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This mock test of CAT Mock Test - 10 for CAT helps you for every CAT entrance exam.
This contains 100 Multiple Choice Questions for CAT CAT Mock Test - 10 (mcq) to study with solutions a complete question bank.
The solved questions answers in this CAT Mock Test - 10 quiz give you a good mix of easy questions and tough questions. CAT
students definitely take this CAT Mock Test - 10 exercise for a better result in the exam. You can find other CAT Mock Test - 10 extra questions,
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QUESTION: 1

Group Question

Answer the questions based on the passage given below.

Scientists recently declared that the evidence is compelling enough to say that humanity’s impact on the Earth’s atmosphere, oceans and wildlife has pushed the world into the new epoch.

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. Which of the following is true in regard to UK’s exit from the EU?**

Solution:

The passage does not state either that the EU is more dependent on UK or that the EU will be as impacted as UK will be if the latter leaves the former. This eliminates options 1 and 3. The last paragraph claims that UK's exit would lead to some loss at least for the EU. So, option 4 can be eliminated. The passage provides sufficient information to prove UK’s dependency on the EU. Option 2 is therefore the right option.

Hence, the correct answer is option 2.

QUESTION: 2

Scientists recently declared that the evidence is compelling enough to say that humanity’s impact on the Earth’s atmosphere, oceans and wildlife has pushed the world into the new epoch.

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. Paragraph 1 talks about 'humanity’s impact in pushing the word in a new era'. Which word best describes this time period?**

Solution:

The time period during which human activity has been the dominant influence in changing the climate and the environment is known as ‘Anthropocene’. (The student can also use elimination technique to answer this question. ‘Anthropo’ means ‘human’ and is used in the formation of compound words.) Hence, the correct answer is option 2.

QUESTION: 3

Scientists recently declared that the evidence is compelling enough to say that humanity’s impact on the Earth’s atmosphere, oceans and wildlife has pushed the world into the new epoch.

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. What is the primary purpose of the author?**

Solution:

Options 1,2, and 3 are extreme: the passage doesn't say that the UK is the most environmentally sensitive country; its ecological problems have not yet been solved; it will not collapse if it leaves the EU. None of these points are supported by the passage. The entire passage makes a case for how being a part of the EU has benefited UK.

Hence, the correct answer is option 4.

QUESTION: 4

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. What are the problems that the EU has not helped UK tackle?**

Solution:

It is very clear from the passage that the EU has established legislations and policies to address the issue of biodiversity loss, reduce the carbon footprint, and define standards for energy efficiency. Options 1,2, and 3 are covered here.

Animal health is not discussed in the passage.

Hence, the correct answer is option 4.

QUESTION: 5

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. What could the Tories have done to make the author comment “they talked green but acted blue”?**

**I. They tried to sell off England’s forests.
II. They increased solar subsidies.
III. They scrapped support for wind farm subsidies.
IV. They focused on investing in low-carbon projects.**

Solution:

In the context of the passage, ‘talked green but acted blue’ would mean that the Tories talked about being eco-friendly but weren't. Statements II and IV are eco-friendly actions. So, logically, only I and III can be correct since they would indicate that the Tories were not sticking to their eco-friendly stance.

Hence, the correct answer is option 2.

QUESTION: 6

Britain is a world leader on the environment and has played a pivotal role in the European Union on this issue since 1986, when Margaret Thatcher signed the Single European Act, which established the EU’s competence in this area. Yet the impact that leaving the EU would have on the UK’s environmental standards rarely features in discussions. The evidence so far is clear: families in Britain, rivers, beaches and special places would pay the price if UK voted to leave.

In 1995, under the last Conservative government, the UK was dirty man of Europe. Some 83% of the household waste went to landfill and just 7% was recycled or composted. By 2014, thanks to a series of EU directives, the UK’s recycling rate had reached 45%.

The UK currently recycles 90% of construction materials, well ahead of other countries. The Birds and Habitats Directives enabled bird and carnivore species to recover. The Natura 2000 Directive obliges the UK government to provide protected nature zones. Renewable energy capacity is growing, thanks to national targets set by the EU Renewable Energy Directive. In 2013, 15% of electricity produced in the UK came from renewable sources. Not only is the carbon footprint shrinking, it has created opportunities for renewable energy companies to grow. EU environmental legislation allows the phasing out of inefficient lightbulbs on an EU-wide basis. Also, higher standards on new car efficiency help lower fuel costs. Such strong regulations allow monitoring of environmental standards and tracking deviations. All this progress is at risk if the UK votes to leave. Anyone who thinks the environment will be better off if UK left the EU should take a long hard look at the Tory record.

The Tories have talked green but acted blue.

The Chinese and Indian governments have invited the European commission to help them to clean up their water and air. The EU now has global expertise in the environment. The evidence is clear. The EU has more influence globally with the UK as a member. And as a member, UK has more influence globally. UK’s voice in the Paris climate change talks was amplified because it is a part of a club of 28 countries. Leaving would mean implementing EU environment law without a seat at the table and a vote in decisions. When the UK can lead from the inside, why would it walk away? Ensuring the UK has a cleaner, greener future relies on the EU membership. Anyone who argues otherwise will be on the wrong side of history.

**Q. The tone of the author can best be said to be ______.**

Solution:

The author gives details on how the environment in UK has changed for the better because of the policies and standards set by the EU and makes a case for why it shouldn’t exit the EU. So the author can be said to be ‘concerned’. ‘Sarcastic’ and ‘controversial’ are negative tones and are thus unwarranted.

The author does not adopt a pessimistic approach towards the future; he only feels that on the basis of past evidence, the UK should stay in the EU.

Hence, the correct answer is option 1.

QUESTION: 7

Group Question

Answer the questions based on the passage given below.

The US Treasury Department recently announced that it would start demanding details of the shell companies that rich foreigners use to buy real estate in Manhattan and Miami-Dade County. This is a good step that should help law enforcement agencies crack down on money laundering, tax evasion and other crimes. The program should be broadened to cover the whole country, and must be forcefully carried out.

In recent years, there have been certain sections of people that have stashed billions of dollars of wealth in the United States by buying property and other costly assets. These purchases are generally made through limited liability corporations that are not required to disclose their wealthy owners or beneficiaries. While limited liability corporations have many legitimate purposes, there is no justification for allowing owners to shield their identities even from law enforcement and regulators. The secrecy is so complete that law enforcement officials say they are often unable to identify the true owners. All efforts by lawmakers have been thwarted by lobbying from the financial and real estate industries and state governments.

The department currently requires mortgage lenders to know the identities of the true owners of shell companies in transactions that involve loans. Under the new policy, the department’s Financial Crimes Enforcement Network will require details of limited liability companies that buy properties without loans. However, the order applies only to Manhattan and Miami-Dade County, and will be effective for only 180 days, starting in March.

The department should also adopt pending regulations that would require financial firms to know who owns the limited liability companies whose accounts they manage. It is absurd that regulators would not require such basic transparency as a matter of course. The current system practically lays out the welcome mat for some foreigners hiding assets from their governments, making United States one of the world’s biggest tax havens.

Supporters of the current system may argue that requiring more transparency would burden financial institutions without ending money laundering and tax evasion, since determined criminals will find ways to thwart the law. But that doesn’t justify doing nothing about this hole in financial regulations.

**Q. From the context, a ‘shell company’ can be inferred to be:**

Solution:

From the first sentence of the paragraph, it can be inferred that a shell company is used by some foreigners for the ulterior motive of buying real estate. Though the first part of option 1 is true, the purpose of a shell company does not seem to be to raise loans according to the paragraph. Option 2 is also not true as foreigners don't stash money in the company per se; they use it to buy assets in which they stash their money. There is no information in the paragraph that warrants 4.

Hence, the correct answer is option 3.

QUESTION: 8

The US Treasury Department recently announced that it would start demanding details of the shell companies that rich foreigners use to buy real estate in Manhattan and Miami-Dade County. This is a good step that should help law enforcement agencies crack down on money laundering, tax evasion and other crimes. The program should be broadened to cover the whole country, and must be forcefully carried out.

In recent years, there have been certain sections of people that have stashed billions of dollars of wealth in the United States by buying property and other costly assets. These purchases are generally made through limited liability corporations that are not required to disclose their wealthy owners or beneficiaries. While limited liability corporations have many legitimate purposes, there is no justification for allowing owners to shield their identities even from law enforcement and regulators. The secrecy is so complete that law enforcement officials say they are often unable to identify the true owners. All efforts by lawmakers have been thwarted by lobbying from the financial and real estate industries and state governments.

The department currently requires mortgage lenders to know the identities of the true owners of shell companies in transactions that involve loans. Under the new policy, the department’s Financial Crimes Enforcement Network will require details of limited liability companies that buy properties without loans. However, the order applies only to Manhattan and Miami-Dade County, and will be effective for only 180 days, starting in March.

The department should also adopt pending regulations that would require financial firms to know who owns the limited liability companies whose accounts they manage. It is absurd that regulators would not require such basic transparency as a matter of course. The current system practically lays out the welcome mat for some foreigners hiding assets from their governments, making United States one of the world’s biggest tax havens.

Supporters of the current system may argue that requiring more transparency would burden financial institutions without ending money laundering and tax evasion, since determined criminals will find ways to thwart the law. But that doesn’t justify doing nothing about this hole in financial regulations.

**Q. What is the primary purpose of the author?**

**A. To emphasize the importance of identity disclosure in business transactions
B. To educate us on the ill effects of money laundering and tax evasion
C. To highlight the efforts being taken by the US government to control money laundering
D. To show why the US is the biggest tax haven**

Solution:

The passage primarily discusses how the existence of unknown identities in business transactions leads to money laundering and tax evasion, along with the initiatives being taken by the US Treasury Department to control it. Statements A and C are justified.

The author does not discuss the ill effects of money laundering and tax evasion at all. Statement B is not one of the author's primary purposes.

Even though at various points in the passage there are instances to support what has made the US the biggest tax haven of the world, this is not the primary purpose of the author. Statement D is incorrect.

Hence, the correct answer is option 2.

QUESTION: 9

The US Treasury Department recently announced that it would start demanding details of the shell companies that rich foreigners use to buy real estate in Manhattan and Miami-Dade County. This is a good step that should help law enforcement agencies crack down on money laundering, tax evasion and other crimes. The program should be broadened to cover the whole country, and must be forcefully carried out.

In recent years, there have been certain sections of people that have stashed billions of dollars of wealth in the United States by buying property and other costly assets. These purchases are generally made through limited liability corporations that are not required to disclose their wealthy owners or beneficiaries. While limited liability corporations have many legitimate purposes, there is no justification for allowing owners to shield their identities even from law enforcement and regulators. The secrecy is so complete that law enforcement officials say they are often unable to identify the true owners. All efforts by lawmakers have been thwarted by lobbying from the financial and real estate industries and state governments.

The department currently requires mortgage lenders to know the identities of the true owners of shell companies in transactions that involve loans. Under the new policy, the department’s Financial Crimes Enforcement Network will require details of limited liability companies that buy properties without loans. However, the order applies only to Manhattan and Miami-Dade County, and will be effective for only 180 days, starting in March.

The department should also adopt pending regulations that would require financial firms to know who owns the limited liability companies whose accounts they manage. It is absurd that regulators would not require such basic transparency as a matter of course. The current system practically lays out the welcome mat for some foreigners hiding assets from their governments, making United States one of the world’s biggest tax havens.

Supporters of the current system may argue that requiring more transparency would burden financial institutions without ending money laundering and tax evasion, since determined criminals will find ways to thwart the law. But that doesn’t justify doing nothing about this hole in financial regulations.

**Q. Paragraph 2 talks about sections of people who have invested in various assets in the US for tax evasion. In the context of this passage, choose the group of people who are most likely to partake in this overall activity.**

Solution:

Paragraph 2 discusses how certain sections of people have done money laundering for billions of dollars and used it to buy expensive assets in the US. There is no information in the passage regarding the role of spiritual leaders and teachers. Options 2 and 4 can therefore be eliminated.

Even though the passage describes the role of business owners in tax evasion, it has no information to support if the owners are typically monopolists. Option 3 can also be ruled out.

The passage discusses how lobbying by the government weakens the lawmakers' efforts and allows business owners to mobilise their black money by investing in assets. This clearly justifies option 1.

Hence, the correct answer is option 1.

QUESTION: 10

Group Question

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

Pierre Boulez was the last survivor of the generation of composers who defined the European Avant-garde after World War II. Through his activities as a conductor and musical educator, his influence on musical life on both sides of the Atlantic has been incalculable. In the 1950s and early 60s, his activities as a fierce polemicist railing against the musical establishment and its traditions, dismissing opera as an outmoded art form, went hand in hand with his greatest productivity as a composer. Boulez’s ever-increasing activities as a conductor from the 1960s onwards coincided with a distinct falling off in his activities as a composer. Though the sonic world he created acquired a whole dimension with the use of techniques developed at the Paris research institute he founded, at the behest of the French government his new work suffered and tended to appear less frequently. Whether interpreting the music of the past had become a welcome surrogate for his dwindling creativity, or merely took up too much of the time he had previously spent

composing, is hard to say. But the story of the second half of Boulez’s career as a composer will remain a tantalising litany of unrealised projects.

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

Like everything he conducted, it was the precision of his performances that was so revealing, and which illuminated a range of 20th-century music in a way that few conductors before him had ever approached. And while a handful of Boulez’s own works will endure, it is his achievement as a conductor and educator in moving the music of our time and of the immediate past into the mainstream that is likely to be his legacy.

**Q. What role did Boulez not play in his life?**

Solution:

The passage clearly says that Boulez played the role of a polemicist (one who practises disputation or controversy), an educator (teacher), and a conductor of music (maestro). Therefore, options 1,2, and 3 can be eliminated. ‘Trooper’ means a ‘state police officer’ and makes for an absurd option.

Hence, the correct answer is option 4.

QUESTION: 11

Pierre Boulez was the last survivor of the generation of composers who defined the European Avant-garde after World War II. Through his activities as a conductor and musical educator, his influence on musical life on both sides of the Atlantic has been incalculable. In the 1950s and early 60s, his activities as a fierce polemicist railing against the musical establishment and its traditions, dismissing opera as an outmoded art form, went hand in hand with his greatest productivity as a composer. Boulez’s ever-increasing activities as a conductor from the 1960s onwards coincided with a distinct falling off in his activities as a composer. Though the sonic world he created acquired a whole dimension with the use of techniques developed at the Paris research institute he founded, at the behest of the French government his new work suffered and tended to appear less frequently. Whether interpreting the music of the past had become a welcome surrogate for his dwindling creativity, or merely took up too much of the time he had previously spent

composing, is hard to say. But the story of the second half of Boulez’s career as a composer will remain a tantalising litany of unrealised projects.

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

Like everything he conducted, it was the precision of his performances that was so revealing, and which illuminated a range of 20th-century music in a way that few conductors before him had ever approached. And while a handful of Boulez’s own works will endure, it is his achievement as a conductor and educator in moving the music of our time and of the immediate past into the mainstream that is likely to be his legacy.

**Q. What is the primary purpose of the author?**

Solution:

The passage does not throw light on why Boulez was successful as a conductor and unsuccessful as a composer (in the later parts of his life). The author speculates about the latter, but is not sure. So, option 1 can be eliminated. A eulogy is high praise or recommendation, but this passage discusses Boulez's unsuccessful attempts at composing too. So, it is not a eulogy. Also, the author is not remembering specific works of Boulez. Thus, option 3 can be eliminated. The passage mainly focuses on Boulez's career, not his personality. The latter is being talked about in just one or two sentences; it cannot be described as the primary purpose of the author. So, option 4 should also be eliminated.

The passage largely focuses on the impact Boulez has had on music. The first few and last few sentences of the paragraph clearly indicate the intention of the author.

Hence, the correct answer is option 2.

QUESTION: 12

Pierre Boulez was the last survivor of the generation of composers who defined the European Avant-garde after World War II. Through his activities as a conductor and musical educator, his influence on musical life on both sides of the Atlantic has been incalculable. In the 1950s and early 60s, his activities as a fierce polemicist railing against the musical establishment and its traditions, dismissing opera as an outmoded art form, went hand in hand with his greatest productivity as a composer. Boulez’s ever-increasing activities as a conductor from the 1960s onwards coincided with a distinct falling off in his activities as a composer. Though the sonic world he created acquired a whole dimension with the use of techniques developed at the Paris research institute he founded, at the behest of the French government his new work suffered and tended to appear less frequently. Whether interpreting the music of the past had become a welcome surrogate for his dwindling creativity, or merely took up too much of the time he had previously spent

composing, is hard to say. But the story of the second half of Boulez’s career as a composer will remain a tantalising litany of unrealised projects.

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

Like everything he conducted, it was the precision of his performances that was so revealing, and which illuminated a range of 20th-century music in a way that few conductors before him had ever approached. And while a handful of Boulez’s own works will endure, it is his achievement as a conductor and educator in moving the music of our time and of the immediate past into the mainstream that is likely to be his legacy.

**Q. The term 'supermarket music' was used by Boulez to describe music that**

Solution:

In the passage, Boulez clearly says that supermarket music is the kind that will be soon forgotten. So, option 2, which says that the music will sell well, can be eliminated immediately.

Option 1 takes the term too literally: Boulez was talking about a supermarket aesthetic to music, not music that is literally made for supermarkets.

Out of the remaining options, 4 is again extremely literal. Only 3 gives a logical reason for use of the term 'supermarket'.

Hence, the correct answer is option 3.

QUESTION: 13

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

**Q. The author mentions a question he wanted to ask Boulez. What is that question most likely to be?**

Solution:

It is at the end of the second paragraph that the author mentions that a question came to his mind. The previous sentence "... it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy" clearly gives the context for that question. This sentence relates to only option 4 out of the given options.

Hence, the correct answer is option 4.

QUESTION: 14

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

**Q. What word describes Boulez's conducting?**

Solution:

The passage doesn't state that Boulez's conducting inspired others.

We know from the passage that it wasn't ineffectual (inadequate or futile).

The last paragraph says that few conductors had illuminated a range of twentieth century music like he did. This means that some conductors certainly had managed to achieve the same results in the past. So, Boulez's conducting was not unprecedented (without previous instance/unparalleled).

None of the options appropriately describes Boulez's conducting.

Hence, the correct answer is option 4.

QUESTION: 15

It took a long time in public perception for the uncompromising radical to morph into the hugely revered figure later. When I first met him in the mid-1970s, some of that forbidding earlier aura remained, but his warmth and humour were immediately disarming. As he mellowed further, he also began to conduct music by a number of composers he would surely have dismissed out of hand in his early years. That inevitably required some quiet revisionism. However, he never kept himself from giving out candid statements. Looking at the music scenario in the 80’s Boulez said "If you want a kind of supermarket aesthetic, do that, nobody will be against it, but everybody will eventually forget it because each generation will create its own supermarket music”. The last time we met, in 2011, it was a surprise to hear him enthuse about the works of the Polish composer Szymanowski and to hear him claim that it was music he had admired since he first heard it as a schoolboy in 1942. It got me thinking of a question I wasn’t sure I should ask him.

**Q. What has been cited as the possible reason for Boulez’s downfall as a composer?**

Solution:

The last few sentences of the first paragraph point towards only option 1 as the answer: “Whether interpreting the music of the past... or merely took up too much of the time he had previously spent composing ... second half of Boulez’s career as a composer will remain a tantalising litany of unrealised projects.” The other options are not supported by the passage.

Hence, the correct answer is option 1.

QUESTION: 16

Group Question

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

"I think of Ceres actually as a game changer in the Solar System," said Britney Schmidt in 2013, science team liaison for the Dawn Mission. "Ceres is arguably the only one of its kind. Ceres is like the gatekeeper to the history of water in the middle solar system." "Ceres is a 'planet' that you've probably never heard of,” said Robert Mase, Dawn project manager at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California. Ceres, the largest body between Mars and Jupiter in the main asteroid belt, has a diameter of about 590 miles (950 kilometers). Some scientists believe the dwarf planet harbored a subsurface ocean in the past and liquid water may still be lurking under its icy mantle.

Ceres is a unique body in the Solar System, bearing many similarities to Jupiter's moon Europa and Saturn's moon Enceladus, both considered to be potential sources for harboring life. In March of 2015, NASA's Dawn mission will arrive at the dwarf planet Ceres, the first of the smaller class of planets to be discovered and the closest to Earth.

When Ceres was discovered in 1801, astronomers first classified it as a planet. The massive body traveled between Mars and Jupiter, where scientists had mathematically predicted a planet should lie. Further observations revealed that a number of small bodies littered the region, and Ceres was downgraded to just another asteroid within the asteroid belt. It wasn't until Pluto was classified as a dwarf planet in 2006 that Ceres was upgraded to the same level.

Ceres is the most massive body in the asteroid belt, and larger than some of the icy moons scientists consider ideal for hosting life. It is twice the size of Enceladus, Saturn's geyser-spouting moon that may hide liquid water beneath its surface.

Unlike other asteroids, the Texas-sized Ceres has a perfectly rounded shape that hints toward its origins. As NASA's Dawn mission draws closer to its encounter with the dwarf planet Ceres in early 2015, excitement continues to mount for scientists looking forward to what the satellite might observe.

**Q. According to the passage, which of the following is not true about Ceres?**

Solution:

Option 1 is validated from “In March of 2015, NASA's Dawn mission will arrive at the dwarf planet Ceres” Option 2 misquotes the passage which states “Some scientists believe the dwarf planet harbored a subsurface ocean in the past and liquid water may still be lurking under its icy mantle.”

Option 3 is validated by “Ceres is a unique body in the Solar System, bearing many similarities to Jupiter's moon Europa and Saturn's moon Enceladus”

Option 4 is validated by “The massive body traveled between Mars and Jupiter, where scientists had mathematically predicted a planet should lie ... and Ceres was downgraded to just another asteroid ... It wasn't until Pluto was classified as a dwarf planet in 2006 that Ceres was upgraded to the same level.” Hence, the correct answer is option 2.

QUESTION: 17

"I think of Ceres actually as a game changer in the Solar System," said Britney Schmidt in 2013, science team liaison for the Dawn Mission. "Ceres is arguably the only one of its kind. Ceres is like the gatekeeper to the history of water in the middle solar system." "Ceres is a 'planet' that you've probably never heard of,” said Robert Mase, Dawn project manager at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California. Ceres, the largest body between Mars and Jupiter in the main asteroid belt, has a diameter of about 590 miles (950 kilometers). Some scientists believe the dwarf planet harbored a subsurface ocean in the past and liquid water may still be lurking under its icy mantle.

Ceres is a unique body in the Solar System, bearing many similarities to Jupiter's moon Europa and Saturn's moon Enceladus, both considered to be potential sources for harboring life. In March of 2015, NASA's Dawn mission will arrive at the dwarf planet Ceres, the first of the smaller class of planets to be discovered and the closest to Earth.

When Ceres was discovered in 1801, astronomers first classified it as a planet. The massive body traveled between Mars and Jupiter, where scientists had mathematically predicted a planet should lie. Further observations revealed that a number of small bodies littered the region, and Ceres was downgraded to just another asteroid within the asteroid belt. It wasn't until Pluto was classified as a dwarf planet in 2006 that Ceres was upgraded to the same level.

Ceres is the most massive body in the asteroid belt, and larger than some of the icy moons scientists consider ideal for hosting life. It is twice the size of Enceladus, Saturn's geyser-spouting moon that may hide liquid water beneath its surface.

Unlike other asteroids, the Texas-sized Ceres has a perfectly rounded shape that hints toward its origins. As NASA's Dawn mission draws closer to its encounter with the dwarf planet Ceres in early 2015, excitement continues to mount for scientists looking forward to what the satellite might observe.

**Q. Ceres is considered a game changer in the Solar System because...**

Solution:

A “game changer” refers to some significant event. Except option 3, none of the other options is apt. The passage talks about Ceres possibly having had water and having the potential of sustaining life. If NASA finds more support for this, it would mean that there could be life on another planet and not just Earth. This would definitely be a game-changer. Hence, the correct answer is option 3.

QUESTION: 18

"I think of Ceres actually as a game changer in the Solar System," said Britney Schmidt in 2013, science team liaison for the Dawn Mission. "Ceres is arguably the only one of its kind. Ceres is like the gatekeeper to the history of water in the middle solar system." "Ceres is a 'planet' that you've probably never heard of,” said Robert Mase, Dawn project manager at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California. Ceres, the largest body between Mars and Jupiter in the main asteroid belt, has a diameter of about 590 miles (950 kilometers). Some scientists believe the dwarf planet harbored a subsurface ocean in the past and liquid water may still be lurking under its icy mantle.

Ceres is a unique body in the Solar System, bearing many similarities to Jupiter's moon Europa and Saturn's moon Enceladus, both considered to be potential sources for harboring life. In March of 2015, NASA's Dawn mission will arrive at the dwarf planet Ceres, the first of the smaller class of planets to be discovered and the closest to Earth.

When Ceres was discovered in 1801, astronomers first classified it as a planet. The massive body traveled between Mars and Jupiter, where scientists had mathematically predicted a planet should lie. Further observations revealed that a number of small bodies littered the region, and Ceres was downgraded to just another asteroid within the asteroid belt. It wasn't until Pluto was classified as a dwarf planet in 2006 that Ceres was upgraded to the same level.

Ceres is the most massive body in the asteroid belt, and larger than some of the icy moons scientists consider ideal for hosting life. It is twice the size of Enceladus, Saturn's geyser-spouting moon that may hide liquid water beneath its surface.

Unlike other asteroids, the Texas-sized Ceres has a perfectly rounded shape that hints toward its origins. As NASA's Dawn mission draws closer to its encounter with the dwarf planet Ceres in early 2015, excitement continues to mount for scientists looking forward to what the satellite might observe.

**Q. “Ceres is a 'planet' that you've probably never heard o f implies that...**

Solution:

The word planet is mentioned in single quotation marks which implies that Ceres was not known as a planet until recently. The passage goes on to say that it was given the status of a dwarf planet only in 2006. Option 1 is a fact about Enceladus. Option 2 is contrary to what the passage is stating. Ceres was considered an asteroid but is not anymore; option 3 can be eliminated.

Option 4 is the only apt option, since it explains why it is possible that not many people know of Ceres as a planet.

Hence, the correct answer is option 4.

QUESTION: 19

Group Question

Answer the questions based on the passage given below.

Sugata Mitra did an odd experiment. He placed a PC inside a wall behind a plastic shield in a New Dehli slum. Connected to the internet, with a mouse to manipulate it, Mitra simply powered it up and left it behind. “I left it to the wolves, knowing that it would be smashed, opened up and and sold,” Mitra says. “I left it, just to see what would happen.”

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. According to the passage, which of these is true about “Schools in the cloud”?**

Solution:

The passage states that the schools in the cloud encourage self-learning by providing encouragement to the children when they need it. Students can learn exploring by themselves, thus letting learning happen in a more organic way. Option 1 and option 2 are not accurate as per the passage. In fact, Mitra states that for the time being the schools in the cloud concept can be piloted to help students learn English. Only time would tell if options 1 and 2 will be a reality.

Option 3 is clearly apt from the passage - “The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud.” Option 4 with “better on assessments” is inaccurate.

Hence, the correct answer is option 3.

QUESTION: 20

Sugata Mitra did an odd experiment. He placed a PC inside a wall behind a plastic shield in a New Dehli slum. Connected to the internet, with a mouse to manipulate it, Mitra simply powered it up and left it behind. “I left it to the wolves, knowing that it would be smashed, opened up and and sold,” Mitra says. “I left it, just to see what would happen.”

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. The Hole in the Wall experiment made Mitra realize that:**

Solution:

The author states that it was the Hole in the Wall experiment that made Mitra recognize the concept of selflearning. This means that although he probably knew selflearning as a concept, he saw it for real in the experiment. This supports option 3.

Option 1 is contrary to what the passage states.

Option 2 is incorrect; the Hole in the Wall experiment showed that self-learning exists and need not happen only in dire situations as seen in the case of the schools in the cloud.

Option 4 is incorrect. Although 21^{st }century academia may be more conventional, we cannot say on the basis of the passage that it totally ignores self-learning.

Hence, the correct answer is option 3.

QUESTION: 21

Sugata Mitra did an odd experiment. He placed a PC inside a wall behind a plastic shield in a New Dehli slum. Connected to the internet, with a mouse to manipulate it, Mitra simply powered it up and left it behind. “I left it to the wolves, knowing that it would be smashed, opened up and and sold,” Mitra says. “I left it, just to see what would happen.”

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. What was Sugata Mitra expecting out of his odd experiment?**

Solution:

The first paragraph states that Mitra "... left it (the computer) to the wolves, knowing that it would be smashed, opened up and sold ...” This validates option 2.

None of the other options are validated in any way by the information given in the passage.

Hence, the correct answer is option 2.

QUESTION: 22

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. According to Mitra, what is missing in the world?**

Solution:

The last lines of the passage reveal that Mitra is talking about leveling the playing field (to give everyone the same advantages or opportunities). The passage is about education. While current education systems exist (existent learning opportunities), the schools in the cloud would help children learn through self- exploration, experience, and a deeper hands-on understanding (innovation in learning). This validates option 4.

Option 1 takes the “playing field” phrase literally; option 2 with “technology” does not capture the essence of the passage; option 3 is vague with its terms. The passage is more about innovative learning than self-growth.

Hence, the correct answer is option 4.

QUESTION: 23

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. Which of the following would be an example of “brick-and- mortar” learning?**

Solution:

Learning the “brick and mortar” way means to have physically experienced the situation through materials, going to a place, actually performing related activities etc. Option 1 is an apt example of this.

Option 2 focuses on technology; it is not a hands-on experience for the child.

Option 3 is incorrect; brick and mortar learning would not just mean learning in the slums but learning anything in the environment appropriate to that activity.

Option 4 is incorrect. Older women or grannies were used in the schools in the cloud experiment, and this fact from the passage is distorted in option 4.

Hence, the correct answer is option 1.

QUESTION: 24

When Mitra came back after two months he found the kids playing games and browsing the Internet. One kid sauntered up to Mitra and said, “We could use a better mouse and a faster processor.” And there was a small complaint. “You’ve given us a machine that only works in English, so we had to teach ourselves English.”

Via what became known as the Hole in the Wall experiment, Mitra recognized for the first time the concept of self-learning. Mitra spread his concept of self-learning to hundreds of elementary schools across India, then to the United Kingdom, Australia, Hong Kong, Southeast Asia and Latin America.

In England, Mitra recruited an army of retired teachers, all women, whom he dubbed the “granny cloud.” The grannies connected to Mitra’s schools via Skype, and when the kids were assembled in groups of four to six, the grannies asked questions like “Can anything be less than zero?” “Will robots be conscious one day?” and “How do my eyes know to cry when I am sad?” Then they sat back and let the kids do the learning, injecting themselves only to offer the kind of encouragement that only grannies can. What Mitra saw was that the Granny cloud kids’ English improved, their Science scores soared. By most measures they were learning more and more quickly, and doing it mostly on their own.

What Mitra envisions are “schools in the cloud,” classes of 24 students in actual brick-and-mortar spaces managed in person by his volunteer grannies. The grannies ask the questions, offer the encouragement, everything else happens remotely, the lights, heating, and locks are all manipulated via the cloud. For now Mitra envisions that these cloud schools will function as a supplement to the daily education the kids already get - operating on the weekends and before and after school. They’ll offer English language learning initially, he says. “I’ll present it as a safe cyber cafe for children where they can learn good English,” Mitra says. “For now I cannot afford to say that this is a replacement for school.”

But just give him time.

“If it works, then we have an alternative that I can tell you with confidence will level the playing field,” Mitra says. “And leveling the playing field is what’s missing in this world.”

**Q. According to the passage, the Granny Cloud kids’ English/Science improved in the School in the Cloud experiment. This implies:**

Solution:

According to the passage, the teachers facilitated the selflearning of the students. So, if the students improved in their learning, it was because the grannies were facilitating well. The education level and motivation of the grannies may be indicators of good teaching outcomes, but given the passage information which states that the teachers were there to encourage the child only when required, option 1 is validated.

None of the other options can be satisfactorily inferred from the passage.

Hence, the correct answer is option 1.

QUESTION: 25

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 mass extinction of languages is a process that can be resisted and mitigated, though surely not halted completely. The first imperatives are toleration and accommodation: the cessation of active persecution and a serious struggle against linguistic chauvinism and privilege everywhere, starting at home. Where the remaining indigenous languages look to be in terminal decline, as in the United States, Canada, or Australia, the question is how best to bolster the many new Native-led revitalization programs, as some state and provincial governments are starting to do.

Solution:

Option 1 is ruled out since it interprets the paragraph incorrectly and has an extreme tone to it.

Option 3 with “global emergency” presents the paragraph in a different form with the spotlight being shifted to the response of the world nations to this extinction. So, eliminate it.

Option 4 links the terminal decline of indigenous languages in the countries like United States, Canada, or Australia with their participation in the revitalization programs, which has not been mentioned in the passage.

Only option 2 includes the key points of the passage and links them appropriately to come out with a message to its readers.

Hence, the correct answer is option 2.

QUESTION: 26

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 photograph and the words arrive simultaneously. They guarantee each other. You believe the words more because the photograph verifies them, and trust the photograph because you trust the words. Additionally, each puts further pressure on the interpretation: A war photograph can, for example, make a grim situation palatable, just as a story about a scandal can make the politician depicted look pathetic. But images, unlike words, are often presumed to be unbiased. The facticity of a photograph can conceal the craftiness of its content and selection.

Solution:

The passage says that viewers tend to believe in the presentation of a photograph and interpret it as the truth. Words do not make as deep an impact as a photograph on the viewers. The influence of a photograph overshadows the accompanied content which is likely to be avoided by the viewers. This is captured by option 4 and makes for an apt summary.

Option 1 is vague with respect to the central idea of the passage as it talks about the viewer and the presenter which cannot be found explicitly in the passage. So eliminate option 1.

Option 2 tries to explore the relation between the photograph's truth and reality which is not the topic of discussion. So eliminate option 2.

Option 3 talks about what the viewers ought to do while assessing an image and its truthfulness. It tends to represent the perspective of the viewer while the passage talks about the photographs themselves. So eliminate option 3.

Hence, the correct answer is option 4.

QUESTION: 27

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.

For decades, Americans believed that they had the world's healthiest and safest diet. They worried little about this diet's effect on the environment or on the lives of the animals (or even the workers) it relies upon. Nor did they worry about its ability to endure -- that is, its sustainability. That didn't mean all was well. And they've come to recognize that their diet is unhealthful and unsafe. Many food production workers labor in difficult, even deplorable, conditions, and animals are produced as if they were widgets. It would be hard to devise a more wasteful, damaging, unsustainable system.

Solution:

Options 3 and 4 are inconsequential to the main idea of the paragraph as they are imprecisely framed as opposed to a concise summary. So eliminate options 3 and 4.

The passage only talks about Americans and their eating habits. Option 1 with “national and global security” takes the topic to a global level which is unaccounted for in the passage. So eliminate option 1.

Hence, the correct answer is option 2.

*Answer can only contain numeric values

QUESTION: 28

Arrange statements A-E 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. BDCEA.

1. Sometimes, that just meant attending the theatre - frowned upon because of the indecency of the performances, and the audience.

2. But a mask also allowed a lady to flirt outrageously without losing her reputation, and was an indispensable accessory when sneaking off to an assignation.

3. But women soon realised that masks also protected one’s identity, and began to wear them when they were up to no good.

4. Typically made of silk and velvet, masks were first popularised as a means of protecting one’s complexion from the sun - and one’s modesty from the gaze of impertinent men.

5. In short, as soon as people put on masks they begin to violate social norms.

Solution:

The sequence starts with statement 4, which talks about the initial purpose of masks. This is followed by statement 3, which describes women's realization that their identity could be protected using masks, allowing them to behave in a way not approved of by society. This is elaborated upon in statement 1, which talks about a mild way in which women could break society's rules- attending the theatre. Next comes statement 2, which describes more bold behaviour facilitated by the maskflirting and meeting men. The sequence is given closure with statement 5, which summarises the topic by saying that masks allowed people to violate social norms.

Hence, the correct answer is 43125.

*Answer can only contain numeric values

QUESTION: 29

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. The distinct species is diseased and deserves compassion, not censure.

2. Japan has m anga and graphic violence as its most mim icked genre— w hat e lse can release the collective imagination stilled to a scorched shadow on a lost wall?

3. Crime and romance are the easiest to mimic, and have the widest audience, because they fuel the twin human urges of eros and thanatos.

4. America needs to believe in monsters as a distinct species co-existing with normal decent Americans.

5. It is easy to understand the sub-Thomas Harris genre of psychopath thrillers as an American phenomenon.

Solution:

The paragraph details upon how certain genres are mimicked and how it happens in countries like America and Japan. The first sentence puts forth the two most common genres that can be mimicked as they have the widest audience. This makes statement 3 the best choice for beginning the sequence. Statement 3 must be followed by statement 2 as it goes on to give the example of Japan and its most mimicked genres to indicate the popularity of mimicked genres around the world. Then statement 5 goes on to speak about America and its mimicked genre based on the sub-Thomas Harris genre of psychopath thrillers. Statements 4 and 1 then elaborate on why the aforesaid genre is an American phenomenon.

Hence, the sequence is 32541.

*Answer can only contain numeric values

QUESTION: 30

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. In Hughes's case it was certainly delusory.

2. But without question Hughes suffered blows greater than those it is given to most writers to suffer.

3. Hughes’s feeling of not writing enough is common among writers, sometimes even among the most prolific.

4. The posthumous volume of Hughes’s collected poems is over a thousand pages long and there are five volumes of prose and seven volumes of translations.

5. His life had been ruined not just once, but twice.

Solution:

Sentence 3 commences the paragraph by stating the fear of not having written enough that afflicts even prolific writers. It says that even Hughes suffered from it. The next sentence should be 1 as the pronoun "it" here relates to 'the feeling of not writing enough'. Then sentence 4 explains why Hughes's case has been called delusory- as his posthumous volume consisted of a plethora of works which suggests that he had done enough of writing indeed. Sentences 2 and 5 together are trying to make a point that Hughes had had a dismal life as compared to other writers.

Hence, the sequence is 31425.

*Answer can only contain numeric values

QUESTION: 31

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. Middle-class people began to worry that great wealth would bring corruption, while extreme poverty would prevent workers from acting as independent citizens.

2. The word “progressive” came into widespread use in the early 1900s, a moment when many Americans believed democracy was failing.

3. They went in search of a new politics that would enable both the government and the citizenry to rebalance th is distribution of power.

4. At the same time, millions of Americans — many of them immigrants from Eastern and Southern Europe — were huddled in urban tenements and yoked to the factory clock.

5. Over the previous generation, industrial titans like John D. Rockefeller and Andrew Carnegie amassed huge fortunes.

Solution:

Of all the sentences, statement 2 seems to present the topic of discussion which is the volatile situation of American democracy in the early 1990s and how the word “progressive” gained popularity during this time. Statement 5 with “over the previous generation” provides a background for the following discussion on the issue and should follow statement 2. Statements 5 and 4 form a pair as both of them together present a contrasting situation as to how on one hand the rich got wealthier and on the other the needy strove for this wealth. Statement 1 follows logically as it says how this disproportionate wealth distribution is likely to have a negative consequence on the citizens. Statement 3 provides an apt conclusion to the paragraph by saying that the concerned middle-class mentioned in statement 1 went in pursuit of a new politics that may have the capability to solve this issue.

Hence, the correct sequence is 25413.

QUESTION: 32

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.

Solution:

The given set of statements presents a complete scenario in which the protagonist is trying to find a ring and an earring.

Statements 1, 2, 4, and 5 aptly give the development of events as Wille embarks on his quest for the missing ornaments.

Statement 3 talks about the quality of a successful Ring Finder; this is incongruous since there is no actual mention in the other statements of the person who found the ring or the earring.

Hence, the correct answer is 3.

QUESTION: 33

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.

Solution:

The paragraph discusses the work of Garrett Price, a well known writer, and his work called White Boy. Statement 1 makes the most suitable start to the paragraph as it introduces the topic which is "Garrett Price" and his role in writing for a magazine.

Now, most of the sentences talk about a particular work of his called White Boy. Sentence 2 ought to follow sentence 1 as it completes the purpose of the introduction of Garrett Price by highlighting his work. Sentence 3 properly describes White Boy and how it represents Price's flavour. Sentence 4 continues the description by stating that White Boy is based on the mysteries of girls and Indians. Sentence 5 cannot be linked to the sequence as it refutes the argument that Price's interest lies in Indians which lacks prior clarity.

Hence, sentence 5 is the odd one out.

QUESTION: 34

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.

Solution:

The passage delves into the concept of minimalist artwork and how it is different from regular artwork. Sentence 5 begins the paragraph by stating the conventional approach of artists in creating artwork. Sentence 1 gives an example to justify the heterogeneity reflected in the work of artists. Sentence 2 changes the flow by arriving at the core point of the paragraph, and shifting the spotlight onto minimalist art and its simplified presentation. The next sentence should throw some light on the relation between heterogeneity and minimalist artwork. Sentence 3 does so by pointing out how conventional heterogeneity is compromised when it comes to minimalist art. Sentence 4, however, disputes the claim that simplicity is a positive factor abruptly- it is too early to debate on the topic of simplicity diluting art's value before the underlying concept is comprehended.

Hence, the correct answer is sentence 4.

*Answer can only contain numeric values

QUESTION: 35

Group Question

Answer the following question based on the information given below.

Study the given chart carefully and answer the questions.

Additional Information: The total number of graduates produced when compared to the previous year increased every alternate year starting from 2002 (i.e. 2004, 2006 ...) and decreased in the remaining years.

The total number of graduates placed when compared to the previous years decreased every year from 2002.

**Q. What can be the maximum possible number of years from 2003 to 2013 in which the total number of Engineers produced increased over the previous year?**

Solution:

It is given that the total number of graduates placed when compared to the previous years decreased every year from 2002. And further we also have the details of the Engineers placed for each of these years.

From this we can conclude the following:

1. The number of Engineers placed would definitely decrease if the share of the number of engineers placed when compared to total graduates placed decreases.

2. The number of Engineers placed may or may not decrease or increase or remain same, if the share of the Engineers placed increases when compared to the total graduates placed.

The same theory will also be applicable to the number of Engineers produced also but in alternate years.

The maximum possible number of years in which the number of engineers produced increased will be 2004, 2006, 2008, 2010, 2012 and 2013, i.e. a total of 6 years.

Answer: 6

*Answer can only contain numeric values

QUESTION: 36

Study the given chart carefully and answer the questions.

Additional Information: The total number of graduates produced when compared to the previous year increased every alternate year starting from 2002 (i.e. 2004, 2006 ...) and decreased in the remaining years.

The total number of graduates placed when compared to the previous years decreased every year from 2002.

**Q. In which of the following years-2006, 2007, 2008, 2013, could the number of Engineers placed be the same as that of in 2011?**

Solution:

As the total number of graduates placed has decreased every year from 2002, the number of graduates placed in 2011 was the lowest till that point starting from 2002.

As the number of Engineers placed is given as a percentage of graduates placed and as the percentages in 2006 and 2007 are higher than that in 2011, they cannot be the same as that in 2011.

In 2008, as the percentage value is less than that in 2011, they can be equal.

In 2013, the total number of graduates placed is less than that in 2011 and the percentage value is also less so they cannot be same.

*Answer can only contain numeric values

QUESTION: 37

Study the given chart carefully and answer the questions.

Additional Information: The total number of graduates produced when compared to the previous year increased every alternate year starting from 2002 (i.e. 2004, 2006 ...) and decreased in the remaining years.

The total number of graduates placed when compared to the previous years decreased every year from 2002.

**Q. What is the minimum possible number of years from 2003 to 2013 in which the total number of Engineers placed decreased when compared to the previous year?**

Solution:

The total number of Graduates placed keeps on decreasing every year.

Thus, the number of engineers placed in a certain year will definitely decrease compared to the previous year if the percentage of engineers placed in that year is less than the percentage of engineers placed in the preceding year.

This percentage condition is satisifed in four years i.e. 2003, 2008, 2009 and 2013.

Thus, the number of engineers placed has definitely decreased in these 4 years.

For the remaining years, the number of engineers may or may not have decreased, depending on the rate of decrease of graduates placed.

Thus, the minimum possible number of years is 4.

Answer: 4

*Answer can only contain numeric values

QUESTION: 38

Study the given chart carefully and answer the questions.

The total number of graduates placed when compared to the previous years decreased every year from 2002.

**Q. In how many of the following years- 2008, 2007, 2012, can the number of Engineers placed can be equal to 5/4 times the Engineers placed in 2003?**

Solution:

The number of Engineers placed in 2003 is 24%. 5/4 times the number of Engineers placed in 2003 = (5/4) x 24% = 30%.

But the number of graduates placed has decreased every year.

Hence the percent of Engineers placed should be more than 30% for the years following 2003 and it should be less than 30% for the years preceding 2003.

This has happened only for 2005, 2006, 2007, 2011 and 2012.

So, in two(i.e., 2007 and 2012) of the given years, the number of Engineers placed can be equal to 5/4 times the Engineers placed in 2003.

Answer: 2

QUESTION: 39

Group Question

Answer the following question based on the information given below.

The following diagrams represent the total input (in terms of hours) that a group of six students is expected to put in for their project in five subjects, namely Finance, Marketing, HR, Operations and Systems.

The four numbers inside the triangles represent the number of hours put in by four of the six students, who put in the maximum number of hours in the project in that particular subject. The percentage in the semi-circle expresses the number of hours put in by those four students for the project in that particular subject as a percentage of the total input (in hours) required for that subject..

For example, out of the total number of hours required by the project in Finance, A puts in 50 hours of work, B puts in 30 hours of work, C puts in 20 hours of work and F puts in 20 hours of work. Also A, B, C and F put in 80% of the total input required, in terms of hours. D and E together put in the remaining 20%. This percentage information for the proportion of input put in by the four students in the project in Systems has been intentionally removed.

Additional Information:

1. Number of hours of work put in by each student in each subject is a multiple of five.

2. No person puts in 0 (zero) hours of work in any subject.

3. A student whose number of hours of work for a particular subject is not mentioned did not put in the same hours as any other student whose input in terms of hours is mentioned for that subject.

**Q. What could be the maximum number of hours of work put in by B in all the subjects taken together?**

Solution:

The representation using the above graphs makes interpretation of the data very cumbersome. Therefore, first convert the above data in the form of a table.

In case of Finance, A, B, C and F spend a total of 120 hours on the project, which corresponds to 80% of the time required for the project.

Thus, the total time required for the project is (120 x 100)/80 i.e. 150 hours. The total hours required for each subject (except Systems) can be similarly calculated.

Thus, D and E together spend 30 hours on the project in Finance.

Since each person's input in terms of number of hours is a multiple of 5, the time spent by D can be 5, 10, 15, 20 or 25. Correspondingly the time spent by E is 25, 20, 15, 10 or 5. Note that no person spends zero hours on a project in any particular subject.

Note that the time given per person is for the top 4 contributors (in terms of hours) for the project in a particular subject.

In Finance, the minimum time mentioned is for C and F (20 hours each).

Hence, the number of hours spent by D or E on Finance cannot be more than 20.

Thus, the number of hours spent by D on Finance is 10, 15 or 20. Correspondingly, the number of hours for E is 20, 15 or 10.

Now, it has been given that a person whose number of hours have not been mentioned does not put in the same hours as any other student whose input in terms of number of hours has been mentioned for that subject.

Since C and F have spent 20 hours each on the project in Finance, neither D nor E can spend 20 hours on this project.

Therefore, neither of them can spend 10 hours on this project as well. (This is because if one of them spends 10 hours, the other spends 20 hours, which is invalid.) Hence, both D and E spend 15 hours each on the project in Finance.

Similarly, the number of hours for each person in each subject can be filled up as shown in the table below.

For Systems, the percentage contribution of the top 4 students is not known. Therefore, the total number of hours required, and consequently, the number of hours put in by D and E cannot be calculated.

Input (in terms of hours) by B in Finance, Marketing and Systems is 30, 40 and 40 hours respectively.

B's maximum input in Human Resource as well as in Operations can be 15 hours each.

The maximum number of hours of work put in by B in total can be (30 + 40 + 15 + 15 + 40) = 140 hours.

Hence, option 4.

QUESTION: 40

The following diagrams represent the total input (in terms of hours) that a group of six students is expected to put in for their project in five subjects, namely Finance, Marketing, HR, Operations and Systems.

The four numbers inside the triangles represent the number of hours put in by four of the six students, who put in the maximum number of hours in the project in that particular subject. The percentage in the semi-circle expresses the number of hours put in by those four students for the project in that particular subject as a percentage of the total input (in hours) required for that subject..

For example, out of the total number of hours required by the project in Finance, A puts in 50 hours of work, B puts in 30 hours of work, C puts in 20 hours of work and F puts in 20 hours of work. Also A, B, C and F put in 80% of the total input required, in terms of hours. D and E together put in the remaining 20%. This percentage information for the proportion of input put in by the four students in the project in Systems has been intentionally removed.

Additional Information:

1. Number of hours of work put in by each student in each subject is a multiple of five.

2. No person puts in 0 (zero) hours of work in any subject.

3. A student whose number of hours of work for a particular subject is not mentioned did not put in the same hours as any other student whose input in terms of hours is mentioned for that subject.

**Q. What could be the minimum number of hours of work put in by F?**

Solution:

Refer to the table given in the solution to the first question of the set.

Input (in terms of hours) by F in Finance, Marketing, Human Resource and Systems is 20, 15, 20 and 60 hours respectively.

F's minimum input (in terms of hours) in Operations is 5 hours.

The minimum number of hours of work put in by F in total can be (20 + 15 + 20 + 60 + 5) = 120 hours.

Hence, option 3.

QUESTION: 41

The following diagrams represent the total input (in terms of hours) that a group of six students is expected to put in for their project in five subjects, namely Finance, Marketing, HR, Operations and Systems.

The four numbers inside the triangles represent the number of hours put in by four of the six students, who put in the maximum number of hours in the project in that particular subject. The percentage in the semi-circle expresses the number of hours put in by those four students for the project in that particular subject as a percentage of the total input (in hours) required for that subject..

For example, out of the total number of hours required by the project in Finance, A puts in 50 hours of work, B puts in 30 hours of work, C puts in 20 hours of work and F puts in 20 hours of work. Also A, B, C and F put in 80% of the total input required, in terms of hours. D and E together put in the remaining 20%. This percentage information for the proportion of input put in by the four students in the project in Systems has been intentionally removed.

Additional Information:

1. Number of hours of work put in by each student in each subject is a multiple of five.

2. No person puts in 0 (zero) hours of work in any subject.

3. A student whose number of hours of work for a particular subject is not mentioned did not put in the same hours as any other student whose input in terms of hours is mentioned for that subject.

**Q. Which subject required the second highest number of hours?**

Solution:

From the table in the solution to the first question of this set, the total number of hours put in for four of the subjects is known.

Finance : 150

Marketing : 120

Human Resource: 100

Operations: 200

Systems : 150 (Using data for only the top 4 students)

Since every student spends some non zero time on the project of every subject, the total number of hours for Systems has to be more than 150 hours.

Consequently, either Systems or Operations requires the second highest number of hours.

Hence, option 3 can be eliminated.

Now, total hours put in by A, B, C and F in Systems are 30, 40,

20 and 60 respectively.

Since the number of hours put in D and E has to be less than the smallest of the above mentioned 4 values, D and E can spend a maximum of 15 hours each on this project.

If D and E spend 15 hours each on the Systems project, the total number of hours required by Systems is 150+ 15 + 15 = 180 hours.

Thus, the maximum time required for the Systems project is less than the time required for the Operations project.

Hence, Systems required the second highest number of hours.

Hence, option 2.

QUESTION: 42

The four numbers inside the triangles represent the number of hours put in by four of the six students, who put in the maximum number of hours in the project in that particular subject. The percentage in the semi-circle expresses the number of hours put in by those four students for the project in that particular subject as a percentage of the total input (in hours) required for that subject..

For example, out of the total number of hours required by the project in Finance, A puts in 50 hours of work, B puts in 30 hours of work, C puts in 20 hours of work and F puts in 20 hours of work. Also A, B, C and F put in 80% of the total input required, in terms of hours. D and E together put in the remaining 20%. This percentage information for the proportion of input put in by the four students in the project in Systems has been intentionally removed.

Additional Information:

1. Number of hours of work put in by each student in each subject is a multiple of five.

2. No person puts in 0 (zero) hours of work in any subject.

3. A student whose number of hours of work for a particular subject is not mentioned did not put in the same hours as any other student whose input in terms of hours is mentioned for that subject.

**Q. Assume that the two students whose input is not mentioned for a subject put in equal efforts (in terms of hours) in that particular subject. If this is true for all five subjects, which student puts in maximum number of hours across all subjects?**

Solution:

From the table in the solution to the first question, the actual hours for 2 students are not known for 3 subjects viz.

Human Resource, Operations and Systems.

From the table, it is clear the the input for A and B in Human Resource is 10 hours each.

Similarly, the input for B and F in Operations is 10 hours each.

In case of Systems, as mentioned in the solution to the previous question, both D and E can put in 5, 10 or 15 hours each.

Thus, the number of hours put in by each student in all the five 3 subjects can be tabulated as shown below:

It is evident that irrespective of the input of D and E in Systems, A puts in maximum number of hours across all subjects.

Hence, option 1.

QUESTION: 43

Group Question

Answer the following question based on the information given below.

The graphs below show the details of sales of high end computer systems by the Data Miners Ltd and the total market sales of similar systems for the period 1999 - 2008.

**Q. If in the year 2005, the sales of high end computer systems formed 50% of the total market sales by volume, then what was the average selling price of each system sold by all the other companies put together in 2005?**

Solution:

Total market sales by value is the actual revenue earned while the total market sales by volume is the number of units sold.

Let the total volume of sales of the market be 100x and the value be Rs. 10Oy.

Thus, Data Miners earned Rs. 40y by selling 50x units at Rs. 3,000 each.

The remaining companies earned a total of Rs. 60y and sold 50x units in all.

The average selling price per system of all other companies was

Hence, option 2.

QUESTION: 44

The graphs below show the details of sales of high end computer systems by the Data Miners Ltd and the total market sales of similar systems for the period 1999 - 2008.

**Q. In how many years from 2000 to 2007, did the value of sales of the computer systems sold by Data Miners increase and the profit earned by them decrease as compared to the previous year?**

Solution:

Since the total market sales is given in terms of value and the market share of Data Miners in value terms is known, the value of sales of computer systems sold by Data Miners can be found.

Since the profit is a percentage of the sales, the profit can also be found once the sales are known.

It can be seen that the the sales increased and the profit decreased compared to the previous year on three different occasions i.e. in 2001, 2002 and 2006.

Hence, option 1.

QUESTION: 45

The graphs below show the details of sales of high end computer systems by the Data Miners Ltd and the total market sales of similar systems for the period 1999 - 2008.

**Q. The ratio of profit earned by Data Miners in the year 2004 to that earned in 2008 is**

Solution:

Ratio of the profit earned by the company in the year 2004 to that earned in 2008 is:

Hence, option 4.

QUESTION: 46

**Q. If the percentage share by volume of the sales of systems by Data Miners in the total sales of the market increases by 10 percentage points from 2002 to 2003, then what would be the percentage change in the total volume of sales of high end systems in the market from 2002 to 2003?**

Solution:

The percentage share by volume of the sales of systems by Data Miners in the total sales of the market is not known for any year.

Since this value is not known, the total sales by volume for high end systems cannot be found for any year.

Thus, the percentage change cannot be calculated.

Hence, option 4

QUESTION: 47

Group Question

Answer the following question based on the information given below.

The ‘Alchemy Academy’ announced its results of Class X students who had appeared for the recently held pre-board exams in all the subjects that the students were to take in the final as well. ‘Alchemy Academy’ had a total of 360 students in Class X who were equally divided among the six classes that this school had for Class X.

The chart below gives the details of the number of students passing in each subject class wise.

**Q. What could have been the maximum number of students who passed in all the subjects in any single class?**

Solution:

In a particular class, the maximum number of students who can pass in all the subjects is equal to the number of students passing in the subject where the least number of students have passed.

For instance, Science is the subject where the least number of students have passed i.e. 15.

Thus, in Class A, as only 15 students had passed in Science, at the most 15 students can have passed in all the subjects.

Similarly in Class B, at the most 15 students could have passed in all the subjects.

Similarly, the maximum number of students who could have passed in all the subjects in all other classes can be 15, 21, 26 and 23 in Class C, D, E and F respectively.

Thus, in this school, the maximum number of students in a single class who can have passed in all the subjects is 26.

Hence, option 3.

QUESTION: 48

The ‘Alchemy Academy’ announced its results of Class X students who had appeared for the recently held pre-board exams in all the subjects that the students were to take in the final as well. ‘Alchemy Academy’ had a total of 360 students in Class X who were equally divided among the six classes that this school had for Class X.

The chart below gives the details of the number of students passing in each subject class wise.

**Q. What could have been the minimum number of students who passed in atleast two subjects, in class F?**

Solution:

In Class F, the total number of instances is 132. An instance, here, is the sum total of all the number of students passing in one or two or three or four or five subjects, (i.e. sum total of 23, 27, 25, 29 and 28).

We have to find the least possible number of students with atleast two instances. This would happen when the maximum number of students have passed in either one subject or all the five subjects.

Let x represent the number of students who have passed in a single subject and y represent the number of students who have passed in all the five subjects.

i.e. x + 5y=132 ... (i)

Further, the total number of students is x + y = 60 ... (ii)

Solving (i) and (ii) for x and y, we have y = 18 and x = 42

Hence there has to be a minimum of 18 students who have passed in two subjects in Class F.

Hence, option 2.

QUESTION: 49

The ‘Alchemy Academy’ announced its results of Class X students who had appeared for the recently held pre-board exams in all the subjects that the students were to take in the final as well. ‘Alchemy Academy’ had a total of 360 students in Class X who were equally divided among the six classes that this school had for Class X.

The chart below gives the details of the number of students passing in each subject class wise.

**Q. What could have been the maximum number of students who passed in atmost two subjects, in class D?**

Solution:

In Class D, the total number of instances is 129. Now these instances have to be distributed among 60 students in such a way that each student gets at most two instances.

129 - (60 x 2) = 9 Now, these 9 instances can be distributed among at least three other students, i.e. 3 instances each.

Except these three students, the other students (57) now have atmost two instances, implying that this is the number of students who have passed in atmost two subjects.

Hence, option 3.

QUESTION: 50

The chart below gives the details of the number of students passing in each subject class wise.

**Q. What could have been the minimum number of students who passed in exactly three subjects, in class E?**

Solution:

In Class E, the total number of instances is 155.

Now, in order to minimise the number of students passing in exactly three subjects, find the maximum number of students that could have passed in all five subjects, in exactly 4 subjects, in exaclt 2 subjects and in only 1 subject.

Consider the number of students who have passed in each subject:

Maths : 26

Science : 32

Social Studies : 41

English : 27

Hindi: 29

Now, to maximise the number of students who passed in all subjects, assume that all 26 students who have passed in Maths have also passed in the other four subjects.

This provides 26 x 5 = 130 instances.

Now, using a similar logic, assume that the sole student left in English has also passed in Science, Social Studies and Hindi.

This provides 4 more instances.

Now, there are 5, 14 and 2 students left in Science, Social Studies and Hindi respectively.

Using a similar logic, assume that these 2 students who passed in Hindi have also passed in exactly one from Science and Social Studies.

This again provides 2 + 2 = 4 instances.

Finally, there are either 3 and 14 or 5 and 12 students left in the remaining 2 subjects. These 17 students can pass in exactly one subject.

This provides exactly 17 instances.

Thus, the total number of instances =130+ 4 + 4 + 17 = 155.

Thus, there is a possibility of there being no instance of a student passing in exactly 3 subjects.

Hence, option 1.

*Answer can only contain numeric values

QUESTION: 51

Group Question

Answer the following question based on the information given below.

In the jungle of Hullabaloo land, there exist only three types of animals - rats, snakes and hawks. At the end of 18^{th} November 2007, there were 5000 rats, 600 snakes and 100 hawks. Each day, the number of rats increases to twice its value on the previous day, due to birth of new ones.

This doubled number of rats is reduced by the number of rats eaten by snakes to get the tally at the end of the day. The day’s end value is doubled the next day. The number of snakes increases by 150 per day due to new births, and it is known that each of the snakes that currently exist now proceed to eat three rats per day. However, after the snakes have had this lavish meal, the number of snakes is reduced due to hawks eating up one snake per day. The number of hawks is increased by 20 each day, due to the birth of new ones. Hawks have a life span of 11 days, snakes have a life span of 18 days and rats have a life span of 16 days. Assume that all the animals in this jungle are zero days old on 18^{th} November 2007.

**Q. What is the number of rats at the end of 22nd November 2007?**

Solution:

The count of animals at the end of 18th November 2007 is as follows:

Total number of hawks = 100

Total number of snakes = 600

Total number of rats = 5000

On 19^{th} November 2007:

The number of hawks increase by 20, the number of snakes increase by 150, and the number of rats double, due to new births that take place in each species. Hence, there will be 120 hawks, 750 snakes and 10000 rats. (In the table shown, these values are written as the 'Start' of day values.)

However, this increase in population is mitigated because some of the animals are eaten.

Since each of the snakes that currently exist eat 3 rats per day,

The population of rats becomes (10000 - 3 * 750) = 7750 The hawks are not preyed upon and their number remains 120. These 120 hawks eat one snake per day,

The population of snakes becomes (750 - 120) = 630 (In the table, these values are shown as the 'End' of day values.)

Similarly, we continue for the remaining days. The population at the beginning and the end of each day for the given animals is as shown in the above table.

There are 45560 rats at the end of 22^{nd} November 2007.

Answer: 45560

*Answer can only contain numeric values

QUESTION: 52

In the jungle of Hullabaloo land, there exist only three types of animals - rats, snakes and hawks. At the end of 18^{th} November 2007, there were 5000 rats, 600 snakes and 100 hawks. Each day, the number of rats increases to twice its value on the previous day, due to birth of new ones.

This doubled number of rats is reduced by the number of rats eaten by snakes to get the tally at the end of the day. The day’s end value is doubled the next day. The number of snakes increases by 150 per day due to new births, and it is known that each of the snakes that currently exist now proceed to eat three rats per day. However, after the snakes have had this lavish meal, the number of snakes is reduced due to hawks eating up one snake per day. The number of hawks is increased by 20 each day, due to the birth of new ones. Hawks have a life span of 11 days, snakes have a life span of 18 days and rats have a life span of 16 days. Assume that all the animals in this jungle are zero days old on 18^{th} November 2007.

**Q. What is the total number of rats eaten by snakes on 24th November 2007?**

Solution:

From the table given in the solution of the first question of the set, we see that 2100 rats were eaten by snakes on 24^{th} November 2007.

Answer: 2100

*Answer can only contain numeric values

QUESTION: 53

In the jungle of Hullabaloo land, there exist only three types of animals - rats, snakes and hawks. At the end of 18^{th} November 2007, there were 5000 rats, 600 snakes and 100 hawks. Each day, the number of rats increases to twice its value on the previous day, due to birth of new ones.

This doubled number of rats is reduced by the number of rats eaten by snakes to get the tally at the end of the day. The day’s end value is doubled the next day. The number of snakes increases by 150 per day due to new births, and it is known that each of the snakes that currently exist now proceed to eat three rats per day. However, after the snakes have had this lavish meal, the number of snakes is reduced due to hawks eating up one snake per day. The number of hawks is increased by 20 each day, due to the birth of new ones. Hawks have a life span of 11 days, snakes have a life span of 18 days and rats have a life span of 16 days. Assume that all the animals in this jungle are zero days old on 18^{th} November 2007.

**Q. What is the total number of animals at the end of 22 ^{nd} November 2007?**

Solution:

From the table given in the solution of the first question of the set, we can see that,

The total number of animals at the end of 22^{nd} November 2007 = 180 + 600 + 45560 = 46340

Answer: 46340

*Answer can only contain numeric values

QUESTION: 54

^{th} November 2007, there were 5000 rats, 600 snakes and 100 hawks. Each day, the number of rats increases to twice its value on the previous day, due to birth of new ones.

This doubled number of rats is reduced by the number of rats eaten by snakes to get the tally at the end of the day. The day’s end value is doubled the next day. The number of snakes increases by 150 per day due to new births, and it is known that each of the snakes that currently exist now proceed to eat three rats per day. However, after the snakes have had this lavish meal, the number of snakes is reduced due to hawks eating up one snake per day. The number of hawks is increased by 20 each day, due to the birth of new ones. Hawks have a life span of 11 days, snakes have a life span of 18 days and rats have a life span of 16 days. Assume that all the animals in this jungle are zero days old on 18^{th} November 2007.

Q. What is the total population of hawks in the jungle at the end of 30^{th} November 2007?

Solution:

The total population of hawks at the end of 30^{th} November 2007 is 320 + 2 0 - 100 = 240 100 hawks (which were zero years old on 18^{th} November 2007) will die as the life span of hawks is only 11 days and as 30^{th} November 2007 is the 12thday counting from 18^{th} November 2007.

QUESTION: 55

Group Question

Answer the following question based on the information given below.

In Mr. A’s will, he specified the details of the family members who would inherit his wealth and his property. Mr. A’s sons B and D would each receive 29% of his wealth.

Mr. A’s daughter C would get 21% of his wealth along with the apartment in Malaysia. Mr. A’s house located in the city was inherited by one of his two daughters-in-law E and F. H and I are the grandsons of Mr. A. I is married to U and has a daughter L.

J is a musician and inherited Mr. A’s piano. J has a son Y and a daughter Z. D inherited Mr. A’s house in the country and lives there with his wife E and two children which include a daughter X. H, F’s son, is the only child of his parents. C is Z’s mother. E’s daughter-in-law is a teacher by profession. M is the granddaughter of F. W is H’s wife.

Mr. A decides to divide the rest of the 21 % wealth among his great granddaughters and great grandsons. L is the great granddaughter of Mr. A. Also, none of the couples inherited more than one house.

**Q. Which of Mr. A’s daughters in law inherited the house in the city?**

Solution:

A has two sons B and D and a daughter C.

His daughters-in-law are E and F.

As E is D’s wife, F is B’s wife. H is B’s and F’s son.

C and J have a son Y and daughter Z. I is the grandson of A.

As D and E have two children, one of them being X, the other is I.

I is married to U. W is H’s wife and M is W’s and H’s daughter. We can form Mr. A’s family tree as follows :

Mr A's house located in the city was inherited by one of his daughters-in-law and D inherited Mr A's house in the country.

Also it is given that none of the couples inherited more than one house.

F has inherited A’s house in the city.

Hence, option 2.

QUESTION: 56

In Mr. A’s will, he specified the details of the family members who would inherit his wealth and his property. Mr. A’s sons B and D would each receive 29% of his wealth.

Mr. A’s daughter C would get 21% of his wealth along with the apartment in Malaysia. Mr. A’s house located in the city was inherited by one of his two daughters-in-law E and F. H and I are the grandsons of Mr. A. I is married to U and has a daughter L.

J is a musician and inherited Mr. A’s piano. J has a son Y and a daughter Z. D inherited Mr. A’s house in the country and lives there with his wife E and two children which include a daughter X. H, F’s son, is the only child of his parents. C is Z’s mother. E’s daughter-in-law is a teacher by profession. M is the granddaughter of F. W is H’s wife.

Mr. A decides to divide the rest of the 21 % wealth among his great granddaughters and great grandsons. L is the great granddaughter of Mr. A. Also, none of the couples inherited more than one house.

**Q. Who is the teacher married to?**

Solution:

We know that, E’s daughter-in-law is a teacher by profession.

From the family tree, it is clear that U is the teacher and is married to I.

Hence, option 4

QUESTION: 57

In Mr. A’s will, he specified the details of the family members who would inherit his wealth and his property. Mr. A’s sons B and D would each receive 29% of his wealth.

Mr. A’s daughter C would get 21% of his wealth along with the apartment in Malaysia. Mr. A’s house located in the city was inherited by one of his two daughters-in-law E and F. H and I are the grandsons of Mr. A. I is married to U and has a daughter L.

J is a musician and inherited Mr. A’s piano. J has a son Y and a daughter Z. D inherited Mr. A’s house in the country and lives there with his wife E and two children which include a daughter X. H, F’s son, is the only child of his parents. C is Z’s mother. E’s daughter-in-law is a teacher by profession. M is the granddaughter of F. W is H’s wife.

Mr. A decides to divide the rest of the 21 % wealth among his great granddaughters and great grandsons. L is the great granddaughter of Mr. A. Also, none of the couples inherited more than one house.

**Q. How are B and X related to each other?**

Solution:

From the family tree it is clear that B and X are uncle and niece.

Hence, option 1.

QUESTION: 58

Mr. A’s daughter C would get 21% of his wealth along with the apartment in Malaysia. Mr. A’s house located in the city was inherited by one of his two daughters-in-law E and F. H and I are the grandsons of Mr. A. I is married to U and has a daughter L.

J is a musician and inherited Mr. A’s piano. J has a son Y and a daughter Z. D inherited Mr. A’s house in the country and lives there with his wife E and two children which include a daughter X. H, F’s son, is the only child of his parents. C is Z’s mother. E’s daughter-in-law is a teacher by profession. M is the granddaughter of F. W is H’s wife.

Mr. A decides to divide the rest of the 21 % wealth among his great granddaughters and great grandsons. L is the great granddaughter of Mr. A. Also, none of the couples inherited more than one house.

**Q. How many people does the 21 % wealth meant for the great granddaughters and grandsons get distributed amongst?**

Solution:

The 21% wealth meant for the great granddaughters and grandsons gets distributed amongst L and M.

Hence, option 3.

QUESTION: 59

Group Question

Answer the following question based on the information given below.

Akash has 8 T-shirts, from which he has to select which to wear to college from Monday to Saturday. He does not repeat his clothes within a week.

1. Each T-shirt is of a different colour i.e. blue, green, red, lavender, magenta, cream, black and pink.

2. If he wears green on Monday, he has to wear cream on Thursday and vice versa. If doesn't wear green on Monday, he has to wear magenta on Thursday.

3. If he doesn’t wear magenta on Tuesday, he wears either black or red on Wednesday, otherwise he can not wear them on any day of the week.

4. He can wear the cream T-shirt only after he wears the pink T shirt.

5. He wears only lavender T-shirt on Friday.

6. If he wears the blue T-shirt, he has to wear the green T-shirt as well in the week, and the green T-shirt should always be worn before the blue one.

**Q. If Akash wears the magenta coloured T-shirt on Tuesday, then what is the colour of the T-shirt that he wears on Saturday?**

Solution:

Akash wears the magenta coloured T-shirt on Tuesday.

Thus, he cannot wear the black or red T-shirt on any day.

Akash normally has two options for Thursday, cream and magenta.

Since he has worn the magenta T-shirt on Tuesday, he cannot repeat it on Thursday.

Hence, he has to wear cream on Thursday, and consequently, green on Monday.

Since the pink T-shirt has to be worn before the cream one, he has to wear the pink T-shirt on Wednesday.

It is known that Akash wears lavender on Friday.

Thus, the only T-shirt that he can possibly wear on Saturday is the blue one.

Hence, option 4.

QUESTION: 60

Akash has 8 T-shirts, from which he has to select which to wear to college from Monday to Saturday. He does not repeat his clothes within a week.

1. Each T-shirt is of a different colour i.e. blue, green, red, lavender, magenta, cream, black and pink.

2. If he wears green on Monday, he has to wear cream on Thursday and vice versa. If doesn't wear green on Monday, he has to wear magenta on Thursday.

3. If he doesn’t wear magenta on Tuesday, he wears either black or red on Wednesday, otherwise he can not wear them on any day of the week.

4. He can wear the cream T-shirt only after he wears the pink T shirt.

5. He wears only lavender T-shirt on Friday.

6. If he wears the blue T-shirt, he has to wear the green T-shirt as well in the week, and the green T-shirt should always be worn before the blue one.

**Q. If Akash wears the green T-shirt on Tuesday, then which coloured T-shirt will he not wear in that week? Assume that the relative order between the green and blue t-shirts is interchanged for this question.**

Solution:

Since Akash wears the green T-shirt on Tuesday, he cannot wear the magenta T-shirt on Tuesday.

Hence, as per the conditions, he will wear one of black and red on Wednesday.

Since Akash is not wearing green on Monday, he will wear magenta on Thursday.

It is already known that he wears lavender on Friday.

Since the relative order between the green and blue T-shirts is interchanged, he has to wear blue before green.

To satisfy this condition, he has to wear blue on Monday.

Thus, he can wear either of pink or cream on Saturday.

However, Akash cannot wear cream before he wears pink.

If Akash wears cream on Saturday, there is no day left where he can wear pink.

So, he cannot wear cream in that week.

Hence, option 4.

QUESTION: 61

Akash has 8 T-shirts, from which he has to select which to wear to college from Monday to Saturday. He does not repeat his clothes within a week.

1. Each T-shirt is of a different colour i.e. blue, green, red, lavender, magenta, cream, black and pink.

2. If he wears green on Monday, he has to wear cream on Thursday and vice versa. If doesn't wear green on Monday, he has to wear magenta on Thursday.

3. If he doesn’t wear magenta on Tuesday, he wears either black or red on Wednesday, otherwise he can not wear them on any day of the week.

4. He can wear the cream T-shirt only after he wears the pink T shirt.

5. He wears only lavender T-shirt on Friday.

6. If he wears the blue T-shirt, he has to wear the green T-shirt as well in the week, and the green T-shirt should always be worn before the blue one.

**Q. On which day should Akash wear the green t-shirt to have maximum choice of t-shirts for the week?**

Solution:

Akash cannot wear green on Thursday (either of magenta or cream) or Friday (only lavender).

He also cannot wear green on Saturday as then blue cannot come in the week.

If he wears green on Wednesday black and red would be removed from choice and thus he would not have any choice.

If he wears green on Monday as seen above, he would not have any choice.

If he wears green on Tuesday, he would have choice of wearing black/red on Wednesday and thus his choices would increase.

Hence, option 2.

QUESTION: 62

1. Each T-shirt is of a different colour i.e. blue, green, red, lavender, magenta, cream, black and pink.

2. If he wears green on Monday, he has to wear cream on Thursday and vice versa. If doesn't wear green on Monday, he has to wear magenta on Thursday.

3. If he doesn’t wear magenta on Tuesday, he wears either black or red on Wednesday, otherwise he can not wear them on any day of the week.

4. He can wear the cream T-shirt only after he wears the pink T shirt.

5. He wears only lavender T-shirt on Friday.

6. If he wears the blue T-shirt, he has to wear the green T-shirt as well in the week, and the green T-shirt should always be worn before the blue one.

**Q. Sahil is twice as old as Karan was when Sahil was as old as what Karan is now. After 10 years Karan will be 4/5th as old as Sahil will be when Karan will be as old as Sahil now. How old are Sahil and Karan respectively?**

Solution:

Let Sahil’s age be x years and Karan’s age be y.

By first condition - x = 2 {y - (x - y)}3x = 4 y .....(I)

By second condition - y + 10 = 4/5[ x + (x - y)] .....(II)

By solving (I) and (II) we get y = 30 years.

So x = 40 years.

Hence, option 3.

QUESTION: 63

Group Question

Answer the following question based on the information given below.

In a scientific experiment, five students P, Q, R, S and T are asked to stand around a circular track, facing towards the centre of the track, according to the following instructions.

a. Exactly Three students are to take positions around the track such that the distance between adjacent students is 70°.

b. There should be exactly two pairs of students such that angular distance between two students of a pair is 140°.

Three of them are doctors and two of them are engineers. Further it is known that:

i. An engineer is to the immediate right of T.

ii. Both the engineers cannot be together or opposite each other.

iii. The person adjacent to T must be either both P and R or neither of P and R.

**Q. P is an engineer, and distance between T and P is the least possible. If R is not next to Q, find the angular distance between R and Q.**

Solution:

Let the points at which P, Q, R, S and T are standing be 1 to 5 in any order.

From the given data, the only possible arrangement is:

The distance between T and P is the least possible.

If T is at 5, P has to be at 1 and hence R at 4. From (i), R must be an engineer which contradicts (ii).

Case i: T is at 1.

P is at 5 and R is at 2. As R is not next to Q, Q has to be at 4. The distance between 1 and 4 is 110°.

Case ii: T is at 4.

P is at 3 and R is at 5. Hence, Q has to be at 2. The distance between 2 and 5 is 110°.

Case iii: T is at 3.

P is at 4 and R is at 2. Q has to be at 5. The distance between 2 and 5 is 110°.

Thus, the angular distance between R and Q is 110°.

Hence, option 3.

QUESTION: 64

In a scientific experiment, five students P, Q, R, S and T are asked to stand around a circular track, facing towards the centre of the track, according to the following instructions.

a. Exactly Three students are to take positions around the track such that the distance between adjacent students is 70°.

b. There should be exactly two pairs of students such that angular distance between two students of a pair is 140°.

Three of them are doctors and two of them are engineers. Further it is known that:

i. An engineer is to the immediate right of T.

ii. Both the engineers cannot be together or opposite each other.

iii. The person adjacent to T must be either both P and R or neither of P and R.

**Q. P, a doctor, is to the immediate left of T. Who among the following is definitely an engineer?**

Solution:

Since P is adjacent to T, R also has to be adjacent to T. P is on T’s left. So, R must be on his right. From (i), R is an engineer.

Hence, option 2.

QUESTION: 65

In a scientific experiment, five students P, Q, R, S and T are asked to stand around a circular track, facing towards the centre of the track, according to the following instructions.

a. Exactly Three students are to take positions around the track such that the distance between adjacent students is 70°.

b. There should be exactly two pairs of students such that angular distance between two students of a pair is 140°.

Three of them are doctors and two of them are engineers. Further it is known that:

i. An engineer is to the immediate right of T.

ii. Both the engineers cannot be together or opposite each other.

iii. The person adjacent to T must be either both P and R or neither of P and R.

**Q. If P is to the immediate right of R, then which of the following persons are doctor?**

Solution:

P is to the immediate right of R, both P and R will not be adjacent to T.

So, Q and S are adjacent to T. One on T’s right is an engineer. It is also possible that both Q and S are engineers.

Thus, it is not possible to determine the exact doctors in the given conditions.

Hence, option 4.

QUESTION: 66

b. There should be exactly two pairs of students such that angular distance between two students of a pair is 140°.

i. An engineer is to the immediate right of T.

ii. Both the engineers cannot be together or opposite each other.

iii. The person adjacent to T must be either both P and R or neither of P and R.

**Q. Assuming the data given in the first question of the set, find the least possible angular distance between P and R.**

Solution:

From the solution to the first question of the set, the least angular distance between P and R is possible in case(i) and case (iii).

So, the least angular distance = 110° Hence, option 3.

QUESTION: 67

Let A and B be two solid sphere such that the surface area of B is 800% more than the surface area of A. Then volume of A is how much lesser than volume of B?

Solution:

Let the radii of sphere A and B is a and b respectively.

Surface area of B is 800% more than A.

Hence, option 4.

*Answer can only contain numeric values

QUESTION: 68

S is set of positive integers less than 50 such that each number in the set when divided by five gives remainder three and is not a prime. How many odd numbers are there in S?

Solution:

Each number in the set has more than two factors i.e. the numbers in the set should be composite numbers.

As each element of S when divided by 5 gives remainder 3, the number has to be of the form 5k + 3, where k = 0, 1,2,...

The composite numbers of the form 5k + 3, less than 50 are 8, 18, 28, 33, 38 and 48.

S = {8, 18, 28, 33, 38, 48}

Only one number in S is odd.

Answer: 1

QUESTION: 69

The roots of the equation x^{2} - 2ax + 4a^{2} - 1 = 0 are real. If p = 5 - a^{2}, then which of the following is true?

Solution:

x^{2} - 2 ax + 4a2 -1 = 0

As roots are real, 1 - 3a^{2} __>__ 0

a^{2} has to be non-negative.

Hence, option 1.

QUESTION: 70

A sum of money is distributed among A, B and C. The amount received by A and B is in the ratio 7 : 9 and that of B and C is in the ratio 5 : 8. If the difference between the amount received by A and C is Rs. 1110 then what is the amount received by B?

Solution:

Ratio of amounts of A : B is 7 : 9 and that of B : C is 5 : 8. A : B : C = 35 : 45 : 72

Let amount received by A is 35x and that of C is 72x.

Different between the amounts of A and C = 1110

(72 - 35)x = 1110

x = 30

Amount received by B = 45 * 30 = Rs. 1350

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 71

A father tells his son - “when I was twice your current age, I was six times as old as you were then”. What is the current age of the father, if the difference of their current ages is 30 years?

Solution:

Let the current age of the son be x years.

So, the current age of the father is x + 30 years.

When the father was twice the son’s current age i.e. 2x years old, he was six times as old as the son.

Hence, son’s age at that time = 2x/6 years

Since the difference between their ages is always 30,

Hence, father’s current age = x + 30 = 48 years.

Answer: 48

QUESTION: 72

In how many ways can 325 students be arranged in the form of rows and columns such that in every possible arrangement, 1 student is extra?

Solution:

In each case, one student is to be left out.

Thus, factors of 325 - 1 = 324 need to be found out.

324 = 1 x 324 = 2 x 162 = 3 x 108 = 4 x 81 = 6 x 54 = 9 x 36 = 12 x 27 = 18 x 18

However, 1 x 324 can be ignored as an extra student cannot be obtained in this case.

In each of these cases, two arrangements are possible, (i.e., x rows and y columns OR x columns and y rows.)

Students can also be arranged in 18 columns and 18 rows.

Total arrangements = (2 x 6) + 1 =13.

Hence, option 4.

*Answer can only contain numeric values

QUESTION: 73

16 badminton players are playing in a knockout tournament. Each player is of a different skill level. When two players with different skill levels meet, the player with the lower skill level always loses. In each round, a player winning against another player advances to next level while the loser gets eliminated This continues till only one player remains. How many different players can reach the round which has only 2 players remaining?

Solution:

Since there are 16 players playing a knock-out format, the number of rounds played is 4 (final, semi-final, quarter-final and pre-quarter-final).

The question can be restated as, “what is the rank of the lowest ranked player who can reach the final?”.

If we divide the players into two halves, one having players from rank 1 to 8 and the other from rank 9 to 16, then the player ranked 9 will reach the final.

To prove that this is the lowest possible rank, we need to prove that the player having rank 10 cannot reach the final.

If the player having rank 10 reaches the final, he/she must beat a lower ranked player in the semis which must be atleast rank 11.

Now, these two must have beaten two lower ranked players in the quarterfinals.

Also, the losers of the quarterfinals and the players ranked 10 and 11 must have together beaten 4 lower ranked players in the pre-quartefinal round.

Hence 6 players, ranked lower than 11, were beaten.

As there are only 16 players in the tournament, it is not possible to have 6 players having their rank lower than 11.

Hence, the lowest rank player who can reach the final is 9.

Hence, we can have 9 different players in the finals.

Hence, option 4.

Alternatively,

Each finalist must be better than the players he beat in the semifinals, quarterfinals and in the first round.

Hence, the worst 7 (1 +2 + 4) players cannot reach the finals.

Hence, 9 players can reach the finals.

Answer: 9

QUESTION: 74

An unscrupulous shopkeeper buys a certain amount of salt at mixes it with white sand so as to earn more profit. The white sand is available free of cost and the two are mixed in equal quantity of weight. Find the percentage profit/loss in selling the adulterated salt if he claims to sell it at 10% loss.

Solution:

Let the cost price of salt be Rs. x per kg.

The cost price of 2 kg salt will be Rs. 2x

The shopkeeper sells it at 2 * x * 0.9 = 1.8x

But the shopkeeper gets it for Rs. x only

Hence, option 2.

QUESTION: 75

X alone can build a castle in 5 days. Y can do the same in 10 days. Z destroys that castle in few days. If they all start working at the same time, the castle is built in 8 days. How many days (integral value) does Z take to destroy the castle? (e.g., take 1.2 days as 2 days)

Solution:

Let Z take z days to destroy the castle.

Z takes 6 days to destroy the castle. Hence, option 3.

QUESTION: 76

The sum of roots of the equation x^{2} + bx + c = 0 is 6. The sum of the squares of the roots of the equation is 37/12. What is the value of c?

Solution:

Let α and β be the roots of the equation.

Now, (α + β)^{2} = 36

α^{2} + β2 + 2αβ = 36

Hence, option 3.

QUESTION: 77

If the equation x^{3} + px^{2} - qx + p = 0 has three real roots, then it must be the case that,

Solution:

x^{3} + px^{2} - qx + p = x^{2}(x + p) - qx + p

x^{2}(x + p) - qx + p = 0

If q = -1 then x^{2}(x + p) + (x + p) = (x + p)(x^{2} + 1) = 0

(x + p) = 0 or (x^{2} + 1) = 0

But (x^{2} + 1) = 0 does not have real roots and the question states that the equation has three real roots.

Hence, option 2.

QUESTION: 78

A square of side 4 cm is cut from four corners such that a regular octagon is formed. What is the area of this octagon?

Solution:

Four right angled triangles are cut from the square to form the regular octagon. Hence, hypotenuse of the right angled triangle is equal to the side of the octagon.

Let the side of the triangle that is cut be x units.

Hypotenuse of triangle = side of octagon = √2

Also, side o f square = 4 = x + √2 x + x = x (2 + √2)

Area of octagon = Area of square - (4 * Area of cut triangles)

Hence, option 2.

QUESTION: 79

A train approaches a tunnel AB. Inside the tunnel, a dog is located at a point that is 3/8 of the distance AB measured from the entrance A. When the train whistles, the dog starts running. If the dog moves to the entrance of the tunnel A, the train hits the dog exactly at the entrance A. If the dog moves to exit B, the train hits the dog exactly at the exit. What is the ratio of the excess speed of the train over the dog’s speed to the speed of the dog?

Solution:

Let length of the tunnel AB = 8L km and speed of the dog = L km/hr

Time taken by the dog to reach the entrance of the tunnel = 3 hr

And time taken to reach exit of the tunnel by the dog = 5 hr

Train will cover the total length (8L km) of the tunnel in 5 - 3 = 2 hr

Speed of the train = 4L km/hr

Excess speed of the train over speed of the dog = 4L - L = 3L

Ratio of the excess speed of the train over the dog’s speed to the speed of the dog = 3 : 1

Hence, option 1.

*Answer can only contain numeric values

QUESTION: 80

There is a polygon of 2k sides. The following exercise is undertaken on the polygon:

2 of its adjacent sides with the common vertex are removed and one side is added to join the vertices to complete the polygon. This is continued till the polygon with the least number of sides is formed.

If the sum of the total number of diagonals of all polygons formed is 210 then k is:

Solution:

Here a new polygon with number of sides lesser than its parent polygon by 1 is formed after every exercise.

For any polygon the number of diagonals =

So the number of diagonals will be summation of the number of diagonals upto n = 4.

We see 2k = 12 satisfies the given equation.

Therefore, k = 6

Answer: 6

QUESTION: 81

What is the approximate sum of the following series:

Solution:

Dividing (i) by 11, we get,

Subtracting (ii) from (i)

Dividing (iii) by 11,

Subtracting (iv) from (iii),

S= 1.342

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 82

It is given that a_{n} is the n^{th} term of an arithmetic progression. If a_{x} = y and a_{y} = x (x and y are both positive integers), what is the value of a_{x+y}?

Solution:

a_{n} = a + (n - 1)d, where a is the first term and d the common difference of the progression.

Thus, a_{x} = a + ( x - 1)of = y ...(i)

and a_{y} = a + (y - 1)d = x ...(ii)

Subtracting (ii) from (i), y - x = (x - y) d ,

d = - 1 and a = x + y - 1

a_{x+y} = a + (x + y - 1)d = (x + y - 1) - (x + y - 1) = 0

Answer: 0

QUESTION: 83

If a real valued function f is such that f(x^{2} +1) = x^{4} + 4x^{2} - 2, for all real numbers x then f(x^{2} - 1) =

Solution:

We need to express x^{4} + 4x^{2} - 2 in terms of x^{2} + 1.

x^{4} + 4x^{2} - 2 = (x^{2} + 1)^{2} + 2(x^{2} + 1) - 5

Let y = x^{2} + 1.

f(y) = y^{2} + 2y - 5, for all real numbers y. ... f(x^{2} - 1) = (x^{2} - 1)^{2} + 2(x^{2} - 1) - 5

= x^{4} - 6

Hence, option 3.

QUESTION: 84

In year 2008, the price of the item A rises up by a% and in year 2009, the price of A decreases by a%. The difference between the prices of A at the end of the years 2007 and 2009 is Rs. 243. In year 2010, the price of A again rises up by a% and in year 2011, the price of A again decreases by a%. The difference between the prices of A at the end of the years 2009 and 2011 is Rs. 221.13. What was the price of the item A at the end of the year 2007?

Solution:

Let the price of item A at the end of the year 2007 be Rs. P.

The difference in prices = P - Py - 243

Similarly, the difference between the prices at the end of the years 2011 and 2009

= Py - Py^{2} = 221.13

y = 0.91

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 85

An aptitude test has 25 questions. A student scores 1 mark for a correct answer, -1/4 for a wrong answer, and -1/2 for not attempting a question. If the net score of a student is 14, what is the number of correct answers given by the student?

Solution:

Let R, W and N be the number of questions with right answers, questions with wrong answers and not attempted questions respectively.

From the conditions given in the question, we have, R+ W + N = 25 ...(i) R - W/4 - N/2 = 14 ...(ii)

Solving equations (i) and (ii), we get, W = (44 - 6N)/5

Only for N = 4, W is an integer.

...N = 4, W= 4 and R = 17

Answer: 17

QUESTION: 86

A roadside vendor starts the business of buying duplicate electronic goods and selling them at 5% profit. In the next year, the cost price increases by 5% and so he increases the selling price by 5% too. In the third year, the cost price decreases by 5% but he increases the selling price further by 5%. What is his profit percentage now?

Solution:

Let initial C.P. be 100

Initial S.P. = 105

In the second year,

C.P. = 1.05 x 100 = 105

S.P. = 1.05 x 105 = 110.25

In the third year,

C.P. = 0.95 x 105 = 99.75

S.P. = 1.05 x 110.25* 115.76

Hence, option 4.

QUESTION: 87

If a, b, c and d are in continuous proportion ,then is equal to:

Solution:

a, b, c and d are in continuous proportion.

Hence, a - dk^{3}, b - dk^{2} and c = dk

Substituting this in the given equation, we get,

Multiplying and dividing by d, we get,

Hence, option 1.

QUESTION: 88

ABCDEF is a regular hexagon. G is the centroid of ΔAOF and L is the midpoint of FO. HK joins the midpoints of AB and CD. Find A(ΔOGL):

Solution:

ABCDEF is composed of 6 equilateral triangles. Let the area of each triangle be x.

In trapezium ABCD, H is the mid-point of AB and K is the mid-point of DC.

BC II HK II AD

Since,

In an equilateral triangle, medians divide the triangle into 6 equal parts.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 89

The number of solutions of the equation

Solution:

Case 1:

7x - 11 < 0

x < 11/7

Equation reduces to 3x^{2} - 7x + 2 = 0

(3x - 1 )(x - 2) = 0

⇒ x= 1/3, 2 (but x < 11/7)

x = 1/3 ... (i)

Case 2:

7x - 11 __>__ 0

x __>__ 11/7

Equation reduces to 3x^{2} + 7 x - 20 = 0

(3x - 5)(x +4) = 0

⇒ x = 5/3, - 4 (but x __>__ 11/7)

x = 5/3 ... (ii)

Thus x can take 2 values 1/3, 5/3 Answer: 2

QUESTION: 90

In a rectangular farm of length 50 m and breadth 40 m, mango trees are planted in a square portion of length 30 m such that the centre of the rectangle and square coincide. Outside the square portion, the farmer is supposed to refill the mixture of sand and fertilizers. The depth of this portion is 6.56 feet. What will be the volume of the mixture to be filled? (1 inch = 2.54 cm and 1 feet = 12 inch)

Solution:

Area of the rectangle = 50 * 40 = 2000 m^{2}

Area of square = 900 m^{2}

Remaining area = 2000 - 900 = 1100 m^{2}

Volume of soil required = 1100 * 2 = 2200 m^{3}

Hence, option 4.

QUESTION: 91

Anjali has a pencil which is p cm long. She draws two intersecting circles of radius 15 cm and 20 cm such that the distance between the centres of the two circles is 25 cm. If the pencil exactly fits between the point of intersection of two circles then p =

Solution:

p = Length of the common chord of the circles = 2 * AP

In ΔABC,

AB^{2} + AC^{2} = BC^{2}

∠BAC = 90°

Let BP = x

PC = 25 - x

20^{2} = x^{2} + AP^{2} ...(i)

In ΔAPC,

225 = AP^{2} + (25 - x)^{2}

225 = AP^{2} + 625 + x^{2} - 50x ...(ii)

From (i) and (ii) we get,

225 = 625 + 400 - 50x

50x = 800

x = 16 cm

AP^{2} = 20^{2} - 16^{2} = 12^{2}

AP = 12 cm

p = Length of the chord = 2 x AP = 24 cm

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 92

Strings, consisting of 10 digits only, are made using zeroes and ones. How many such strings consist of an even number of ones, with no zero immediately following another zero?

Solution:

If the string has 10 ones, then there is only 1 possible string.

If the string has 8 ones, then the ones can arrange themselves in 1 way. In the 9 gaps formed by the ones, the zeroes can be placed in ^{9}C_{2} = 36 ways.

If the string has 6 ones, then the ones can arrange themselves in 1 way. In the 7 gaps formed by the ones, the zeroes can be placed in ^{7}C_{4} = 35 ways.

The string cannot have ones less than 6 as the condition of no zero being followed by another zero will hold only upto 6 ones.

Hence, there are 1 + 36 + 35 = 72 such strings.

Answer: 72

QUESTION: 93

After grading the examination papers of a class of 18 students, a teacher noticed that when arranged in ascending or descending order, the scores formed an arithmetic progression. When the teacher was done recording the marks of the students, calculating average score of the class and finalizing individual ranks of the students (rank 1 being awarded to the student with highest marks), she noticed that the number of papers that had been graded was one more than the number of her students. It was then found that the paper of a student of another class was present in the l o t . Due to this mix up, the teacher had to rearrange the scores and calculate the average marks of her class. To her surprise, the average remained the same as before. What was the rank of the student of the other class in the initial arrangement?

Solution:

Let us say that in the initial arrangement the scores of the nineteen students in ascending order is a_{1} , a_{2 }, a_{3} , ..., a_{19}, where a_{1} is the lowest marks scored by any student.

Since these numbers are in arithmetic progression, a_{2} = a_{1} + d, a_{3} = a_{1} + 2d ... and so on

where d is the common difference of the arithmetic progression.

= 19[a_{1} + 9d]

Average of 19 students = a_{1} + 9d

= Marks obtained by the student ranked 10^{th}

If the student at the 10^{th} rank belonged to the other class then the average of the students will remain unchanged.

Hence, option 4.

*Answer can only contain numeric values

QUESTION: 94

10 < N < 10^{8}

If sum of the digits of N is 4 then how many different values of N exist?

Solution:

10 < N < 10^{8}

Looking at this inequality we know that N is an eight-digit number.

Let the digits be a, b, c, d, e, f, g, h.

a + b + c + d + e + f + g + h = 4

Case 1:

a = 1

⇒ b + c + d + e + f + g + h = 3

The number of ways in which ‘n’ identical things can be divided into ‘r’ groups, some of them may be empty = (n + r- 1)C_{(r -1)}

Here, we want to distribute 3(i.e., three 1s) among 7(i.e., among b, c, d, e, f, g, and h.).

(e.g., Two 1s are given to b and one is given to c. i.e., b = 2 and c = 1 and all others are equal to 0.)

This can be done in ^{3+7-1}C_{7-1} = ^{9}C_{e} = 84 ways.

Case 2:

a = 2

⇒ b + c + d + e + f + g + h = 2

As explained above, distributing 2 among 7 can be done in ^{2+7-1}C_{7-1} = ^{8}C_{6} = 28 ways.

Case 3:

a - 3

b + c + d + e + f + g + h = 1

Number of ways: ^{7}C_{1} = 7

Case 4:

a = 4

Number of ways: 1

Total number of ways = 84 + 28 + 7 + 1 = 120

Answer: 120

QUESTION: 95

Ashok has to swim from one bank of the river to the other. The width of the river is 500 m. Speed of the river current is 3 m/s. The maximum speed at which Ashok can swim is 2 m/s. If Ashok has to reach the other end in minimum time, what is the distance between his start and end points?

Solution:

Ashok has to reach the other bank in the minimum time.

Therefore, he swims perpendicular to the river current.

Time taken by Ashok to cover 500 m i.e. the width of the river = 500/2 = 250 seconds

But the river flows at a speed of 3 m/s.

In 250 seconds, Ashok travels 250 * 3 = 750 m in the direction of the current.

Distance between Ashok’s start and end points

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 96

Solution:

log_{2}8 + log_{5}625 = log_{2}2^{3} + log_{5}5^{4} = 3 + 4 = 7

log_{2}8 x 2^{Iog}2^{8}= 3 x 8 = 24

logk^{256} = log_{k}4^{4} = 4 x log_{k}4

LHS = 5^{log}k^{256} = 5^{4}xlog_{k}4

RHS = 24^{2} + 7^{2}

24^{2} + 7^{2} = 25^{2} = 5^{4}

LHS = 5^{4}xlog_{k}4 = 5^{4}

4 x log_{k}4 = 4

log_{k}4 = 1

k = 4

Answer: 4

QUESTION: 97

There is an isosceles concyclic trapezium ABCD. AB II CD and AB > CD. AB = 10 cm. The perpendicular distance from the centre of the circle to AB is 5√3 cm . What is the radius of the circle?

Solution:

In ΔAEO,

AE = AB/2 = 5 cm

EO = 5√3 cm

AO = 10 cm

Hence, option 1.

QUESTION: 98

Costs of petrol, ethanol and kerosene are Rs. 80, Rs. 50 and Rs. 30 per litre respectively. A clever dealer mixes petrol with ‘e’ litres of ethanol and ‘k’ litres of kerosene and sells at Rs. 75 making a profit of 20%. He has used 10 barrels of petrol each containing 15 litres. Which of the following options shows the quantity of kerosene he had used? (Note that e and k are integer values. The total mixture with him is less than 250 litres.)

Solution:

S.R of the mixture = Rs. 75 per litre

As profit = 20%; C.P. of mixture = 75/1.2 = Rs. 62.5 per litre

The ratio of petrol to ethanol that will give mixture that costs Rs. 62.5 is:

The ratio of petrol to kerosene that will give mixture that costs Rs. 62.5 is:

Assume that 12x litres of mixture containing petrol and ethanol is mixed with 20y litres of mixture containing petrol and kerosene. The resultant mixture will cost Rs. 62.5 per litre.

Petrol in the mixture = 5x + 13y = 150

Ethanol in the mixture; e = 7x

Kerosene in the mixture; k = 7y

x and y are integers as e and k are integers.

5x + 13y = 150 holds true for x = 4 and y = 10

Thus, quantity of kerosene the dealer had used = 7 * 10 = 70 litres

Hence, option 3.

QUESTION: 99

Let a, p be the roots of the quadratic equation x^{2} - px + q = 0. Then the product of the roots of the quadratic equation whose roots are ‘α2 - β^{2}’ and ‘α^{3} - β^{3}’ is

Solution:

Consider the product of the roots = (α^{2} - β^{2})(α^{3} - β^{3})

= (α + β) (α - β)(α - β)(α^{2} + β + αβ)

= (or + p)(a - P)2[a2 + P2 + 2ap - aP]

But α, β are the roots of the quadratic equation x^{2} - px + q = 0

or + β = p and αβ = q

Products of the roots = p(p^{2} - 4q)(p^{2} - q)

Hence, option 2.

QUESTION: 100

Let p, q, r and s be the roots of the equation 2X^{4} + 3X^{3} - 10x^{2} - 24x + 15 = 0. What is the value of pqr + pqs + qrs?

Solution:

If p, q, r and s are the roots of the equation, then pqr + pqs + prs + qrs = 24/2 = 12

Now, pqr + pqs + qrs will give a unique value only when p = q = r = s

As the equation is not symmetric, at least one root will be different from the other three.

Thus, the value of pqr + pqs + qrs will vary depending on the order of p, q, r, s.

Thus, a unique value of pqr + pqs + qrs cannot be determined.

Hence, option 4.

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