, possess. It is presumably related in some way to expression, and yet cannot simply be expression for the reason just given. Most theorists also distinguish between expressivity and representation, claiming that music is expressive of emotions, rather than representing them. To give a non-musical example, one might paint a person crying, yet do so in a clinical style such that the painting represents the person's sadness, yet is itself not a sad painting, that is, expressive of sadness, but rather a cool, detached one. The emotions in a piece of music are thus, more closely tied to it than mere descriptions of emotional states.

An obvious way to connect expressivity with expression is to argue that pieces of music or performances of them are expressions of emotion - not the piece's or performance's emotions, but rather those of the composer or performer. There are two major problems with this ‘expression theory’. The first is that neither composers nor performers often experience the emotions their music is expressive of as it is produced. Nor does it seem unlikely that a composer could create, or a performer perform, a piece expressive of an emotion that she had never experienced. This is not to deny that a composer could write a piece expressive of her emotional state, but two things must be observed. The first is that for the expression theory to be an account of musical expressivity, at least all central cases of expressivity must follow this model, which is not the case. The second is that if a composer is to express her sadness, say, by writing a sad piece, she must write the right kind of piece. In other words, if she is a bad composer she might fail to express her emotion. This brings us to the second major problem for the expression theory. If a composer can fail to express her emotions in a piece, then the music she writes is expressive independently of the emotion she is experiencing. Thus, music's expressivity cannot be explained in terms of direct expression.

Q. Which of the following is untrue about a piece of music?

Solution:

Option 1 is true about music as can be validated by “Expressivity is something artworks, and possibly other things, possess.”.Option 2 is vindicated as true by “The first is that neither composers nor performers often experience the emotions their music is expressive of...This is not to deny that a composer could write a piece expressive of her emotional state, but two things must be observed.”.According to the passage, “Thus, music's expressivity cannot be explained in terms of direct expression.”. The example of the expressivity of the music of a poor composer as stated in the latter half of the second paragraph helps substantiate the claim made in option 4.Option 3 contradicts what has been stated in, “The emotions in a piece of music are thus, more closely tied to it than mere descriptions of emotional states.”. Thus, it is untrue about music. Hence, the correct answer is option 3.

QUESTION: 8

The passage given below is followed by a set of questions. Choose the most appropriate answer to each question.

Jane Austen, one of the most admired English writers of all time, died in 1817. Although she lived two centuries ago, the society she depicts in her novels is surprisingly familiar. Every few years, distinguished British actors squeeze themselves into breeches and ball gowns for yet another televised adaptation of one of Austen’s stories. We take an imaginary tour through a few decorous Georgian balls and tea parties, then return to modern life.

However, new records aim to challenge our comfortable view of Jane Austen’s England. Historians Roy and Lesley Adkins turn their attention away from the respectable world of polite society that appears in Austen’s novels and instead, try to uncover a little of what life was really like at the turn of the 19th Century.

What emerges is a world much less civilised than we imagine - one in which children toiled in coal mines or up chimneys; in which men could be dragged away to serve in rat-infested navy ships, or to fight the brutal battles of the long Napoleonic War; in which the wives and daughters of the poor could be sold in marketplaces like cattle. The streets of this world were so thick with horse dung - and sometimes human too - that in some towns there were special street sweepers who would scrape a path across the road for you, for a fee. Out of town, travelers on highways would sometimes be subjected to the sight of an executed criminal, swinging on a gibbet. Those who received a normal burial were not safe either: London cemeteries were plagued by grave-robbers, who supplied fresh corpses to surgeons for dissection. Even upper-class life was not immune from squalor. Personal sanitation in Jane Austen’s time was not up to modern standards. Piped hot water was an unheard-of luxury; mass-produced soap was a recent innovation; ‘shampoo’ was a mystery of the Far East and deodorant was nonexistent. Lack of toothpaste would very likely have given Mr. Darcy - along with the rest of Austen’s romantic leads- terrible bad breath. When teeth decayed, the rich paid to have them replaced with fresh ones plucked from corpses.

Q. Which of the following is one not likely to find in one of Jane Austen's novels?

Solution:

Option 1 is an aspect that can be found in Jane Austen's novels.

It is vindicated by “...the respectable world of polite society that appears in Austen’s novels...”.

Option 2 is ratified by “...Georgian balls and tea parties...”. Garments such as breeches and ball gowns are associated with wealth. According to the passage, “Every few years, distinguished British actors squeeze themselves into breeches and ball gowns for yet another televised adaptation of one of Austen’s stories.”. Thus, “sartorial flamboyance” meaning 'of or pertaining to style or clothing' can very much be found in Austen's novels. Eliminate option 3.

The passage puts forth the reality of 19th century England as being extremely grim. According to it, “Historians Roy and Lesley Adkins turn their attention away from the respectable world of polite society that appears in Austen’s novels and instead, try to uncover a little of what life was really like at the turn of the 19th Century.”. Thus, what appears is Jane Austen's novels in no manner represents reality let alone celebrate it. This vindicates option 4.

Hence, the correct answer is option 4.

QUESTION: 9

Jane Austen, one of the most admired English writers of all time, died in 1817. Although she lived two centuries ago, the society she depicts in her novels is surprisingly familiar. Every few years, distinguished British actors squeeze themselves into breeches and ball gowns for yet another televised adaptation of one of Austen’s stories. We take an imaginary tour through a few decorous Georgian balls and tea parties, then return to modern life.

However, new records aim to challenge our comfortable view of Jane Austen’s England. Historians Roy and Lesley Adkins turn their attention away from the respectable world of polite society that appears in Austen’s novels and instead, try to uncover a little of what life was really like at the turn of the 19th Century.

What emerges is a world much less civilised than we imagine - one in which children toiled in coal mines or up chimneys; in which men could be dragged away to serve in rat-infested navy ships, or to fight the brutal battles of the long Napoleonic War; in which the wives and daughters of the poor could be sold in marketplaces like cattle. The streets of this world were so thick with horse dung - and sometimes human too - that in some towns there were special street sweepers who would scrape a path across the road for you, for a fee. Out of town, travellers on highways would sometimes be subjected to the sight of an executed criminal, swinging on a gibbet. Those who received a normal burial were not safe either: London cemeteries were plagued by grave-robbers, who supplied fresh corpses to surgeons for dissection. Even upper-class life was not immune from squalor. Personal sanitation in Jane Austen’s time was not up to modern standards. Piped hot water was an unheard-of luxury; mass-produced soap was a recent innovation; ‘shampoo’ was a mystery of the Far East and deodorant was nonexistent. Lack of toothpaste would very likely have given Mr Darcy - along with the rest of Austen’s romantic leads- terrible bad breath. When teeth decayed, the rich paid to have them replaced with fresh ones plucked from corpses.

Q. Which of the following is the author of this passage most likely to disagree with about 19th century England?

Solution:

According to the passage, “The streets of this world were so thick with horse dung - and sometimes human too...”. The author would agree that option 1 is true about 19th century England.

The passage mentions that “Out of town, travellers on highways would sometimes be subjected to the sight of an executed criminal, swinging on a gibbet.”. Option 2 contradicts this. Thus, the author is most likely to disagree with it.

The passage describes the condition of children, men, poor women as being deplorable. Eliminate option 3.

The passage mentions instances of “...grave-robbers, who supplied fresh corpses to surgeons for dissection.”. Thus, the author would agree with option 4.

Hence, the correct answer is option 2.

QUESTION: 10

Jane Austen, one of the most admired English writers of all time, died in 1817. Although she lived two centuries ago, the society she depicts in her novels is surprisingly familiar. Every few years, distinguished British actors squeeze themselves into breeches and ball gowns for yet another televised adaptation of one of Austen’s stories. We take an imaginary tour through a few decorous Georgian balls and tea parties, then return to modern life.

However, new records aim to challenge our comfortable view of Jane Austen’s England. Historians Roy and Lesley Adkins turn their attention away from the respectable world of polite society that appears in Austen’s novels and instead, try to uncover a little of what life was really like at the turn of the 19th Century.

What emerges is a world much less civilised than we imagine - one in which children toiled in coal mines or up chimneys; in which men could be dragged away to serve in rat-infested navy ships, or to fight the brutal battles of the long Napoleonic War; in which the wives and daughters of the poor could be sold in marketplaces like cattle. The streets of this world were so thick with horse dung - and sometimes human too - that in some towns there were special street sweepers who would scrape a path across the road for you, for a fee. Out of town, travellers on highways would sometimes be subjected to the sight of an executed criminal, swinging on a gibbet. Those who received a normal burial were not safe either: London cemeteries were plagued by grave-robbers, who supplied fresh corpses to surgeons for dissection. Even upper-class life was not immune from squalor. Personal sanitation in Jane Austen’s time was not up to modern standards. Piped hot water was an unheard-of luxury; mass-produced soap was a recent innovation; ‘shampoo’ was a mystery of the Far East and deodorant was nonexistent. Lack of toothpaste would very likely have given Mr Darcy - along with the rest of Austen’s romantic leads- terrible bad breath. When teeth decayed, the rich paid to have them replaced with fresh ones plucked from corpses.

Q. Which of the following best represents the tone of the author towards Jane Austen's works?

Solution:

The author highlights the contrast between life as presented by Jane Austen's novels and what the situation was really like in 19th century England. By examining the nature of the language used by the author, which is mocking in a light manner, one can infer that he/she has been “satirical” in his/her tone. This vindicates option 3.

Though the passage presents very grim situations, on the whole the tone and language used by the author is lighthearted. He/she has not provided a detailed 'critique' nor has he/she been “dismissive” of Jane Austen's works. Eliminate options 1 and 4.

The author has not been as 'condescending' or “patronizing” as much as he/she has been mocking of Jane Austen's works.

Eliminate option 2. Hence, the correct answer is option 3.

QUESTION: 11

Answer the following question based on the information given below.

There’s a poster on the wall of the gym I use, a place frequented by many aspiring British athletes. It says simply: “You lose 100% of the chances you don’t take.” No one likes to be rejected, to take a chance, to put in huge effort only to be rebuffed. But if you want to succeed at anything in life, you have to put yourself forward. You have to take the chance that you’ll be rejected.

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Start by learning not to take a rejection personally. Instead of saying, “What’s wrong with me?”, step back. See if you can figure out what might be lacking in what you’ve created, or in the way you’ve gone about trying to achieve your dream. The artist Dexter Dalwood, speaking recently to creative arts students at their graduation ceremony, warned his audience: “If you want your ideas to succeed, be prepared to be rejected. Often, It comes with the territory.”

Anders Ericsson, a professor at the University of Colorado, observed the practice habits of violin students in Berlin from the age of five until they reached adulthood. He found that the most powerful predictor of success, of whether students became “elite” violinists, was how many hours of practice they put in and how determined they were to improve. The author Malcolm Gladwell popularised this idea, which has become known as the “10,000-hour rule”. It seems that it takes approximately 10,000 hours of dedication, of being criticised and reacting constructively to that criticism, to succeed and achieve true excellence.

Q. A thought like “What’s wrong with me?” implies that:

A. You are reflecting on reasons for your rejection.

B. You are learning through failure.

C. You are open to feedback. * *

Solution:

The passage states “Instead of saying, “What’s wrong with me?”, step back. See if you can figure out what might be lacking in what you’ve created, or in the way you’ve gone about trying to achieve your dream.” The highlighted text “What’s wrong with me?” would mean one is being defensive, rigid and closed to change. It would also mean that the person is taking rejection personally. Statements A, B and C are all positive statements which do not reflect the quoted text.

Hence, the correct answer is option 4.

QUESTION: 12

There’s a poster on the wall of the gym I use, a place frequented by many aspiring British athletes. It says simply: “You lose 100% of the chances you don’t take.” No one likes to be rejected, to take a chance, to put in huge effort only to be rebuffed. But if you want to succeed at anything in life, you have to put yourself forward. You have to take the chance that you’ll be rejected.

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Start by learning not to take a rejection personally. Instead of saying, “What’s wrong with me?”, step back. See if you can figure out what might be lacking in what you’ve created, or in the way you’ve gone about trying to achieve your dream. The artist Dexter Dalwood, speaking recently to creative arts students at their graduation ceremony, warned his audience: “If you want your ideas to succeed, be prepared to be rejected. Often, It comes with the territory.”

Anders Ericsson, a professor at the University of Colorado, observed the practice habits of violin students in Berlin from the age of five until they reached adulthood. He found that the most powerful predictor of success, of whether students became “elite” violinists, was how many hours of practice they put in and how determined they were to improve. The author Malcolm Gladwell popularised this idea, which has become known as the “10,000-hour rule”. It seems that it takes approximately 10,000 hours of dedication, of being criticised and reacting constructively to that criticism, to succeed and achieve true excellence.

Q. Which of the following would be an example of the “10,000-hour rule” ?

Solution:

The “10,000-hour rule” talks about showing determination, grit and a positive attitude towards criticism. This is only seen in option 2.

Options 1,3 and 4 are eliminated as they miss out on the aspect of reacting towards criticism.

Hence, the correct answer is option 2.

QUESTION: 13

There’s a poster on the wall of the gym I use, a place frequented by many aspiring British athletes. It says simply: “You lose 100% of the chances you don’t take.” No one likes to be rejected, to take a chance, to put in huge effort only to be rebuffed. But if you want to succeed at anything in life, you have to put yourself forward. You have to take the chance that you’ll be rejected.

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Start by learning not to take a rejection personally. Instead of saying, “What’s wrong with me?”, step back. See if you can figure out what might be lacking in what you’ve created, or in the way you’ve gone about trying to achieve your dream. The artist Dexter Dalwood, speaking recently to creative arts students at their graduation ceremony, warned his audience: “If you want your ideas to succeed, be prepared to be rejected. Often, It comes with the territory.”

Anders Ericsson, a professor at the University of Colorado, observed the practice habits of violin students in Berlin from the age of five until they reached adulthood. He found that the most powerful predictor of success, of whether students became “elite” violinists, was how many hours of practice they put in and how determined they were to improve. The author Malcolm Gladwell popularised this idea, which has become known as the “10,000-hour rule”. It seems that it takes approximately 10,000 hours of dedication, of being criticised and reacting constructively to that criticism, to succeed and achieve true excellence.

Q. What can be a valid assumption from Dexter Dalwood’s words “If you want your ideas to succeed, be prepared to be rejected. Often, It comes with the territory.” ?

Solution:

The line “If you want your ideas to succeed, be prepared to be rejected. Often. It comes with the territory.” validates option 4 because the word "territory" in the highlighted text connects with the idea of 'road to success'. Options 1 and 3 contradict what is said in the passage. Option 2 is a misinterpretation of the quoted text where it takes the word "territory" literary.

Hence, the correct answer is option 4.

QUESTION: 14

There’s a poster on the wall of the gym I use, a place frequented by many aspiring British athletes. It says simply: “You lose 100% of the chances you don’t take.” No one likes to be rejected, to take a chance, to put in huge effort only to be rebuffed. But if you want to succeed at anything in life, you have to put yourself forward. You have to take the chance that you’ll be rejected.

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Q. According to the author, people do not realize their dreams because:

A. They do not take chances.

B. They do not have a choice.

C. They do not like rejection.

Solution:

The passage states “No one likes to be rejected, to take a chance, to put in huge effort only to be rebuffed. But if you want to succeed at anything in life, you have to put yourself forward. You have to take the chance that you’ll be rejected." This validates statements A and C.

The paragraph talks about us not having a choice but to take chances. Not having a choice to fulfil one’s dreams is not mentioned in the passage. This negates statement B.

Hence, the correct answer is option 3.

QUESTION: 15

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Q. Which of these is not true about rejection?

Solution:

The passage mentions, “Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside.” This validates options 2, 3 and 4. The following paragraph talks about learning from rejection and failure. Option 1 contradicts that. Hence, the correct answer is option 1.

QUESTION: 16

There’s no choice - what it says on that poster is absolutely right. The alternative is to be 100% certain you’ll never realise your dreams.

It’s one thing to understand why you feel bad when you’ve been rejected. But why stop there? Why not take things a step further? Instead of thinking about rejection as something you hope to avoid, see if you can make it work for you rather than distress you. When you do this, rejection will actually help you create something even better than the offering that’s been cast aside. Here’s how.

Learning through failure is how rejection helps. It can spur you on to do it again, do it better.

Q. The quote “You lose 100% of the chances you don’t take.” was Marks put in the gym to:

Solution:

The author states that aspiring British athletes frequented the gym. Also, a gym is a place where people would benefit from motivation and inspiration. Option 1 is not supported by the content in the passage. Option 2 is incorrect as the quoted text is not an “example” but a statement. Option 4 is not correct as the passage is not about “competition”. Option 3 is apt as it talks about opportunities while the quote mentions chances. Hence, the correct answer is option 3.

QUESTION: 17

Answer the questions based on the passage given below.

Scholars and savants, sociologists and political scientists, across ages and across continents, have cautioned against rampant nationalism and its close cousin patriotism (famously described by Mark Twain as the “last refuge of a scoundrel”). But in country after country, from America to Europe to Asia, nationalistic fervor is all the rage, fuelled by everything from border disputes to sporting rivalry, from trade protectionism to cultural expansionism. The latest to join the list of triggers that spark patriotic and nationalistic outrage (always expressed loudly rather than quietly): terrorism.

Consider this: More than a million infants die every year of malnutrition and more than 100,000 youngsters are killed in road accidents every year in India — doesn’t evoke an iota of embarrassment from the nationalistic brigade. There are some 30,000 casualties from gun violence in the US every year, including more than 300 instances of mass shooting in 2015. No nationalistic outrage. Both are shrugged off. But a single terrorist attack, particularly if it comes from a perceived foreign source, can trigger a nationalistic outpouring that can dominate the media for days and weeks.

Every death is different, and indeed every terrorist attack is different, depending on its geography and its victims. While America and Europe fret about terrorist incidents in their territory, provoking nationalistic fury, there is little concern for terrorist attacks in distant India. Within India itself, a terrorist attack in Delhi or Mumbai has a different resonance from the one in Dantewada or Aizawl, which are outside national — and nationalistic — mainstream conscience. And no one cares for attacks in Africa, including within Africa itself: Burkina Faso, Mali, and Ivory Coast have all seen attacks as bloody and lethal as the ones in Brussels and San Bernardino without getting a fraction of the coverage.

All this is broadly in tune with the first principles of patriotism (when love of your people comes first) and nationalism (when hate for people other than your own comes first). The difference between patriotism and nationalism, explained the late American columnist Sydney Harris, is that the patriot is proud of his country for what it does, and the nationalist is proud of his country no matter what it does. The first attitude creates a feeling of responsibility, but the second a feeling of blind arrogance that often leads to war, as has been demonstrated again and again in history.

Q. According to Sydney Harris patriotism is being proud of one’s country for what it does. Which of the following would strengthen this argument? * *

Solution:

The last paragraph states “....the American columnist Sydney Harris, is that the patriot is proud of his country for what it does, and the nationalist is proud of his country no matter what it does.” This means patriotism is expressed by being proud of what good your country is doing and not blindly or arrogantly loving your country. Option 1 talks about war, option 2 talks about genocide and option 4 talks about regressive laws. Being proud of these events would go against true patriotism. Option 3 with health and sanitation is apt as these are true indicators of human development and a nation’s progress. Hence, the correct answer is option 3.

QUESTION: 18

Scholars and savants, sociologists and political scientists, across ages and across continents, have cautioned against rampant nationalism and its close cousin patriotism (famously described by Mark Twain as the “last refuge of a scoundrel”). But in country after country, from America to Europe to Asia, nationalistic fervor is all the rage, fuelled by everything from border disputes to sporting rivalry, from trade protectionism to cultural expansionism. The latest to join the list of triggers that spark patriotic and nationalistic outrage (always expressed loudly rather than quietly): terrorism.

Consider this: More than a million infants die every year of malnutrition and more than 100,000 youngsters are killed in road accidents every year in India — doesn’t evoke an iota of embarrassment from the nationalistic brigade. There are some 30,000 casualties from gun violence in the US every year, including more than 300 instances of mass shooting in 2015. No nationalistic outrage. Both are shrugged off. But a single terrorist attack, particularly if it comes from a perceived foreign source, can trigger a nationalistic outpouring that can dominate the media for days and weeks.

Every death is different, and indeed every terrorist attack is different, depending on its geography and its victims. While America and Europe fret about terrorist incidents in their territory, provoking nationalistic fury, there is little concern for terrorist attacks in distant India. Within India itself, a terrorist attack in Delhi or Mumbai has a different resonance from the one in Dantewada or Aizawl, which are outside national — and nationalistic — mainstream conscience. And no one cares for attacks in Africa, including within Africa itself: Burkina Faso, Mali, and Ivory Coast have all seen attacks as bloody and lethal as the ones in Brussels and San Bernardino without getting a fraction of the coverage.

All this is broadly in tune with the first principles of patriotism (when love of your people comes first) and nationalism (when hate for people other than your own comes first). The difference between patriotism and nationalism, explained the late American columnist Sydney Harris, is that the patriot is proud of his country for what it does, and the nationalist is proud of his country no matter what it does. The first attitude creates a feeling of responsibility, but the second a feeling of blind arrogance that often leads to war, as has been demonstrated again and again in history.

Q. “More than a million infants die every year of malnutrition and more than 100,000 youngsters are killed in road accidents every year in India — doesn’t evoke an iota of embarrassment from the nationalistic brigade.... But a single terrorist attack, particularly if it comes from a perceived foreign source, can trigger a nationalistic outpouring that can dominate the media for days and weeks..” implies that:

Solution:

The quoted text talks about deaths due to malnutrition and accidents, and goes on to say how this does not affect the nationalist ideology while a terrorist attack triggers a nationalist outrage. Therefore, it can be implied from the text that the nationalists discriminate between the sufferings of the people of their country. This supports option 1.

The "nationalistic outpouring" mentioned in the passage clearly indicates the presence of nationalism in India. So, eliminate option 2.

Option 3 is with “government” is out of context as the main focus is the nationalist ideology.

Option 4 is uncalled for, as it is too extreme with “irresponsible citizens”.

Hence, the correct answer is option 1.

QUESTION: 19

Scholars and savants, sociologists and political scientists, across ages and across continents, have cautioned against rampant nationalism and its close cousin patriotism (famously described by Mark Twain as the “last refuge of a scoundrel”). But in country after country, from America to Europe to Asia, nationalistic fervor is all the rage, fuelled by everything from border disputes to sporting rivalry, from trade protectionism to cultural expansionism. The latest to join the list of triggers that spark patriotic and nationalistic outrage (always expressed loudly rather than quietly): terrorism.

Consider this: More than a million infants die every year of malnutrition and more than 100,000 youngsters are killed in road accidents every year in India — doesn’t evoke an iota of embarrassment from the nationalistic brigade. There are some 30,000 casualties from gun violence in the US every year, including more than 300 instances of mass shooting in 2015. No nationalistic outrage. Both are shrugged off. But a single terrorist attack, particularly if it comes from a perceived foreign source, can trigger a nationalistic outpouring that can dominate the media for days and weeks.

Every death is different, and indeed every terrorist attack is different, depending on its geography and its victims. While America and Europe fret about terrorist incidents in their territory, provoking nationalistic fury, there is little concern for terrorist attacks in distant India. Within India itself, a terrorist attack in Delhi or Mumbai has a different resonance from the one in Dantewada or Aizawl, which are outside national — and nationalistic — mainstream conscience. And no one cares for attacks in Africa, including within Africa itself: Burkina Faso, Mali, and Ivory Coast have all seen attacks as bloody and lethal as the ones in Brussels and San Bernardino without getting a fraction of the coverage.

All this is broadly in tune with the first principles of patriotism (when love of your people comes first) and nationalism (when hate for people other than your own comes first). The difference between patriotism and nationalism, explained the late American columnist Sydney Harris, is that the patriot is proud of his country for what it does, and the nationalist is proud of his country no matter what it does. The first attitude creates a feeling of responsibility, but the second a feeling of blind arrogance that often leads to war, as has been demonstrated again and again in history.

Q. According to the author, nationalistic fervour is fuelled by all of the following except:

A. Growth of a Culture

B. Discord among nations

C. Economics of trade

Solution:

The passage mentions "... nationalistic fervor is all the rage, fuelled by everything from border disputes to sporting rivalry, from trade protectionism to cultural expansionism.” A, B and C find support in the passage. Hence, the correct answer is option 4.

QUESTION: 20

Scholars and savants, sociologists and political scientists, across ages and across continents, have cautioned against rampant nationalism and its close cousin patriotism (famously described by Mark Twain as the “last refuge of a scoundrel”). But in country after country, from America to Europe to Asia, nationalistic fervor is all the rage, fuelled by everything from border disputes to sporting rivalry, from trade protectionism to cultural expansionism. The latest to join the list of triggers that spark patriotic and nationalistic outrage (always expressed loudly rather than quietly): terrorism.

Q. Which of the following cannot be inferred about Burkina Faso, Mali, and Ivory Coast?

Solution:

The passage mentions “And no one cares for attacks in Africa, including within Africa itself: Burkina Faso, Mali, and Ivory Coast have all seen attacks as bloody and lethal as the ones in Brussels and San Bernardino without getting a fraction of the coverage.” This validates options 3 and 4. The paragraph in which this line is embedded talks about terrorism and terrorist attacks, hence option 1 is validated. The paragraph states that these African countries have seen attacks “as lethal” as their western countries and not “more than”. Thus, option 2 cannot be inferred. Hence, the correct answer is option 2.

QUESTION: 21

Q. Why does Mark Twain call patriotism as the “last refuge of a scoundrel”?

Solution:

"Last refuge of a scoundrel" literally means a dishonest person seeking (misusing) a secure place/ haven under the guise of patriotism/loyalty to country, etc. Option 1 is a positive example of patriotism . Option 3 is unrelated to what Mark Twain is saying. Between options 2 and 4, the former is stronger as it talks about misusing patriotism for one’s vested interest. Option 4 with “nationality” is incorrect as the question stem talks about patriotism.

Hence, the correct answer is option 2.

QUESTION: 22

Q. How does the geography of a place and its victims influence the perception of a terrorist attack?

A. Terrorist attacks are seen more in the west than in the east.

B. Within a country, terrorism in the more industrious areas cause more outrage.

Solution:

The passage states “While America and Europe fret about terrorist incidents in their territory, provoking nationalistic fury, there is little concern for terrorist attacks in distant India. Within India itself, a terrorist attack in Delhi or Mumbai has a different resonance from the one in Dantewada or Aizawl, which are outside national — and nationalistic — mainstream conscience.” The passage talks about people in the West being more concerned with the terrorist attacks that affect “them” directly. It does not talk about more terrorism being seen in the Western world than the East. Statement A can be ruled out. Statement B is correct if we look at the comparison between Delhi/Mumbai v/s Dantewada /Aizawl. Hence, the correct answer is option 2.

QUESTION: 23

Answer the questions based on the passage given below.

Who and what is an Indian? How we are to characterize the Indian diasporic community as 'Indian' given that it is constituted of such diverse elements as South Asian Hong Kong Muslims, Canadian Sikhs (or shall we say Sikh Canadians?), Punjabi Mexican Californians, Gujarati East Africans now settled in the U.S. by way of England, South African Hindus, and so forth? In the United States, at least, the Indian community has occupied a place of considerable privilege, and many Indians could deflect the moment of recognition that 'Indianness' and being 'American' do not always happily coincide. In recent years, with a declining economy on the one hand, and the congregation of Indians in clusters that visibly put them apart on the other hand, Indians have for the first time become the targets of racial attacks. The Indian woman in her 'native dress', with the vermillion dot on her forehead, is easily seen as an embodiment of sheer otherness, and so she has been perceived by the so-called "dot-busters", a gang of white teenagers operating in New Jersey who have already been responsible for several violent crimes against Indians. In North America and the U.K., the native Indian costume has come up for public scrutiny and discussion in an altogether different respect: Sikhs have insisted that they be exempt from the law that compels bicyclists and motorcyclists to wear helmets, for such helmets cannot be worn over turbans, and their religious faith requires Sikhs to wear turbans. The kirpan has been an issue of contention in California schools. The 'corner shop', a hallowed symbol (if we could recall our Dickens) of English life, is now mainly in the hands of Indians. The obvious question is not only, 'What do the English think of that', but also: 'If the English landscape has been so altered, what is English about England'? The diaspora, in short, affects the center as well.

However unlike Indian communities across the world might be, they all maintain some sort of tenuous link with the motherland. The most likely candidate for a force of bonding would be, of all things, the Hindi feature film, a phenomenon unique to the Indian diaspora: what Hollywood is to Western Europe, the Bombay Hollywood ("Bollywood") is to the Middle East and East Africa. The modesty, not to mention puritanism, of the Hindi film is said to explain its appeal to the Islamic world; and though we may well contest that interpretation, it is worthy of note that Hindi films found in grocery and video stores across the U.S. often carry subtitles in Arabic, one language which is indubitably not spoken by any Indian community in the U.S.

The Indian 'arranged marriage' might furnish another such facet of a 'common culture'. Newspapers published by Indian communities flourish everywhere, and they invariably carry a section with matrimonial ads. Though these very ads help Indians to 'locate' one another, they pose difficult questions about 'otherness', both the otherness' of Indians in relation to 'Americans', and the internal 'otherness' of certain Indians in relation to other Indians.

Q. A suitable title for this passage would be:

Solution:

The passage talks about Indians around the world and the different identities that they have incorporated yet not forgotten their Indianness. It talks about the Indians in different parts of the world - “....we are to characterize the Indian diasporic community as 'Indian' given that it is constituted of such diverse elements.” This validates option 1. Options 2 and 3 do not capture the essence of the passage which is Indians living outside their homeland, which is reflected in the word - Diaspora. Option 4 is too generic.

Hence, the correct answer is option 1.

QUESTION: 24

Who and what is an Indian? How we are to characterize the Indian diasporic community as 'Indian' given that it is constituted of such diverse elements as South Asian Hong Kong Muslims, Canadian Sikhs (or shall we say Sikh Canadians?), Punjabi Mexican Californians, Gujarati East Africans now settled in the U.S. by way of England, South African Hindus, and so forth? In the United States, at least, the Indian community has occupied a place of considerable privilege, and many Indians could deflect the moment of recognition that 'Indianness' and being 'American' do not always happily coincide. In recent years, with a declining economy on the one hand, and the congregation of Indians in clusters that visibly put them apart on the other hand, Indians have for the first time become the targets of racial attacks. The Indian woman in her 'native dress', with the vermillion dot on her forehead, is easily seen as an embodiment of sheer otherness, and so she has been perceived by the so-called "dot-busters", a gang of white teenagers operating in New Jersey who have already been responsible for several violent crimes against Indians. In North America and the U.K., the native Indian costume has come up for public scrutiny and discussion in an altogether different respect: Sikhs have insisted that they be exempt from the law that compels bicyclists and motorcyclists to wear helmets, for such helmets cannot be worn over turbans, and their religious faith requires Sikhs to wear turbans. The kirpan has been an issue of contention in California schools. The 'corner shop', a hallowed symbol (if we could recall our Dickens) of English life, is now mainly in the hands of Indians. The obvious question is not only, 'What do the English think of that', but also: 'If the English landscape has been so altered, what is English about England'? The diaspora, in short, affects the center as well.

However unlike Indian communities across the world might be, they all maintain some sort of tenuous link with the motherland. The most likely candidate for a force of bonding would be, of all things, the Hindi feature film, a phenomenon unique to the Indian diaspora: what Hollywood is to Western Europe, the Bombay Hollywood ("Bollywood") is to the Middle East and East Africa. The modesty, not to mention puritanism, of the Hindi film is said to explain its appeal to the Islamic world; and though we may well contest that interpretation, it is worthy of note that Hindi films found in grocery and video stores across the U.S. often carry subtitles in Arabic, one language which is indubitably not spoken by any Indian community in the U.S.

The Indian 'arranged marriage' might furnish another such facet of a 'common culture'. Newspapers published by Indian communities flourish everywhere, and they invariably carry a section with matrimonial ads. Though these very ads help Indians to 'locate' one another, they pose difficult questions about 'otherness', both the otherness' of Indians in relation to 'Americans', and the internal 'otherness' of certain Indians in relation to other Indians.

Q. “In recent years, with a declining economy on the one hand, and the congregation of Indians in clusters that visibly put them apart on the other hand, Indians have for the first time become the targets of racial attacks.”

Which of these phrases is applicable to the above lines:

A. Desires are nourished by delays

B. Desperate times call for desperate measures.

Solution:

The idiom stated in A means “The longer you have to wait for something you want, the more eager you will be to get it”. The idiom in B means “In adverse circumstances actions that might have been rejected under other circumstances may become the best or only choice.” This does not directly relate to "racial attack" in the question stem.

The fact that both the idioms bear no resemblance to the above lines vindicates option 4 as correct. Hence, the correct answer is option 4.

QUESTION: 25

Who and what is an Indian? How we are to characterize the Indian diasporic community as 'Indian' given that it is constituted of such diverse elements as South Asian Hong Kong Muslims, Canadian Sikhs (or shall we say Sikh Canadians?), Punjabi Mexican Californians, Gujarati East Africans now settled in the U.S. by way of England, South African Hindus, and so forth? In the United States, at least, the Indian community has occupied a place of considerable privilege, and many Indians could deflect the moment of recognition that 'Indianness' and being 'American' do not always happily coincide. In recent years, with a declining economy on the one hand, and the congregation of Indians in clusters that visibly put them apart on the other hand, Indians have for the first time become the targets of racial attacks. The Indian woman in her 'native dress', with the vermillion dot on her forehead, is easily seen as an embodiment of sheer otherness, and so she has been perceived by the so-called "dot-busters", a gang of white teenagers operating in New Jersey who have already been responsible for several violent crimes against Indians. In North America and the U.K., the native Indian costume has come up for public scrutiny and discussion in an altogether different respect: Sikhs have insisted that they be exempt from the law that compels bicyclists and motorcyclists to wear helmets, for such helmets cannot be worn over turbans, and their religious faith requires Sikhs to wear turbans. The kirpan has been an issue of contention in California schools. The 'corner shop', a hallowed symbol (if we could recall our Dickens) of English life, is now mainly in the hands of Indians. The obvious question is not only, 'What do the English think of that', but also: 'If the English landscape has been so altered, what is English about England'? The diaspora, in short, affects the center as well.

However unlike Indian communities across the world might be, they all maintain some sort of tenuous link with the motherland. The most likely candidate for a force of bonding would be, of all things, the Hindi feature film, a phenomenon unique to the Indian diaspora: what Hollywood is to Western Europe, the Bombay Hollywood ("Bollywood") is to the Middle East and East Africa. The modesty, not to mention puritanism, of the Hindi film is said to explain its appeal to the Islamic world; and though we may well contest that interpretation, it is worthy of note that Hindi films found in grocery and video stores across the U.S. often carry subtitles in Arabic, one language which is indubitably not spoken by any Indian community in the U.S.

The Indian 'arranged marriage' might furnish another such facet of a 'common culture'. Newspapers published by Indian communities flourish everywhere, and they invariably carry a section with matrimonial ads. Though these very ads help Indians to 'locate' one another, they pose difficult questions about 'otherness', both the otherness' of Indians in relation to 'Americans', and the internal 'otherness' of certain Indians in relation to other Indians.

Q. Which of the following is true according to the passage?

Solution:

The passage mentions “However unlike Indian communities across the world might be, they all maintain some sort of tenuous link with the motherland....feature films.” This helps negate option 1 as “tenuous” meaning ‘weak’ is contrary to the sense of “patriotism” mentioned in option 1. The quoted text and the first paragraph in general talk about the diversity in Indianness; this vindicates option 2. Option 3 with “deep cultural bond” is also negated by the quoted text, since the text mentions “tenuous link”. Option 4 has no support in the passage.

Hence, the correct answer is option 2.

QUESTION: 26

Who and what is an Indian? How we are to characterize the Indian diasporic community as 'Indian' given that it is constituted of such diverse elements as South Asian Hong Kong Muslims, Canadian Sikhs (or shall we say Sikh Canadians?), Punjabi Mexican Californians, Gujarati East Africans now settled in the U.S. by way of England, South African Hindus, and so forth? In the United States, at least, the Indian community has occupied a place of considerable privilege, and many Indians could deflect the moment of recognition that 'Indianness' and being 'American' do not always happily coincide. In recent years, with a declining economy on the one hand, and the congregation of Indians in clusters that visibly put them apart on the other hand, Indians have for the first time become the targets of racial attacks. The Indian woman in her 'native dress', with the vermillion dot on her forehead, is easily seen as an embodiment of sheer otherness, and so she has been perceived by the so-called "dot-busters", a gang of white teenagers operating in New Jersey who have already been responsible for several violent crimes against Indians. In North America and the U.K., the native Indian costume has come up for public scrutiny and discussion in an altogether different respect: Sikhs have insisted that they be exempt from the law that compels bicyclists and motorcyclists to wear helmets, for such helmets cannot be worn over turbans, and their religious faith requires Sikhs to wear turbans. The kirpan has been an issue of contention in California schools. The 'corner shop', a hallowed symbol (if we could recall our Dickens) of English life, is now mainly in the hands of Indians. The obvious question is not only, 'What do the English think of that', but also: 'If the English landscape has been so altered, what is English about England'? The diaspora, in short, affects the center as well.

Q. “The Indian 'arranged marriage' might furnish another such facet of a 'common culture'.” Imples:

A. Indians are getting married in foreign lands.

B. Arranged marriages are common in the West.

C. The fundamentals of Indian marriage are changing.

Solution:

The passage states the following - “The Indian 'arranged marriage' might furnish another such facet of a 'common culture'. Newspapers published by Indian communities flourish everywhere, and they invariably carry a section with matrimonial ads.” Statement A is incorrect as the passage is talking about Indian diaspora and the practice of arranged marriages being prevalent among Indian communities. Therefore, A cannot be implied from the quoted text. Statement B is incorrect with “common” and “West”. The passage only talks about Indians in the West practicing arranged marriages. Option C may be true if we see Indians marrying into Western communities as validated by examples in the passage -"... South Asian Hong Kong Muslims, Canadian Sikhs (or shall we say Sikh Canadians?), Punjabi Mexican Californians, Gujarati East Africans ...” However, with the given text, it is seen that the fundamentals of Indian arranged marriages, are still going strong. Therefore, C is ruled out as well. Hence, the correct answer is option 4.

QUESTION: 27

Q. Which of the following weakens the concept of “otherness” as mentioned in the passage?

Solution:

The passage mentions, “They pose difficult questions about 'otherness', both the otherness' of Indians in relation to 'Americans', and the internal 'otherness' of certain Indians in relation to other Indians.” The paragraph talks about otherness between the West and India and also the “internal” otherness existing between Indians with respect to social or community identity. Options 1 and 4 strengthen the concept of “otherness”. Option 3 is talking about opportunities of the West where as “otherness” refers to the difference people make between each other. Option 2 talks about the existence of equality among Indian diasporas. This weakens the concept of otherness. Hence, the correct answer is option 2.

QUESTION: 28

Q. “What is English about England?” This statement is based on the assumption that:

Solution:

The passage talks about the Indian diaspora and not of powerful nations. Option 4 can be ruled out. Based on the above quoted sentence - option 1 can be ruled out because there is no evidence to prove the veracity of Indians “populating” England. Option 2 can be ruled out as it states England “has always been..” We cannot confirm this from the passage. “Plural” refers to “diversity”. The fact that the statement questions the English people (number or purity of race ), it is safe to assume that it is a pluralistic nation where people of various nationalities and ethnicities reside.

Hence, the correct answer is option 3.

*Answer can only contain numeric values

QUESTION: 29

Five sentences are given below labeled (1), (2), (3), (4) and (5). Of these, four sentences need to be arranged in a logical order to form a coherent paragraph/passage. Pick out the sentence that does not fit the sequence.

1. Study after study confirms that customer satisfaction and stock price generally tend to move in tandem.

2. Interestingly, they go on to conclude that because the market is insufficiently receptive to ACSI data as a leading indicator of financial performance, It’s possible to beat the market by investing in firms that do well on the ASCI.

3. That shouldn’t be surprising, as both are fairly reliable indicators of a firm’s vitality.

4. However, since many firms nowadays are hard-pressed to satisfy the escalating demands of both digitally-empowered consumers and activist shareholders, there are ever more variables feeding this relationship.

5. CMOs, therefore, need to understand this issue at a deeper level, so they can isolate and control the levers by which customer sentiment comes to influence the market.

Solution:

Statement 1 introduces the topic of the paragraph - the relationship between customer satisfaction and stock price. It can be followed by either statement 2 or statement 3. But statement 2 which talks about ASCI data does not connect with any of the other statements. Statement 3 connects with 4 which also talks about customers and shareholders and it also relates to the customer satisfaction and stock price mentioned in 1. Statement 5 which talks about the need for CMOs to understand the relationship between customer satisfaction and the stock market, tells us for whom it is important to understand this relationship. Hence, the correct answer is 2.

*Answer can only contain numeric values

QUESTION: 30

Five sentences are given below labeled (1), (2), (3), (4) and (5). Of these, four sentences need to be arranged in a logical order to form a coherent paragraph/passage. Pick out the sentence that does not fit the sequence.

1. It’s important they recognize that they have a choice.

2. This means stepping back, and looking at other options open to them rather than mindlessly following their cravings for more.

3. Greed is bad for the society as a whole and we should try to restrain our need for more.

4. Taking this altruistic route, requires persistence, patience, humility, courage and commitment.

5. People suffering from the greed syndrome need to find ways to move on from egoistic strivings to more altruistic ones.

Solution:

Statement 5 introduces the topic of the sentence- dealing with greed syndrome. It talks about how people suffering from greed syndrome can take their first step to recover from it. Statement 1 with “they” relates to “people suffering from greed syndrome” mentioned in statement 5. Thus, 5-1 form a link. As statement 1 says about having a choice, statement 2 continues by saying that it means looking at the choices available. Thus, 1-2 form a link. Statement 5 with “this altruistic route” indicates some connection with the paragraph. Statement 3 is a generic statement about “greed” and cannot be directly connected with “greed syndrome” as “greed” is a character trait and “greed syndrome” is a medical condition.

Hence, the correct answer is 3.

*Answer can only contain numeric values

QUESTION: 31

Four sentences are given below labeled (1), (2), (3) and (4). Of these, three sentences need to be arranged in a logical order to form a coherent paragraph/passage. Pick out the sentence that does not fit the sequence.

1. These debates around Hindutva may be used negatively against BJP in the next elections.

2. The BJP has provoked the nationalism debate because it is central to the Hindutva idea of a strong Hindu nation — and handily detracts from other failures.

3. The problem is that the idea of anti-national blasphemy, still young, could one day grow up and break its chains; India will then start to blend into its neighborhood.

4. From Hyderabad Central University to Jawaharlal Nehru University, and now the National Institute of Technology in Srinagar, where a ‘nationalist’ standoff between students has resulted in condemnable police action and CRPF troops on campus, it is defending and fanning devotional nationalism.

Solution:

Statement 2 opens the paragraph by introducing the nationalism debate spurred by BJP because of its relation with “Hindutva”. Statement 4 continues with presenting the effects of this nationalism debate on the students of various premier institutes. Statement 3 talks about the future situation of this anti-national debates surrounding the country. Statement 1 does not fit in the sequence as the debate is not around Hindutva but “nationalism”.

Hence, the correct answer is 1.

*Answer can only contain numeric values

QUESTION: 32

Four sentences are given below labeled (1), (2), (3) and (4). Of these, three sentences need to be arranged in a logical order to form a coherent paragraph/passage. Pick out the sentence that does not fit the sequence.

1. The city "shit-flow" diagram shows that the situation is grim, as all cities either do not treat or safely dispose of the bulk of human excreta.

2. But the fact is that the bulk of Indian households with access to sanitation are connected to septic tanks-40 per cent of urban India, according to Census 2011.

3. This is because we often confuse toilets with sanitation.

4. But the fact is that toilets are mere receptacles to receive waste; when we flush or pour water, the waste flows into a piped drain, which could be either connected, or not, to a sewage treatment plant (STP).

Solution:

Statement 1 introduces the topic of the paragraph - treatment of human waste. Statement 2 follows by telling us why the ‘situation is grim’ (ref statement 1). Between statements 2 and 4, statement 4 which explains why toilets do not equal to sanitation, connects with the other two statements logically. Statement 2 simply gives us the status of ‘sanitation’ of Indian households. It does not explain the issues raised in the other two statements.

Hence, the correct answer is 2.

*Answer can only contain numeric values

QUESTION: 33

From among the options, choose the summary of the passage that is written in the same style as that of the passage. Enter the correct option number as your answer.

Like many other industries, the telecom industry is increasingly worried about its energy consumption and the associated carbon footprint. This is not just because rising energy prices have made it more expensive to run telecom networks; it is also because telecoms networks and devices account for nearly 1% of global greenhouse-gas emissions, and the industry wants to avoid criticism from green campaigners. Unlike many other firms, however, telecom operators find their carbon footprints quite easy to work out. That is because their footprints are dominated by one thing: running their networks.

1. Telecoms firms are reducing the power consumption of their networks, for economic and environmental reasons.

2. Telecoms firms are reducing the power consumption of their networks because they want to avoid criticism from greenhouse campaigners.

3. Since the operation of their networks has a noticeable carbon foot print, telecoms firms are concerned about the possible criticism from environmentalists.

4. Telecoms firms are worried about the power consumption of their networks, for economic and environmental reasons.

Solution:

The paragraph has these main points: telecoms firms are worried about their carbon foot print; this arises from the power consumption of their networks; they are worried about criticism from environmentalists; power is also costly for them.

Options 1 and 2 are eliminated because the paragraph does not state that telecoms firms are reducing their power consumption.

Option 3 does not mention the economic factor.

Option 4 captures the essence of the paragraph - telecoms firms are worried about their power consumption for economic and environmental reasons. Hence, the correct answer is 4.

*Answer can only contain numeric values

QUESTION: 34

From among the options, choose the summary of the passage that is written in the same style as that of the passage. Enter the correct option number as your answer.

The Keele University team told a conference that a "supermicroscope" could spot changes in brain cells before Parkinson’s disease destroyed them. The team had been using a synchrotron - or Diamond Light Source (DLS) - at Harwell, Oxfordshire. The device is a large doughnut-shaped particle accelerator, the size of five football pitches, which fires particles at just below the speed of light, focusing them into a beam less than a single cell in diameter. It allows researchers to observe iron levels in individual brain cells, which are affected by Parkinson's. The team's work could help doctors detect early signs of Parkinson's using MRI.

1. The Keele University team said that they have developed a ‘super microscope’ using an accelerator that could detect Parkisnson’s disease in its early signs using MRI.

2. The Keele University team said that they have developed a device using an accelerator that could help doctors detect Parkisnson’s disease in its early signs.

3. The Keele University team has stated that a ‘super microscope’ could help doctors detect Parkinson’s disease by observing the iron levels in the brain cells.

4. The Keele University team has developed a device to generate a kind of light that could help doctors detect early signs of Parkinson’s disease using MRI.

Solution:

Options 1, 2 and 4 can be eliminated as they mention that the Keele University team has ‘developed’ a device/super-microscope. This is not borne out by the paragraph. It may be implied that the synchrotron or Diamond Light Source has been developed by researchers at Keele university but a summary should only contain information explicitly mentioned in the paragraph.

The gist of the paragraph is: The Keele University team has stated that a “super microscope” which is a particle accelerator and DLS which generates a kind of light can detect the iron levels in brain cells.

This technology can be used by doctors to detect early signs of Parkinson’s disease using MRI. This gist is best captured by option 3. Hence, the correct answer is 3.

QUESTION: 35

Answer the following question based on the information given below.

Directorate of Techincal Education (DTE) holds an admission counseling round. DTE categorizes the institutes in four different types A, B, C and D. DTE also divides the students into four categories according to their percentiles. In each type of institute, a certain number of seats are reserved for each percentile range and each student has to select exactly one type of institute as their choice. Table 1 shows the percentage breakup of students of various categories interested in the different categories of colleges. Table 2 shows the number of students interested per seat. Table 3 shows the number of colleges in each category and the number of students per college.

Table 1 : Percentage of students interested in a college category with respect to the number of students with the same range of percentiles.

Table 2 : Students interested per seat

Table 3 : Number of seats in an institute and number of institute in a category of college the students with 80 and above percentile

Q. Which of the following MBA institutes has the least number of students interested?

Solution:

Let the number of students with 80-85 percentile be x, 85-90 percentile be y, 90-95 percentile be z and 95-100 percentile be w.

Similarly, the breakup of the number of seats available is as shown in the following table :

The total number of seats in A category colleges = 44 x 4 = 176

x/60 + y/32 + z/14 + w/5 = 176 ...(i) Similarly for B, C and D we get.

x/40 + 3y/50 + z/10 + w/10 = 30 x 6 ...(ii)

x/6 + 23y/400 + z/10 + 7w/150 = 29 x 10..(iii)

5x/24 + 11y/100 + z/15 + w/25 = 29 x 12 ...(iv)

Solving the four equations we get, x = 960, y = 800, z = 630 and w = 450 The following two tables are obtained

Institute D has the least number of students interested. Hence, option 2.

QUESTION: 36

Directorate of Techincal Education (DTE) holds an admission counseling round. DTE categorizes the institutes in four different types A, B, C and D. DTE also divides the students into four categories according to their percentiles. In each type of institute, a certain number of seats are reserved for each percentile range and each student has to select exactly one type of institute as their choice. Table 1 shows the percentage breakup of students of various categories interested in the different categories of colleges. Table 2 shows the number of students interested per seat. Table 3 shows the number of colleges in each category and the number of students per college.

Table 1 : Percentage of students interested in a college category with respect to the number of students with the same range of percentiles.

Table 2 : Students interested per seat

Table 3 : Number of seats in an institute and number of institute in a category of college the students with 80 and above percentile

Q. What percentage of students who are interested in category C have 85-90 percentile?

Solution:

From the solution to the first question of the set, we can see that, The total number of students interested in category C = 432 + 184+ 126 + 63 = 805.

The number of students under 85-90 percentile = 184.

Therefore, the percentage of students with 85-90 interested in category C = 22.857%.

Hence, option 3.

QUESTION: 37

Directorate of Techincal Education (DTE) holds an admission counseling round. DTE categorizes the institutes in four different types A, B, C and D. DTE also divides the students into four categories according to their percentiles. In each type of institute, a certain number of seats are reserved for each percentile range and each student has to select exactly one type of institute as their choice. Table 1 shows the percentage breakup of students of various categories interested in the different categories of colleges. Table 2 shows the number of students interested per seat. Table 3 shows the number of colleges in each category and the number of students per college.

Table 1 : Percentage of students interested in a college category with respect to the number of students with the same range of percentiles.

Table 2 : Students interested per seat

Table 3 : Number of seats in an institute and number of institute in a category of college the students with 80 and above percentile

Q. Which of the following has the least number of seats?

Solution:

From the solution to the first question of the set, the least number of students is 16 in 80-85 percentile in A category. Hence, option 3.

QUESTION: 38

Table 2 : Students interested per seat

Q. Which of the following category of students have the highest probability of making it to the college of their choice?

Solution:

From the solution to the previous question of the set, we can see that

The probability of students of the 80-85 percentile students of being able make it to the college = 400/960 = 0.417 The probability of students of the 85-90 percentile students of being able make it to the college = 207/800 = 0.258 The probability of students of the 90-95 percentile students of being able make it to the college = 213/630 = 0.338 The probability of students of the 95-100 percentile students of being able make it to the college= 174/450 = 0.387 We see that the students in 80-85 range have the highest probability. Hence, option 3.

QUESTION: 39

Group Question

Answer the following question based on the information given below.

A, B, C and D compete in a motorbike race in the same direction. The race is conducted on a circular track of 2000 metres and each of them has to complete four loops or circuits of the track. The one with the minimum time wins the race. The graph given below represents the speed in meters per second of the four racers A, B, C and D respectively at the end of each circuit which is the starting speed for the next circuit. Observe 3 the graph and answer the questions that follow.(Assume that the speed of the racers at the start of Circuit 1 is zero)

Distance covered in a circuit = (1/2) x (Sum of speed at the start of the circuit and end of the circuit) x (Time taken) Average speed = Total distance covered/Total time taken

Q. Find the percentage difference between the average speeds of B in Circuit 1 and D in Circuit 3 (Higher with respect to lower).

Solution:

The distance for each of the circuit is fixed i.e. 2000 metres.

Let the time taken by B in Circuit 1 be t_{1 }and D in Circuit 3 be t_{2}. 0.5 x 25 x t_{1} = 2000 ••• t_{1}= 160 seconds.

Hence, average speed = 12.5 m/s And, 0.5 x (30 + 34) x t_{2 }= 2000, t_{2} = 62.5 seconds.

Average speed = 32 m/s The percentage difference = (19.5/12.5) x 100 = 156 Hence, option 3.

QUESTION: 40

A, B, C and D compete in a motorbike race in the same direction. The race is conducted on a circular track of 2000 metres and each of them has to complete four loops or circuits of the track. The one with the minimum time wins the race. The graph given below represents the speed in meters per second of the four racers A, B, C and D respectively at the end of each circuit which is the starting speed for the next circuit. Observe 3 the graph and answer the questions that follow.(Assume that the speed of the racers at the start of Circuit 1 is zero)

Distance covered in a circuit = (1/2) x (Sum of speed at the start of the circuit and end of the circuit) x (Time taken) Average speed = Total distance covered/Total time taken

Q. Find the circuit in which A and C cross each other.

Solution:

The cumulative time taken by A and C for completing different circuits are

In the table it can be seen that C completed Circuit 2 before A and Circuit 3 after A.

Hence, they must have crossed each other in Circuit 3. Hence, option 3.

QUESTION: 41

A, B, C and D compete in a motorbike race in the same direction. The race is conducted on a circular track of 2000 metres and each of them has to complete four loops or circuits of the track. The one with the minimum time wins the race. The graph given below represents the speed in meters per second of the four racers A, B, C and D respectively at the end of each circuit which is the starting speed for the next circuit. Observe 3 the graph and answer the questions that follow.(Assume that the speed of the racers at the start of Circuit 1 is zero)

Distance covered in a circuit = (1/2) x (Sum of speed at the start of the circuit and end of the circuit) x (Time taken) Average speed = Total distance covered/Total time taken

Q. What is the minimum time in seconds taken to complete a particular circuit for any contestant *?*

Solution:

The minimum time taken to complete a circuit will be the one with the maximum average speed.

The maximum average speed observed = 50 m/s Hence, the minimum time taken = 40 seconds. Hence, option 2.

QUESTION: 42

A, B, C and D compete in a motorbike race in the same direction. The race is conducted on a circular track of 2000 metres and each of them has to complete four loops or circuits of the track. The one with the minimum time wins the race. The graph given below represents the speed in meters per second of the four racers A, B, C and D respectively at the end of each circuit which is the starting speed for the next circuit. Observe 3 the graph and answer the questions that follow.(Assume that the speed of the racers at the start of Circuit 1 is zero)

Q. Who has the highest percentage drop in average speed between any two consecutive circuits?

Solution:

The average speeds of the four racers are as shown in the table below:

We can see that the average speed of C reduces from 32 to 25 which is more than 20% drop. This is the highest possible percentage drop in speed. Hence, option 4.

QUESTION: 43

Group Question

Answer the following question based on the information given below.

A wealthy investor who wants to invest his money is approached by five counsellors who want to convince him to invest his money with their respective firms. Having very little knowledge of finance, the investor decides to just invest a certain sum of money with each one of them and judge for himself. He withdraws a total sum of 100000 from his bank account and gives different amounts of money to the five counsellors and gets a total profit of 22950 in return. After six months he makes the following observations about his money invested and the profits earned:

1. The highest investment has given him the third lowest profit percentage.

2. The least investment is two thousand less than half the highest investment.

3. The second highest investment is twice the second lowest investment.

4. The profit on the highest investment is 1/5 times the investment and the profit on the least investment is 50%.

5. Three sums of his investments are in AP with 1000 as the common difference and all his investments are more than 10000.

6. The profit percentage of the second lowest investment and the percentage share of the highest investment in total investment are the same.

7. The least profit percent is 9% and the second lowest profit percentage is 2.5 percentage points less than the third lowest profit percentage.

8. The second highest profit percent is 30%.

Q. What is the highest profit gained by him on any one of the investments?

Solution:

The profit percentages from (4), (7) and (8) are 9, 17.5, 20, 30 and 50.

Let A, B, C, D, and E be the investments in decreasing order.

From (6) the percentage share of A in total investment can be 9, 17.5 and 30.

Exam Reports

Out of which 30 is the only feasible option as A will have atleast 20% share even if all have equal share. So D will give 30% profit.

Thus we get the highest investment as well as the least investment from (2).

From (5) we get the amounts of the other investments as 14000, 15000 and 28000.

We get the following table

280x + 150y = 6250 the value of x and y can be 9 or 17.5 By iteration x = 17.5 and y = 9.

From the table we can see that the highest profit earned is 6500. Hence, option 3.

QUESTION: 44

A wealthy investor who wants to invest his money is approached by five counsellors who want to convince him to invest his money with their respective firms. Having very little knowledge of finance, the investor decides to just invest a certain sum of money with each one of them and judge for himself. He withdraws a total sum of 100000 from his bank account and gives different amounts of money to the five counsellors and gets a total profit of 22950 in return. After six months he makes the following observations about his money invested and the profits earned:

1. The highest investment has given him the third lowest profit percentage.

2. The least investment is two thousand less than half the highest investment.

3. The second highest investment is twice the second lowest investment.

4. The profit on the highest investment is 1/5 times the investment and the profit on the least investment is 50%.

5. Three sums of his investments are in AP with 1000 as the common difference and all his investments are more than 10000.

6. The profit percentage of the second lowest investment and the percentage share of the highest investment in total investment are the same.

7. The least profit percent is 9% and the second lowest profit percentage is 2.5 percentage points less than the third lowest profit percentage.

8. The second highest profit percent is 30%.

Q. Which investment gave him the least profit?

Solution:

From the solution to the first question of the set we can see that the least profit is earned on the third highest investment.Hence, option 1.

QUESTION: 45

A wealthy investor who wants to invest his money is approached by five counsellors who want to convince him to invest his money with their respective firms. Having very little knowledge of finance, the investor decides to just invest a certain sum of money with each one of them and judge for himself. He withdraws a total sum of 100000 from his bank account and gives different amounts of money to the five counsellors and gets a total profit of 22950 in return. After six months he makes the following observations about his money invested and the profits earned:

1. The highest investment has given him the third lowest profit percentage.

2. The least investment is two thousand less than half the highest investment.

3. The second highest investment is twice the second lowest investment.

4. The profit on the highest investment is 1/5 times the investment and the profit on the least investment is 50%.

5. Three sums of his investments are in AP with 1000 as the common difference and all his investments are more than 10000.

6. The profit percentage of the second lowest investment and the percentage share of the highest investment in total investment are the same.

7. The least profit percent is 9% and the second lowest profit percentage is 2.5 percentage points less than the third lowest profit percentage.

8. The second highest profit percent is 30%.

Q. Which two of the following investments should he exchange to maximise his profits the most (if the percentage profits for a particular investment delivered remains the same)?

Solution:

We can see from the table in the solution to the first question of the set that exchange of investment for the highest and lowest investment with the given profit percentage would give the highest profit.

Hence, option 2.

QUESTION: 46

1. The highest investment has given him the third lowest profit percentage.

2. The least investment is two thousand less than half the highest investment.

3. The second highest investment is twice the second lowest investment.

5. Three sums of his investments are in AP with 1000 as the common difference and all his investments are more than 10000.

8. The second highest profit percent is 30%.

Q. Which of the following investments has the largest percentage point difference between the profit percentage and the investment share?

Solution:

From the solution to the first question of the set, we can see that the highest difference is for the lowest investment.

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 47

Group Question

Answer the following question based on the information given below.

Vijay has just started saving enough money and he wants to learn how to invest it in the best possible manner. His friend Amit has agreed to help him. Amit tells Vijay that he invests his money in four broad categories: fixed deposits, equities, equity mutual funds and debt mutual funds. Amit saves Rs. 40,000 every year and deposits all of it across these four categories on 1st April of every year. He started investing in 2004 with equal amounts in the four categories, but since then, the break-up of his deposits across these four categories has differed. However, he ensures that 50% of his yearly savings go into equities and equity mutual funds and the remaining 50% in the other 2 categories.

Also, Amit maintains a data table recording the total amount he has in each of these four categories as on 1st April of every year (table given below). It is also known that the interest rates on fixed deposits have been decreasing: they were 10%, 9% and 8% per annum in the years 2004-05, 2005-06, and 2006-07 respectively. Amit also remembers that the percentage returns on equities in 2006-07 were five times the percentage returns on debt mutual funds in the same year and the percentage returns on equity mutual funds in 2004-05 and 2005-06 were half of the percentage returns on equities in 2005-06 and 2006-07 respectively. Amit does not remember too many details besides that.

Q. What were the percentage returns on equity mutual funds in the year 2005-06?

Solution:

The interest rates on fixed deposits are given for all years, from which we can find out the interest accruing every year and thus the amount deposited in Fixed Deposits on 1st April every year. In 2006, the amount in FD was Rs. 28,210. Since the interest rate on FD from 2006-07 was 8%, Amit invested 37466.8 - (1.08 * 28210) = Rs. 7,000 in FD in 2007.

Since Amit deposits 50% of his yearly savings in Fixed Deposits + debt funds, we can find the amount deposited in debt funds every year. In 2007, he invested 20000 - 7000 = Rs. 13,000 in DMF.

From that, we can find the percentage returns on debt funds every year. Since he invested Rs. 13,000 in 2007, his interest from 2006-07 is, 55455.6 - (38596 + 13000) = 3859.6

The returns on debt funds were 10% in 2006-07.

The returns on equities were 50% in 2006-07 since these were 5 times the % returns from debt funds.

And the returns on equity mutual funds were 25% in 2005-06 as these were half the % returns on equities.

*Answer can only contain numeric values

QUESTION: 48

Vijay has just started saving enough money and he wants to learn how to invest it in the best possible manner. His friend Amit has agreed to help him. Amit tells Vijay that he invests his money in four broad categories: fixed deposits, equities, equity mutual funds and debt mutual funds. Amit saves Rs. 40,000 every year and deposits all of it across these four categories on 1st April of every year. He started investing in 2004 with equal amounts in the four categories, but since then, the break-up of his deposits across these four categories has differed. However, he ensures that 50% of his yearly savings go into equities and equity mutual funds and the remaining 50% in the other 2 categories.

Also, Amit maintains a data table recording the total amount he has in each of these four categories as on 1st April of every year (table given below). It is also known that the interest rates on fixed deposits have been decreasing: they were 10%, 9% and 8% per annum in the years 2004-05, 2005-06, and 2006-07 respectively. Amit also remembers that the percentage returns on equities in 2006-07 were five times the percentage returns on debt mutual funds in the same year and the percentage returns on equity mutual funds in 2004-05 and 2005-06 were half of the percentage returns on equities in 2005-06 and 2006-07 respectively. Amit does not remember too many details besides that.

Q. What was the amount deposited in equity mutual funds on 1st April, 2007?

Solution:

Carrying on from the explanation for the first question, once we get the percentage returns on equities for 2006-07 as 50%, we can find the amount deposited in equities on 1st April, 2007.

We get, 65200 = (38800 x 1.5) + Amount deposited The amount deposited = 65200 - 58200= 7000

Amit deposits 50% of his savings in Equities and Equity Mutual Funds, the amount deposited in equity mutual funds on 1st April, 2007 is 13000.

Answer: 13000

*Answer can only contain numeric values

QUESTION: 49

Vijay has just started saving enough money and he wants to learn how to invest it in the best possible manner. His friend Amit has agreed to help him. Amit tells Vijay that he invests his money in four broad categories: fixed deposits, equities, equity mutual funds and debt mutual funds. Amit saves Rs. 40,000 every year and deposits all of it across these four categories on 1st April of every year. He started investing in 2004 with equal amounts in the four categories, but since then, the break-up of his deposits across these four categories has differed. However, he ensures that 50% of his yearly savings go into equities and equity mutual funds and the remaining 50% in the other 2 categories.

Also, Amit maintains a data table recording the total amount he has in each of these four categories as on 1st April of every year (table given below). It is also known that the interest rates on fixed deposits have been decreasing: they were 10%, 9% and 8% per annum in the years 2004-05, 2005-06, and 2006-07 respectively. Amit also remembers that the percentage returns on equities in 2006-07 were five times the percentage returns on debt mutual funds in the same year and the percentage returns on equity mutual funds in 2004-05 and 2005-06 were half of the percentage returns on equities in 2005-06 and 2006-07 respectively. Amit does not remember too many details besides that.

Q. What were the percentage returns on equities in the year 2004-05?

Solution:

The answer to the above question tells us that the returns on equity mutual funds were 25% in 2005-06 and so we can find the amount deposited in equity funds in that year, which is 12000.

The amount deposited in equities that year is 8000 and from that, we can find the returns

on equities in that year, as 38800 = 22000 x [1 + ( Percentage returns / 100)] + 8000

∴ Percentage returns = (30800 / 22000 - 1) x 100 = 40%

Percentage returns on equity funds in 2004-05 = half of 40% = 20%

∴ Amount deposited in equity funds on 1st April, 2005 - 23000 - (10000 x 1.2)

=11000

The amount deposited in equities that year is 9000.

∴ Percentage returns on equities =

[22000 - 9000/10000 - 1] x 100 = 30%

*Answer can only contain numeric values

QUESTION: 50

Vijay has just started saving enough money and he wants to learn how to invest it in the best possible manner. His friend Amit has agreed to help him. Amit tells Vijay that he invests his money in four broad categories: fixed deposits, equities, equity mutual funds and debt mutual funds. Amit saves Rs. 40,000 every year and deposits all of it across these four categories on 1st April of every year. He started investing in 2004 with equal amounts in the four categories, but since then, the break-up of his deposits across these four categories has differed. However, he ensures that 50% of his yearly savings go into equities and equity mutual funds and the remaining 50% in the other 2 categories.

Q. What were the percentage returns on debt mutual funds in the year 2005-06?

Solution:

The interest rate on FDs was 9% in 2005-06, so the amount deposited in FDs that year = 28210 - (19000 x 1.09) = 7500 The amount deposited in debt funds that year is 12500.

∴ The percentage returns on debt funds that year = (38596 - 12500 / 23300 - 1) x 100 = 12%

*Answer can only contain numeric values

QUESTION: 51

Group Question

Answer the following question based on the information given below.

CBI confiscated 10 properties of fugitive Don Mohammed Iqbal and put them for auction. Only four brave people who had originally worked for the Indian Army could muster the courage to appear for the auction. The authorities had decided a reserve price (R.P) for each of the properties and any bid below the R.P was discarded. The R.P. of the ten properties were set at Rs. 5,00,000, Rs. 5,00,000, Rs. 5,50,000, Rs. 5,50,000, Rs. 10,00,000, Rs. 15,00,000, Rs. 15,00,000, Rs. 25,00,000, Rs. 1,00,00,000 and Rs. 1,50,00,000. The bid prices (B.P) placed were Rs. 5,00,000, Rs. 6.00,000, Rs. 6,00,000, Rs. 6,50,000, Rs. 10,00,000, Rs. 12,00,000, Rs. 18,00,000, Rs. 30,00,000, Rs. 1,50,00,000 and Rs. 2,00,00,000 in any order. Any property that could not attract a B.P. atleast equal to the R.P. was left unsold. Further, the following information is given :

1. Only two properties remained unsold while exactly two were sold at the lowest possible cost. Two properties were sold at a twice the R.P. both of which were bought by Brigadier Dilip. No property was sold for more than twice the R.P.

2. Major Amar and Naik Birajdar both bought 2 properties each. All of them bought at least 1 property each.

3. Both the properties with R.P. Rs. 5,50,000 have a difference of Rs.50,000 between their R.P. and B.P.

4. The property with B.P. Rs. 1,50,00,000 was the only one bought by Lieutenant Chaudhry.

5. Total amount spent by Naik Birajdar is Rs. 28 lakhs.

6. The reserve price of both the properties bought by Major Amar is same.

7. No property with R.P. Rs. 5 lakh was sold for Rs. 5 lakh.

Answer the following questions based on the information given above.

Q.The total amount spent by Brigadier Dilip in lakhs is:

Solution:

From (1) and (7), properties having R.R 10 lakhs and 150 lakhs were sold at their respective R.R From (5), Naik Birajdar has to buy his maximum two properties with B.R Rs.10 lakhs and Rs.18 lakhs. Thus, the property with R.R Rs.10 lakhs is bought by Naik Birajdar.

From (4), the property with R.R Rs.150 lakhs is bought by Lieutenant Chaudhry. Now, from (1) properties with R.P. Rs.15 lakhs and Rs.100 lakhs are sold at Rs.30 lakh and Rs.200 lakh respectively. Both of these properties are bought by Brigadier Dilip.

From (4), the two properties with R.R Rs.5.5 lakh have B.R of Rs.5 lakh or Rs.6 lakh. Since no properties with B.P. < R.P. are sold, one property with R.P. 5.5L is left unsold.

Thus, from (6) Major Amar buys his two properties with R.P. Rs.5 lakhs at Rs.6 and 6.5 lakhs.

Now, the only sold property remaining is the one with R.P. 15 lakhs. This has to be bought by Brigadier Dilip.

Thus, one of the property with R.P. 15 lakhs is the second property which is left unsold.

The inferences can be summarised below in the given table,

Hence, the amount spent by Brigadier Dilip = 200 + 30 + 6 = Rs. 236 lakhs.

*Answer can only contain numeric values

QUESTION: 52

CBI confiscated 10 properties of fugitive Don Mohammed Iqbal and put them for auction. Only four brave people who had originally worked for the Indian Army could muster the courage to appear for the auction. The authorities had decided a reserve price (R.P) for each of the properties and any bid below the R.P was discarded. The R.P. of the ten properties were set at Rs. 5,00,000, Rs. 5,00,000, Rs. 5,50,000, Rs. 5,50,000, Rs. 10,00,000, Rs. 15,00,000, Rs. 15,00,000, Rs. 25,00,000, Rs. 1,00,00,000 and Rs. 1,50,00,000. The bid prices (B.P) placed were Rs. 5,00,000, Rs. 6.00,000, Rs. 6,00,000, Rs. 6,50,000, Rs. 10,00,000, Rs. 12,00,000, Rs. 18,00,000, Rs. 30,00,000, Rs. 1,50,00,000 and Rs. 2,00,00,000 in any order. Any property that could not attract a B.P. atleast equal to the R.P. was left unsold. Further, the following information is given :

1. Only two properties remained unsold while exactly two were sold at the lowest possible cost. Two properties were sold at a twice the R.P. both of which were bought by Brigadier Dilip. No property was sold for more than twice the R.P.

2. Major Amar and Naik Birajdar both bought 2 properties each. All of them bought at least 1 property each.

3. Both the properties with R.P. Rs. 5,50,000 have a difference of Rs.50,000 between their R.P. and B.P.

4. The property with B.P. Rs. 1,50,00,000 was the only one bought by Lieutenant Chaudhry.

5. Total amount spent by Naik Birajdar is Rs. 28 lakhs.

6. The reserve price of both the properties bought by Major Amar is same.

7. No property with R.P. Rs. 5 lakh was sold for Rs. 5 lakh.

Answer the following questions based on the information given above.

Q. What is the total reserve price, in Rupees, of properties that remain unsold?

Solution:

From the solution to the previous question, The total reserve price of unsold property = Rs. 25,00,000 + 5,50,000 = Rs. 3050000.

*Answer can only contain numeric values

QUESTION: 53

CBI confiscated 10 properties of fugitive Don Mohammed Iqbal and put them for auction. Only four brave people who had originally worked for the Indian Army could muster the courage to appear for the auction. The authorities had decided a reserve price (R.P) for each of the properties and any bid below the R.P was discarded. The R.P. of the ten properties were set at Rs. 5,00,000, Rs. 5,00,000, Rs. 5,50,000, Rs. 5,50,000, Rs. 10,00,000, Rs. 15,00,000, Rs. 15,00,000, Rs. 25,00,000, Rs. 1,00,00,000 and Rs. 1,50,00,000. The bid prices (B.P) placed were Rs. 5,00,000, Rs. 6.00,000, Rs. 6,00,000, Rs. 6,50,000, Rs. 10,00,000, Rs. 12,00,000, Rs. 18,00,000, Rs. 30,00,000, Rs. 1,50,00,000 and Rs. 2,00,00,000 in any order. Any property that could not attract a B.P. atleast equal to the R.P. was left unsold. Further, the following information is given :

1. Only two properties remained unsold while exactly two were sold at the lowest possible cost. Two properties were sold at a twice the R.P. both of which were bought by Brigadier Dilip. No property was sold for more than twice the R.P.

2. Major Amar and Naik Birajdar both bought 2 properties each. All of them bought at least 1 property each.

3. Both the properties with R.P. Rs. 5,50,000 have a difference of Rs.50,000 between their R.P. and B.P.

4. The property with B.P. Rs. 1,50,00,000 was the only one bought by Lieutenant Chaudhry.

5. Total amount spent by Naik Birajdar is Rs. 28 lakhs.

6. The reserve price of both the properties bought by Major Amar is same.

7. No property with R.P. Rs. 5 lakh was sold for Rs. 5 lakh.

Answer the following questions based on the information given above.

Q. What price, in lakhs, was the property with reserve price Rs.1,00,00,000 sold for?

Solution:

From the solution to the first questions, Property worth Rs.100 lakh was sold for Rs.200 lakh.

*Answer can only contain numeric values

QUESTION: 54

4. The property with B.P. Rs. 1,50,00,000 was the only one bought by Lieutenant Chaudhry.

5. Total amount spent by Naik Birajdar is Rs. 28 lakhs.

6. The reserve price of both the properties bought by Major Amar is same.

7. No property with R.P. Rs. 5 lakh was sold for Rs. 5 lakh.

Answer the following questions based on the information given above.

Q. At what price, in Rupees, was the property with reserve price Rs. 5,50,000 sold for?

Solution:

From the solution to the first question, The property with R.P. Rs. 5.5 lakh was sold for Rs. 600000 Answer: 600000

QUESTION: 55

Group Question

Answer the following question based on the information given below.

Six bands - Pink Floyd, Led Zeppelin, Iron Maiden, Megadeth, Rolling Stones and Black Sabbath - are in the running for the "All Time Greatest Rock Act". The bands are given chart positions in 3 countries - USA, UK and Australia - on the basis of decreasing order of record sales in the respective countries. No two bands got the same chart position and no band got the same chart position in any two countries. The following additional information is also known about the chart positions:

I. The band that had the highest chart position in USA, had the lowest chart position in Australia.

II. Some of the chart positions (in the 3 countries put together) of no two bands is the same.

III. The sum of the chart positions of Pink Floyd is 14 and that of Black Sabbath is 7.

IV. Pink Floyd got a better chart position than Black Sabbath in the UK.

V. Led Zeppelin got a better chart position than Rolling Stones in Australia.

VI. In each of the 3 countries, the record sales of Iron Maiden, Rolling Stones and Pink Floyd, respectively, are in the descending order.

Q. Who got the third chart position in USA?

Solution:

From III it can be seen that the chart positions of Pink Floyd and Black Sabbath are (3, 5, 6) and (1,2, 4) respectively.

From IV and the above deduction, it can be observed that Pink Floyd got the 3rd chart position and Black Sabbath got the 4th in the UK.

From I it is evident that Black Sabbath cannot get the highest chart position in USA and Pink Floyd cannot get the lowest in Australia.

Hence, the chart positions of Pink Floyd and Black Sabbath in (USA, Australia) are (6, 5) and (2, 1) respectively.

From VI and the above results, Iron Maiden and Rolling Stones got the 1st and 2nd chart positions respectively in UK. Also, none of them got the last position in any country. As Led Zeppelin had a better chart position than the Rolling Stones in Australia, they cannot have the last position in Australia. Therefore, Megadeth has the sixth position in Australia, first in USA and fifth in UK. Therefore, Led Zeppelin got the sixth position in the UK.

Since no two bands got the same chart position and no band got the same chart position in any two countries, therefore the Rolling Stones can either be ranked 3 or 4 in Australia. From V and VI, the Rolling Stones have to be ranked 4, since two bands have a lower rank than it (Led Zeppelin and Iron Maiden), and Black Sabbath is already ranked 1.

Using the same reasoning, we can also conclude that the Rolling Stones are ranked 5 in the USA. Hence, their sum is 11.

Now, Led Zeppelin could either be ranked 3 or 4 in the USA, and 2 or 3 in Australia. If it is 3 in the USA, then it will be ranked 2 in Australia. In such a case, its sum will be 11, which defies II. So, Led Zeppelin is ranked 4 while Iron Maiden is ranked 3 in the USA. Hence, in Australia, Iron Maiden's rank is 2 and that of Led Zeppelin's is 3.

Thus, the above table can be filled. Iron Maiden held the third in the chart position in USA. Hence, option 3.

QUESTION: 56

Six bands - Pink Floyd, Led Zeppelin, Iron Maiden, Megadeth, Rolling Stones and Black Sabbath - are in the running for the "All Time Greatest Rock Act". The bands are given chart positions in 3 countries - USA, UK and Australia - on the basis of decreasing order of record sales in the respective countries. No two bands got the same chart position and no band got the same chart position in any two countries. The following additional information is also known about the chart positions:

I. The band that had the highest chart position in USA, had the lowest chart position in Australia.

II. Sum of the chart positions (in the 3 countries put together) of no two bands is the same.

III. The sum of the chart positions of Pink Floyd is 14 and that of Black Sabbath is 7.

IV. Pink Floyd got a better chart position than Black Sabbath in the UK.

V. Led Zeppelin got a better chart position than Rolling Stones in Australia.

VI. In each of the 3 countries, the record sales of Iron Maiden, Rolling Stones and Pink Floyd, respectively, are in the descending order.

Q. Which band has the worst average chart position in UK and Australia put together?

Solution:

Megadeth has an average chart position of 5.5 in the countries mentioned.Hence, option 4.

QUESTION: 57

Six bands - Pink Floyd, Led Zeppelin, Iron Maiden, Megadeth, Rolling Stones and Black Sabbath - are in the running for the "All Time Greatest Rock Act". The bands are given chart positions in 3 countries - USA, UK and Australia - on the basis of decreasing order of record sales in the respective countries. No two bands got the same chart position and no band got the same chart position in any two countries. The following additional information is also known about the chart positions:

I. The band that had the highest chart position in USA, had the lowest chart position in Australia.

II. Sum of the chart positions (in the 3 countries put together) of no two bands is the same.

III. The sum of the chart positions of Pink Floyd is 14 and that of Black Sabbath is 7.

IV. Pink Floyd got a better chart position than Black Sabbath in the UK.

V. Led Zeppelin got a better chart position than Rolling Stones in Australia.

VI. In each of the 3 countries, the record sales of Iron Maiden, Rolling Stones and Pink Floyd, respectively, are in the descending order.

Q. The bands are given FINAL chart positions in the increasing order of their total of the chart positions of all the countries put together. Suppose the record sales data from USA is not available - how many FINAL chart positions will now be different from when all three countries are taken into account?

Solution:

Pink Floyd and Megadeth, originally last and fourth respectively, swap positions when the USA chart positions are not taken into account.Hence, option 3.

QUESTION: 58

Six bands - Pink Floyd, Led Zeppelin, Iron Maiden, Megadeth, Rolling Stones and Black Sabbath - are in the running for the "All Time Greatest Rock Act". The bands are given chart positions in 3 countries - USA, UK and Australia - on the basis of decreasing order of record sales in the respective countries. No two bands got the same chart position and no band got the same chart position in any two countries. The following additional information is also known about the chart positions:

I. The band that had the highest chart position in USA, had the lowest chart position in Australia.

II. Sum of the chart positions (in the 3 countries put together) of no two bands is the same.

III. The sum of the chart positions of Pink Floyd is 14 and that of Black Sabbath is 7.

IV. Pink Floyd got a better chart position than Black Sabbath in the UK.

V. Led Zeppelin got a better chart position than Rolling Stones in Australia.

VI. In each of the 3 countries, the record sales of Iron Maiden, Rolling Stones and Pink Floyd, respectively, are in the descending order.

Q. Which band has the highest total record sales in all the countries put together?

Solution:

No information on the number of records sold is available. Hence, the question cannot be answered. Hence, option 4.

QUESTION: 59

Group Question

Answer the following question based on the information given below.

A, B, C, D and E are five students appearing in an examination in which 10 marks are allotted for each question. A student can score a maximum of 100 marks in the examination. There are 9 questions in the examination of 10 marks each and the score of the student in these is called his Base score. The base score when added to the average of the 9 questions is called the Total score of a student. The data below pertains to the performance of each student out of 90 marks.

1. D scored more marks than B.

2. The least base score is 90% and base marks scored by three students are consecutive integers.

3. The average of the least and the highest base scores is same as the mean.

4. A did not score the least base marks.

5. C's base score is in the multiples of three and has less base marks than B and more than A.

6. The average of the base marks is 84 which is also the median.

Q. What is the difference between the total marks of the students who scored highest and second lowest marks respectively?* *

Solution:

From (2) the least base score is 81 From (3) the highest base score is 87 and one of the base scores is 84 which is the median Also, from (2) the other two base scores are 83 and 85 So, the second lowest total score = 83 + 83/9 And the highest total score = 87 + 87/9 Thus the required difference = 4 + 4/9 Hence, option 4.

QUESTION: 60

A, B, C, D and E are five students appearing in an examination in which 10 marks are allotted for each question. A student can score a maximum of 100 marks in the examination. There are 9 questions in the examination of 10 marks each and the score of the student in these is called his Base score. The base score when added to the average of the 9 questions is called the Total score of a student. The data below pertains to the performance of each student out of 90 marks.

1. D scored more marks than B.

2. The least base score is 90% and base marks scored by three students are consecutive integers.

3. The average of the least and the highest base scores is same as the mean.

4. A did not score the least base marks.

5. C's base score is in the multiples of three and has less base marks than B and more than A.

6. The average of the base marks is 84 which is also the median.

Q. What can be the minimum number of questions in which C gets full marks?

Solution:

From the solution to the previous question the scores are 81, 83, 84, 85 and 87 in increasing order From (5) C has scored 84 marks.

If C scores 10 marks in all questions then he gets 90 marks. We reduce 1 marks from as many questions as we can. We can reduce it from 6 questions to get a score of 84. Hence, full marks in atleast 3 questions are still needed to reach the score of 84.

Hence, option 2.

QUESTION: 61

A, B, C, D and E are five students appearing in an examination in which 10 marks are allotted for each question. A student can score a maximum of 100 marks in the examination. There are 9 questions in the examination of 10 marks each and the score of the student in these is called his Base score. The base score when added to the average of the 9 questions is called the Total score of a student. The data below pertains to the performance of each student out of 90 marks.

1. D scored more marks than B.

2. The least base score is 90% and base marks scored by three students are consecutive integers.

3. The average of the least and the highest base scores is same as the mean.

4. A did not score the least base marks.

5. C's base score is in the multiples of three and has less base marks than B and more than A.

6. The average of the base marks is 84 which is also the median.

Q. What can be the least marks awarded in one question amongst all students?

Solution:

To get the least marks in one question the student must score the maximum marks in the remaining others.

From the solution to the first question of the set, we can see that the least marks for each student are 7, 5, 4, 3 and 1. Among them 1 is the lowest.

Hence, option 2.

QUESTION: 62

A, B, C, D and E are five students appearing in an examination in which 10 marks are allotted for each question. A student can score a maximum of 100 marks in the examination. There are 9 questions in the examination of 10 marks each and the score of the student in these is called his Base score. The base score when added to the average of the 9 questions is called the Total score of a student. The data below pertains to the performance of each student out of 90 marks.

1. D scored more marks than B.

2. The least base score is 90% and base marks scored by three students are consecutive integers.

3. The average of the least and the highest base scores is same as the mean.

4. A did not score the least base marks.

5. C's base score is in the multiples of three and has less base marks than B and more than A.

6. The average of the base marks is 84 which is also the median.

Q. Find the student whose percentage increase/decrease in the marks was least compared to the marks out of 90?

Solution:

Let the total marks out of 90 for a student be x. The total marks out of 100 = x + (x/9) .-.The percentage increase = [(x/9)/xj x 100 = (100/9)% So, there will be an increase of (100/9)% irrespective of their individual marks. The percentage increase/decrease in the marks remains the same for all students.

Hence, option 4.

QUESTION: 63

Group Question

Answer the following question based on the information given below.

Four men - Aaron, Brad, Dennis & Ethan and six women - Brianna, Brinda, Carla, Catelyn, Emily, Shae team up to form five teams of two members each. Each team has to choose fo ur different subjects out of - Chemistry, Biology, Physics, Mathematics and Statistics. The teams are formed according to the following rules:

i. Shae teamed up with Brad choosing Mathematics, Biology and Physics while Carla teamed up with Brinda.

ii. Dennis and Emily have exactly three subjects in common while Brianna does not have Biology as one of her subjects.

iii. No man teams up with another man and no two teams have all subjects common.

iv. Emily and Aaron did not choose Chemistry and Physics respectively as one of their subjects.

Q. Which team has Chemistry, Mathematics, Physics and Statistics as their subjects?

Solution:

When we say that a person did not choose one subject, this implies that he has chosen all the other four subjects. Also, as one team skips a subject the other four teams have to choose the skipped subject.

Thus, a subject has to be selected by four out of the five teams. From clues (i) & (iii) we get the following table,

From (ii) we can say that Emily has not teamed with Dennis and from (iii) she is not teamed with Aaron as he has chosen Chemistry.

Thus, Emily is teamed with Ethan and their subjects are Mathematics, Biology, Physics and Statistics.

From (ii), Brianna not choosing Biology implies that Brianna will go with Dennis and they do not choose biology.

Hence, Carla-Brinda pair have not chosen Mathematics.

Thus, the final table will be,

From the table we can see that Dennis-Brianna will have the subjects mentioned in the question. Hence, option 3.

QUESTION: 64

Four men - Aaron, Brad, Dennis & Ethan and six women - Brianna, Brinda, Carla, Catelyn, Emily, Shae team up to form five teams of two members each. Each team has to choose four different subjects out of - Chemistry, Biology, Physics, Mathematics and Statistics. The teams are formed according to the following rules:

i. Shae teamed up with Brad choosing Mathematics, Biology and Physics while Carla teamed up with Brinda.

ii. Dennis and Emily have exactly three subjects in common while Brianna does not have Biology as one of her subjects.

iii. No man teams up with another man and no two teams have all subjects common.

iv. Emily and Aaron did not choose Chemistry and Physics respectively as one of their subjects.

Q. Who teams up with Brianna?

Solution:

From the solution to the first question of the set we can see that Dennis is the team mate of Brianna.Hence, option 4.

QUESTION: 65

Four men - Aaron, Brad, Dennis & Ethan and six women - Brianna, Brinda, Carla, Catelyn, Emily, Shae team up to form five teams of two members each. Each team has to choose fo ur different subjects out of - Chemistry, Biology, Physics, Mathematics and Statistics. The teams are formed according to the following rules:

i. Shae teamed up with Brad choosing Mathematics, Biology and Physics while Carla teamed up with Brinda.

ii. Dennis and Emily have exactly three subjects in common while Brianna does not have Biology as one of her subjects.

iii. No man teams up with another man and no two teams have all subjects common.

iv. Emily and Aaron did not choose Chemistry and Physics respectively as one of their subjects.

Q. Which subjects have Carla-Brinda selected?

Solution:

From the solution to the first question of the set we can see that Carla-Brinda have selected Chemistry, Physics, Biology, Statistics as their subjects.Hence, option 1.

QUESTION: 66

Four men - Aaron, Brad, Dennis & Ethan and six women - Brianna, Brinda, Carla, Catelyn, Emily, Shae team up to form five teams of two members each. Each team has to choose fo ur different subjects out of - Chemistry, Biology, Physics, Mathematics and Statistics. The teams are formed according to the following rules:

iii. No man teams up with another man and no two teams have all subjects common.

iv. Emily and Aaron did not choose Chemistry and Physics respectively as one of their subjects.

Q. If Shae and Emily exchange partners but the new partners refuse to change their subjects then the new subjects of Sahe are :

Solution:

From the solution to the first question of the set we can see that the new team-mate of Shae will be Ethan and thus from the table we can see that Shae’s subjects would be Physics, Statistics, Mathematics and Biology. Hence, option 4.

QUESTION: 67

Image of point (-2, 2) about a line L is (4, 8). What will be the image of point (0,1) about L?

Solution:

Let the required point be (h, k).

Line joining (-2, 2) and (4, 8) is parallel to the line joining (0, 1) and its reflection.

Therefore, slopes of the lines are equal. 1 = (k - 1)/h.

So k - h = 1 .

Only option 1 satisfies the criteria. Hence, option 1.

QUESTION: 68

Consider the two equations x^{2} + Px + 2 = 0 and x^{2} + 2x + P = 0. Find the sum of the all possible values of P for which the equations have atleast one common real root.

Solution:

Subtracting the two equations, the following equation is obtained, (P - 2)x + (2 - P) = 0

⇒(P - 2)(x - 1) = 0 = > (P -2 ) = 0 or (x - 1) = 0 => P = 2 or x = 1

Case 1: P = 2

(P - 2)(x - 1) = 0 = > (P - 2 ) = 0 or (x - 1) = 0 => P = 2 or x = 1

Case 2: x = 1

Substituting x = 1, in any of the equations, we get P = -3 Required sum = -3 Hence, option 4.

QUESTION: 69

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

Solution:

L.C.M. of 6, 9, 15 and 18 is 90.

Let required number be 90k + 4, which is multiple of 7.

Least value of k for which (90k + 4) is divisible by 7 is k = 4.

∴ Required number = (90 x 4) + 4 = 364.

*Answer can only contain numeric values

QUESTION: 70

The average age of Akbar and Birbal is 25. If Chintamani were to replace Akbar, the average age would be 22, and if Chintamani were to replace Birbal, then the average age would be 21. Find the sum of Akbar's age multiplied by 2, Birbal's age multiplied by 3 and Chintamani's age multiplied by 4.

Solution:

Let the ages of Akbar, Birbal and Chintamani be a, b and c years respectively.

a + b = 25 x 2 = 50....(i)

b + c = 22 x 2 = 44 ...(ii)

a + c = 21 x 2 = 42 ...(iii)

Adding (i), (ii) and (iii), we get

2(a + b + c) = 136

So (a + b + c) = 68

Subtracting (i), (ii) or (iii) from this will give us c, a or b respectively,

a = 24, b = 26 and c = 18

2a + 3b + 4c = 48 + 78 + 72 = 198

QUESTION: 71

The average age in the Marketing department of a company is 35. If 4 employees with an average age of 30 join while 3 employees with an average age of 42 leave the company then which of the following statements is true?

Solution:

The change in the total age of the department after 3 employees leave and 4 employees join = -(3 x 42) + (4 x 30) = -6 The total age decreases, while the number of employees increases. Therefore, the average age will decrease.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 72

If a_{0}, a_{1}, a_{2}...... ,a_{m} is the sequence of numbers such that a_{0} = 41, a_{1} = 84, a_{m} = 0 and a_{k+1 = }a_{k-1} - 4/a_{k } for k = 1, 2, 3......,m - 1, then what is the value of m?

Solution:

For 0 < k < m, we have, a_{k} x a_{k+ 1} = a_{k} x a_{k-1}- 4.

Clearly the product a_{k} x a_{k+ 1} is monotonically decreasing, and it decreases by 4 when k increases by 1.

For k = 0, a_{k} x a_{k+ 1} = 41 x 84

When k = 41 x 84/4 = 41 x 21 = 861,a_{k} x a_{k+ 1} will be zero for the first time, which means m = k + 1 = 861 + 1 = 862

QUESTION: 73

If the numbers (4X + 17) and (7X + 33) are not co-prime then, which of the following is the common factor? (X is a natural number)

Solution:

Let the common factor be denoted by f. Both (4X + 17) and (7X + 33) are divisible by f. 4(7X + 33) and 7(4X +17) are also divisible by f. 4(7X + 33) - 7(4X + 17) will also be divisible by f.

4(7X + 33) - 7(4X + 17) = 132 - 119 = 13

13 is divisible by f.

f= 1 or 13

4X + 17 and 7X + 33 are not coprime, f = 13 Hence, option 2.

*Answer can only contain numeric values

QUESTION: 74

Arun was asked to divide 1469 by a certain number. However, instead of 1469, Arun divided 1677 by that number. As a result, the quotient turned out to be 16 more than the correct answer. What was the quotient obtained by Arun? (Assume no remainder in both the cases).

Solution:

Let the quotient obtained by Arun be x.

The correct quotient is x - 16.

Let the divisor be y.

We have xy = 1677 and (x - 16)y = 1469.

On solving the above equations, we get,

x= 129

*Answer can only contain numeric values

QUESTION: 75

Four years ago, the ratio between Rakesh’s age and Sunil’s age is 8/9. The ratio of their individual ages four years ago and today are 4/5 and 9/11 respectively. At present, their total age is 42. Find the present age of Rakesh.

Solution:

Let R_{I} and Rp be the age four years ago and present year age of Rakesh respectively. Let S_{I} and Sp be the age four years ago and present year age of Sunil respectively.

R_{l }/ S_{l} = 8/9 ...(i)

R_{l} / R_{P} = 4/5 ...(ii)

S_{l} / S_{P} = 9/11 ...(iii)

Dividing (i) by (ii), we get,

R_{l }/ S_{l }x R_{p} / R_{l} = 8/9 x 5/4

R_{p }/ S_{l } = 10/9 ...(iv)

Multiplying (iv) and (iii), we get,

R_{p }/ S_{l }x S_{l} / S_{p} = 10/9 x 9/11

R_{p }/ Sp = 10/11

∴ Present age of Rakesh = 42 x 10 / 21 = 20 years

*Answer can only contain numeric values

QUESTION: 76

A function f(x), defined for real numbers, satisfies the following properties. f(1) = 1, f(x + 4) > f(x) + 4 for all real numbers x. f(y + 1) < f(y) + 1 for all real numbers y. If g(x) = f(x) + 1 - x, then what is the value of g(2008)?

Solution:

f(x) + 4 < f(x + 4) < f(x + 3) + 1 <f( x+2 ) + 2 < f { x + 1) + 3 < f(x ) + 4

We can see that the equality holds for all x. f { x + 1) = f(x) + 1

. g(2008) = f(2008) + 1 - 2008 = f(2007) + 1 - 2007 = ... = f(1) + 1 - 1 = 1

g(2008) = 1

QUESTION: 77

Sharmaji purchases 5 horses and 10 cows for Rs. 1,00,000. He sells the horses at 15% profit and cows at 10% loss. Thus, he gets Rs. 3,750 as profit. Find the cost of a horse and a cow.

Solution:

Let x be the cost of a horse and y be the cost of a cow.

5x +10y = 100000

⇒x + 2y= 20000 ... (i)

The selling price of a horse = 1.15x

The selling price of a cow = 0.9y

⇒5.75x + 9y = 103750

⇒23x + 36y=415000 ... (ii)

Multiplying equation (i) by 23, we get,

23x + 46y= 460000 ... (iii)

Subtracting equation (ii) from equation (iii), we get, 10y= 45000

y = 4500

x = 20000 - 2 x 4500 = 11000

Hence, option 4.

*Answer can only contain numeric values

QUESTION: 78

Four buffaloes are tied at four corners of a square field of side 14 m in such a way that any of them can just reach only two other buffaloes. Calculate the area (in sq.m) that remains ungrazed.

Solution:

The buffaloes are able to graze over a circular sector of the field centered at the corner to which they are tied.

Therefore, the ungrazed portion of the field looks like the shaded portion in the figure. The area of the shaded portion = Area of the square - Area of the four quarter circles = 14^{2} - π(14/2)^{2} = 196 - (22/7) x 7 x 7 = 42 m^{2}

QUESTION: 79

a + b + c / 6 = a + 3b / 8 = 2a + b + c / 9 = k

What is the value of 45a + 72b + 18c / 31 ?

Solution:

By theorem on equal ratios,

4a + 5b + 2c / 23 = a + 3b / 8 = k ...(i)

Again by theorem on equal ratios, from (i),

5a + 8b +2c / 31 = k

∴ 45a + 72b + 18c / 31 = 9(5a + 8b + 2c / 31)

= 9 x k = 9k

*Answer can only contain numeric values

QUESTION: 80

A man wished to dig a well for irrigating his fields. On the first day, he dug two meters and on next day with the help of five workers, he dug eight meters. On the third day with three additional men, he dug 12 meters. On the fourth day, with 3 additional men, he dug 16 meters. On the fifth day, with the help of 3 more men he dug 20 meters and so on. He took 25 days to completely finish digging the well. How deep would the well have been at the end of the 25th day?

Solution:

Let D is the depth of the well.

D = 2 + 8 + 12 + 16 + 20 + .... + t_{n}

Let S = 8 + 12 + 16 + 20 + ... + t_{n}

where n = 24

∴ S = n / 2 [2a + (n - 1)d]

Substituting a = 8, d = 4 and n = 24

S = 1296

D = 2 + S = 2 + 1296 = 1298 meters

QUESTION: 81

A solid cylinder of radius 4 cm and height 16/3 cm is melted into 1000 identical solid spheres. Find the radius of the spheres in cm.

Solution:

Let the radius of the sphere be ‘r’ cm

The volume of cylinder = π x 4 x 4 x 16/3

So 4/3 x π x r^{3} x 1000 = π x 4 x 4 x 16/3

r = 4/10= 0.4.

Hence Option 2

QUESTION: 82

Let A and V be respectively the total surface area and volume of a sphere of radius R. If A/π and V/π are both 3 digit integers, how many possible values of R exist?

Solution:

We know that, for a sphere, A = 4πR^{2} and V = 4/3πR^{3}. Thus, A/π = 4R^{2} and V/π = 4R^{3}/3. The possible values of R giving A/π = 3 digit integer are R = 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 and 15.

The possible values of R giving V/π = 3 digit integer are R = 6 and 9.

The only common values of R satisfying both these conditions are R = 6 and R = 9, for which A/π = 144 and V/π = 972.

Hence, option 2.

QUESTION: 83

Let α and β be the roots of the quadratic equation x^{2} - (p - 2)x + p - 6 = 0. What is the minimum possible value of α^{2 }+ β^{2}?

Solution:

α^{2 }+ β^{2 }= (α + β )^{2} - 2αβ

From given equation, α + β = p - 2 and αβ = p - 6

Substituting values in equation (i), we get,

α^{2 }+ β^{2} = p^{2} + 4 - 4p - 2(p - 6)

= p^{2} + 4 - 4p - 2p + 12

= p^{2} - 6p + 9 + 7

= (p - 3)^{2} + 7

Minimum value of α^{2 }+ β^{2} will be obtained by putting (p - 3) = 0

Minimum value = 7

Hence, option 4.

QUESTION: 84

If |x| < 10 and |y| < 11, what is the minimum value of the expression 4x^{4} - 4x^{2}y + 4x^{2} + y^{2} - 2y + 3?

Solution:

4x^{4} - 4x^{2}y + 4x^{2} + y^{2} - 2y + 3 = [(2x^{2})^{2} - 2(2x^{2})y) + y^{2}] + 2(2x^{2} - y) + 3

= (2x^{2} - y)^{2} + 2(2x^{2} - y) + 3

= (2x^{2} - y)^{2} + 2(2x^{2} - y) + 1] + 2

= (2x^{2} - y + 1)^{2} + 2

The minimum value of (2x^{2} - y + 1)^{2}

∴ The minimum value of the expression 4x^{4} - 4x^{2}y + 4x^{2} + y^{2} - 2y + 3 = 2

QUESTION: 85

What value can the expression 1^{3} + 2^{3} + 3^{3} + ....n^{3}, not attain where n is a natural number?

Solution:

1^{3} + 2^{3} + 3^{3} + ....n^{3} = n^{2} (n + 1)^{2} / 2^{2}

the value of 1^{3} + 2^{3} + ...n^{3} has to be a perfect square for all values of n.

784 = 28^{2}

1296 = 36^{2}

2025 = 45^{2}

6084 = 78^{2}

Hence, option 4.

**Alternatively,**

Substituting the value of n as 7, 8, 9 and 12 in (i) we get 784, 1296, 2025 and 6084.

Hence, option 4.

QUESTION: 86

How many sets of the form S* _{i}* = {

Solution:

A set of any 8 numbers will contain 8 or its multiple.

A set of 7 numbers will not contain 8 or its multiple if and only if the smallest number in the set is one more than any multiple of 8. The smallest such value of (/ - 3) is 1.

Thereafter, (/ - 3) can take values 9, 17, 25, 33, 41,49, 57, 65, 73, 81, 89 and 97 ( as /__<__ 100, / - 3 __<__ 97).

There are 13 such sets.

Hence, option 2.

Note: For / = 1, / = 2 and / = 3, we get the element 'O' in the set which is also an integral multiple because any number multiplied to the integer zero gives result as zero.

QUESTION: 87

Anita, Babita and Kavita start running from the same point and in the same direction at speeds of 45 km/hr, 60 km/hr and 90 km/hr respectively. Babita starts two hours after Anita. If Babita and Kavita overtake Anita at the same instant, how many hours after Anita did Kavita start?

Solution:

Anita has travelled 90 km when Babita starts. Babita overtakes Anita in 90/(60 - 45) = 6 hrs

In this time, Babita travels 6 x 60 = 360 km from the starting point. Kavita overtakes Anita at the same point.

Kavita takes 360/90 = 4 hrs to reach there.

Anita takes 360/45 = 8 hrs to reach there.

Kavita starts 8 - 4 = 4 hrs after Anita.

Hence, option 3.

QUESTION: 88

If 3x + 4y = 12, x > 0 and y > 0 then what is the maximum value of x^{2}y^{3 }?

Solution:

3x + 4y = 12

∴ 3x/2 + 3x/2 + 4y/3 + 4y/3 + 4y/3 = 12

The product 3x/2 x 3x/2 x 4y/3 x 4y/3 x 4y/3 will be maximum if 3x/2 = 4y/3 = 12/5

∴ The maximum value of 3x/2 x 3x/2 x 4y/3 x 4y/3 x 4y/3 = (12/5)^{5}

∴ The maximum value of (3/2)^{2} x (4/3)^{3} x x^{2} x y^{3} = (12/5)^{5}

∴ The maximum value of x^{2}y^{3} =

12^{5} / 5^{5} x 3^{3} / 4^{3} x 2^{2} / 3^{2} = 6 x (6 / 5)^{5}

*Answer can only contain numeric values

QUESTION: 89

A triangle is rotated about an axis which coincides with one of its sides. If the sides of triangle are 7 cm, 24 cm and 25 cm, then what is the maximum possible volume(in cm^{3}) that is generated in space by rotating the triangle?

Solution:

7, 24 and 25 is a Pythagorean triplet.When a triangle is rotated about one of its perpendicular sides then a cone is formed in space.

Volume of a cone = 1 / 3 πr^{2}h

To maximize this volume we need to maximize r^{2}. So if the cone is rotated about the 7 cm side, we will get r as 24. This would give the maximum volume.

Volume of a cone = 1 / 3 π(24^{2})(7) = 4224

*Answer can only contain numeric values

QUESTION: 90

An Arab millionaire wants to cross Sahara desert. He has a few gold coins with him. He wants to distribute the coins in 6 villages such that the village people will allow him to cross the village boundary without any harm. He also wants to keep some coins with him for food and water. He keeps one coin with him (for food and water) and gives 1/5th of the remaining coins to the first village people, again keeps 1 coin with him (for food and water) and distributes 1/5th of the remaining coins to the second village people and he does the same in the third village. He distributes the remaining coins in the next three villages in ratio 23 : 46 : 55 (without keeping any coins for him in these villages). What is the minimum number of coins the Arab should have to cross the Sahara desert?

Note - It is given that the Arab will keep the gold coins with him that he separated out for food and water and these coins are not counted in any of the further distributions.

Solution:

He distributes the coins in the last three villages in ratio 23 : 46 : 55.

The last three villages get 23x, 46x, 55x.

The least value that x can take is 1 .... [ GCD (23, 46, 55) = 1]

The minimum number of coins that can be distributed in the last three villages = 23 + 46 + 55 = 124.

Just before he distributes the coin to the last three villages he has given 1/5th of the remaining coins to the third village.

He had (5/4) x 124 = 155 coins and he had kept 1 coin with him. Number of coins with him after he gives coins to the second village is** 156**.

Just before he distributes the coin to the second village, he had (5/4 x 156) = 195 coins and he had kept 1 coin with him.

Number of coins with him after he gives coins to the first village is **196.**

Similarly, number of coins with the Arab initially is (5/ 4 x 196) + 1 = **246**

QUESTION: 91

Consider the quadratic equation x(x - 1) / c(c - 1) + (x - 1)(x - c) / c + x(x - c) / (1 - c) = 1 / c(c - 1). How many real roots does this equation have? (The value of c = 1 + √5 / 2)

Solution:

Multiplying both sides of the equation by **c(c - 1),** we get,

x(x - 1) + (c - 1 )(x - 1 )(x - c) - cx(x - c) = 1

[x^{2} - x] + [(c - 1 )(x^{2} - cx - x + c)] - [cx^{2} - c^{2}x] = 1

x^{2} - x + cx^{2} - C^{2}x - Cx + C^{2} - x^{2} + Cx + x - c - cx^{2} + C^{2} x = 1

**c ^{2} - c = 1**

All the terms in x and x

QUESTION: 92

A car is moving on a circular track of radius r metres. Its average speed (in metres/minute) is πr during the first 30 seconds, πr/2 during next one minute, πr/4 during next 2 minutes, πr/8 during next 4 minutes, and so on. What is the time taken by the car to complete the 10th round?

Solution:

Solution: Let πr = x.

The circumference of the circular path = 2x.

The car covers 2x metres in one round.

The time taken to complete each round is given in the table below:

Thus, we see that the ratio of time taken for the 2nd round to that for the 1st round = 16.

Similarly, ratio of time taken for the 3rd round to that for the 2nd round = 16 and so on.

Time taken to complete the 10th round will be (16^{9} x 7.5) minutes.

Hence, option 1.

*Answer can only contain numeric values

QUESTION: 93

An ant moves along a path on the XY plane such that every point (x, y) on the path satisfies the condition max (|x|, |y|) = 3. What is the area enclosed by this path?

Solution:

(x, y) satisfies max (|x|, |y|) = 3 The path along which the ant moves is |x| = 3 or |y| = 3 or |x| = |y| = 3

An ant moves along the sides of the square as shown below.

The area enclosed by the path = 6 * 6 = 36 square unit

QUESTION: 94

A shop has two electronic items TV and Radio. The cost price of a TV and selling price of a Radio is same. In both the transactions, profit earned is Rs. 60. If discount percentage offered in both cases is the same, which value might represent the ratio of Marked Price of TV to Radio?

Solution:

C.P. of TV = x

S.P. of Radio = x

As profit = Rs. 60

S.P. of TV = Rs. (x + 60)

C.P. of Radio = Rs. (x - 60)

Discount percentage =

MP_{TV} - (x + 60) / MP_{TV} = MP_{Radio} - x / MP_{Radio}

MP_{TV} / MP_{Radio} = x + 60 / x

As N > D, the fraction is greater than 1 it will take values greater than 1.

Hence, option 1.

QUESTION: 95

A solid spherical ball of radius 3 units has a hole of diameter 0.5 units and depth 6 units along the diameter of the ball. It is kept over a cylinder of diameter 6 units and height 12 units such that half of the ball is inside the cylinder. The axis of the hole is perpendicular to the mouth of the cylinder. What is the approximate volume of water that can be filled through the hole without overflowing?

Solution:

Volume of the water that can be filled without overflowing = Volume of cylinder - Volume of hemisphere + volume of cylindrical hole. As the diameter of the cylindrical hole is small, the curvature can be neglected.

Hence assuming the hole to be a cylinder with radius 0.25 units and height 6 units.

Volume of water that can be filled

= (π x 3^{2} x 12) - (2 / 3 x π x 3^{3}) + [π x (0.25)^{2} x 6]

90.375π cu. units.

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 96

If 0 ∈ [0, 2π) then how many real, positive solution sets {x, θ} exist for the following equation?

4 - 4sin^{2} θ = [x^{2} + 1 / x]^{2}

Solution:

4 - 4sin^{2} θ = [x^{2} + 1 / x]^{2}

∴ 4(1 - sin^{2} θ = [x^{2} + 1 / x]^{2}

∴ ± 2 cos θ = [x^{2} + 1 / x]^{2} ...(i)

x^{2} ± 2 x cos θ + 1 = 0.

As x is real, the discriminant of this equation is non-negative. 4cos^{2}θ - 4 > 0⇒ cos^{2}θ > 1 (as cosθ cannot be greater than 1)

⇒ cos θ = ± 1

∴ ± 2 = x^{2} + 1 / x

∴ x = 1 or -1

x = 1 or -1 Since x is only positive, x = 1 The equation has two solutions i.e. {x, θ} = {1, 0} and {x, θ} = {1, π} in the given range.

QUESTION: 97

A company spends Rs. 29,400 for a certain amount of work as daily wages, proportional to the work done by a particular worker. If Ram is hired, the total money gets over in 21 days. If Shyam is hired the total money gets over in 28 days. If both of them are hired, for how long does the money last?

Solution:

Solution: Let the daily wages of Ram and Shyam be Rs. a and Rs. b respectively. Then, 29400 = 21 a = 28b.

Let the money lasts for n days if both of them are hired.

29400 = n(a + b)

∴ 29400 = n(29400 / 21 + 29400 / 28)

n = 12 Hence, option 2.

QUESTION: 98

If log_{15} 5 = x, what is the value of log_{15} 243 in terms of x?

Solution:

log_{15} 5 + log_{15} 3 = log_{15} 15 = 1

∴ log_{15} 3 = 1 - log_{15} 5

= 1 - x

log_{15} 243 = log_{15} (3^{5})

= 5 log_{15} 3

= 5(1 - x)

= 5 - 5x

QUESTION: 99

A shopkeeper has 100 kg of wheat flour which he sells in packets of 5 kg at cost price. Every time after selling one packet, he adds an equal amount of husk to the leftover flour. What percentage profit does the shopkeeper earn on the packet sold to the 4th customer?

Solution:

When the shopkeeper sells for the 4th time, he has replaced flour by husk 3 times.

∴ wheat left =

100 x (1 - 5 / 100)^{3} = 95^{3} / 100^{2} %

If the cost price per kg is Re.1, then in the 4th transaction,

95^{3} / 100^{2} % flour is sold at 100% cost

The percentage profit in the 4th transaction

= 100 - 95^{3} / 100^{2} / 95^{3} / 100^{2} = 16.67%

*Answer can only contain numeric values

QUESTION: 100

If a, b and c are the roots of x^{3} - 6x^{2} + 11x - 6 = 0 then, find the value of [(4 - a)(4 - b)(4 - c)].

Solution:

If a, b, c are the roots of x^{3} - 6x^{2} + 11x - 6 = 0 means that,

(x - a)(x - b)(x - c) = x^{3} - 6x^{2} + 11x - 6 ..(i)

substituting x = 4 in (i), we get,

(4 - a)(4 - b)(4 - c) = 4^{3} - 6 x 4^{2} + 11 x 4 - 6 = 6

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