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This mock test of CAT Mock Test- 5 for CAT helps you for every CAT entrance exam.
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QUESTION: 1

Group Question

A passage is followed by questions pertaining to the passage. Read the passage and answer the questions. Choose the most appropriate answer.

The Mauryan Empire’s achievement lay in the ability to weld the diverse parts of the Indian subcontinent into a single political unit and to maintain an imperial system for almost 100 years. The gradual expansion of the agrarian economy and improvements in the administrative machinery for collecting revenue increased the income from land revenue. This is confirmed by both the theories of Kautilya and the account of Megasthenes; Kautilya maintained that the state should organize the clearing of wasteland and settle it with villages of Sudra cultivators. It is likely that some 150,000 persons deported from Kalinga by Asoka after the campaign were settled in this manner.

Megasthenes writes that there were no slaves in India, yet Indian sources speak of various categories of slaves called dasa, the most commonly used designation being dasa-bhrtaka -slaves and hired labourers. It is likely that there was no large-scale slavery for production, although slaves were used on the land, in the mines, and in the guilds, along with the hired labour. Domestic slavery was common, however. The nature of land revenue has been a subject of controversy. Some scholars maintain that the state was the sole owner of the land, while others contend that there was private and individual ownership as well. References to private ownership would seem to be too frequent to be ignored. There also are references to the crown lands, the cultivation of which was important to the economy. Two types of taxes were levied- one on the amount of land cultivated and the other on the produce of the land. The state maintained irrigation in limited areas and in limited periods. By and large, irrigation systems were privately controlled by cultivators and landowners. There is no support for a thesis that control of the hydraulic machinery was crucial to the political control of the country. Another source of income, which acquired increasing importance, was revenue from taxes levied on both internal and foreign trade. The attempt at improved political administration helped to break the economic isolation of various regions. Roads built to ensure quick communication with the local administration inevitably became arteries of exchange and trade.

*Q. Which of the following is NOT true about the Mauryan empire? *

Solution:

Solution: The passage mentions ‘Slavery’ and not “slave trade”. Nor can it be inferred that other than slavery any kind of ‘trading’ of slaves was present. Therefore, option 4 is not true about the empire.

All the others options are mentioned in the passage.

Option 1 is mentioned in the following extract, “The state maintained irrigation in limited areas and in limited periods. By and large, irrigation systems were privately controlled by cultivators and landowners”.

Option 2 is mentioned in the following extract, “The gradual expansion of the agrarian economy and improvements in the administrative machinery for collecting revenue increased the income from land revenue”.

Option 3 is mentioned in the following extract, “The Mauryan Empire’s achievement lay in the ability to weld the diverse parts of the Indian subcontinent into a single political unit”. Hence, the correct answer is option 4.

QUESTION: 2

The Mauryan Empire’s achievement lay in the ability to weld the diverse parts of the Indian subcontinent into a single political unit and to maintain an imperial system for almost 100 years. The gradual expansion of the agrarian economy and improvements in the administrative machinery for collecting revenue increased the income from land revenue. This is confirmed by both the theories of Kautilya and the account of Megasthenes; Kautilya maintained that the state should organize the clearing of wasteland and settle it with villages of Sudra cultivators. It is likely that some 150,000 persons deported from Kalinga by Asoka after the campaign were settled in this manner.

Megasthenes writes that there were no slaves in India, yet Indian sources speak of various categories of slaves called dasa, the most commonly used designation being dasa-bhrtaka -slaves and hired labourers. It is likely that there was no large-scale slavery for production, although slaves were used on the land, in the mines, and in the guilds, along with the hired labour. Domestic slavery was common, however. The nature of land revenue has been a subject of controversy. Some scholars maintain that the state was the sole owner of the land, while others contend that there was private and individual ownership as well. References to private ownership would seem to be too frequent to be ignored. There also are references to the crown lands, the cultivation of which was important to the economy. Two types of taxes were levied- one on the amount of land cultivated and the other on the produce of the land. The state maintained irrigation in limited areas and in limited periods. By and large, irrigation systems were privately controlled by cultivators and landowners. There is no support for a thesis that control of the hydraulic machinery was crucial to the political control of the country. Another source of income, which acquired increasing importance, was revenue from taxes levied on both internal and foreign trade. The attempt at improved political administration helped to break the economic isolation of various regions. Roads built to ensure quick communication with the local administration inevitably became arteries of exchange and trade.

*Q. Which of the following can be inferred from the passage?*

*A. The empire’s income came from land revenue, and taxes on land , agriculture, and trade.
B. Kautilya instructed Asoka to settle the deportees on reclaimed wastelands.
C. The empire allowed private ownership of cultivable land.
D. Slavery was absent in the empire. *

Solution:

Solution: The settlement was based on what Kautilya had written. We do not know (the passage does not give us data) as to whether Asoka and Kautilya were contemporaries. (In fact they were not). Therefore statement B is incorrect.

Statement D contradicts the data given in the passage. This eliminates options 2, 3 and 4.

Hence, the correct answer is option 1.

QUESTION: 3

The Mauryan Empire’s achievement lay in the ability to weld the diverse parts of the Indian subcontinent into a single political unit and to maintain an imperial system for almost 100 years. The gradual expansion of the agrarian economy and improvements in the administrative machinery for collecting revenue increased the income from land revenue. This is confirmed by both the theories of Kautilya and the account of Megasthenes; Kautilya maintained that the state should organize the clearing of wasteland and settle it with villages of Sudra cultivators. It is likely that some 150,000 persons deported from Kalinga by Asoka after the campaign were settled in this manner.

Megasthenes writes that there were no slaves in India, yet Indian sources speak of various categories of slaves called dasa, the most commonly used designation being dasa-bhrtaka -slaves and hired labourers. It is likely that there was no large-scale slavery for production, although slaves were used on the land, in the mines, and in the guilds, along with the hired labour. Domestic slavery was common, however. The nature of land revenue has been a subject of controversy. Some scholars maintain that the state was the sole owner of the land, while others contend that there was private and individual ownership as well. References to private ownership would seem to be too frequent to be ignored. There also are references to the crown lands, the cultivation of which was important to the economy. Two types of taxes were levied- one on the amount of land cultivated and the other on the produce of the land. The state maintained irrigation in limited areas and in limited periods. By and large, irrigation systems were privately controlled by cultivators and landowners. There is no support for a thesis that control of the hydraulic machinery was crucial to the political control of the country. Another source of income, which acquired increasing importance, was revenue from taxes levied on both internal and foreign trade. The attempt at improved political administration helped to break the economic isolation of various regions. Roads built to ensure quick communication with the local administration inevitably became arteries of exchange and trade.

*Q. Which of the following is most suitable to introduce the passage?*

Solution:

Solution: Answer is option 2. The passage describes the economical situation of the empire - that it was an agrarian economy, its sources of income, its labour, its irrigation, trade etc.; hence the best way to introduce the passage (title) is option 2.

QUESTION: 4

Group Question

Answer the following question based on the information given below.

India’s GDP per capita (in terms of purchasing power parity) almost doubled between 2007 and 2016, from $3,587 to $6,599. Growth slowed after the 2008 crisis, hitting a decade low in 2012-2013. But if anything, this provided the country with the opportunity to rethink its policies and engage more firmly in the reforms necessary to improve its competitiveness. Growth rebounded in 2014, and in 2015 surpassed that of China.

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

In other areas, India has not yet recovered to 2007 levels, with the biggest shortfall coming in financial market development - this pillar taking 0.03 points off India’s 2016 score in comparison to 2007 (a reduced pillar score of 0.52 points, multiplied by a pillar weight of 6%). The Reserve Bank of India has helped increase financial market transparency, shedding light on the large amounts of non-performing loans previously not reported on the balance sheets of Indian banks. However, the banks have not yet found a way to sell these assets, and in some cases need large recapitalizations.

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. “India’s overall competitiveness score was rather stagnant 3 bet ween 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.” We can be inferred from the above statement that:*

Solution:

Solution: Option 1 cannot be assumed from the statement or passage as there is no data available to substantiate if India’s competitiveness score was higher or lower prior to 2007.Option 2 is contextually incorrect as the Global Competitiveness Report only ranks countries based on their competitiveness score.Option 4 cannot be deduced as the statement only states that other countries improved their score. It cannot be said that they did better than India or were ranked higher than India. Taking this point into consideration, option 4 can be eliminated while it would be safe to assume option 3.Hence, the correct answer is option 3.

QUESTION: 5

India’s GDP per capita (in terms of purchasing power parity) almost doubled between 2007 and 2016, from $3,587 to $6,599. Growth slowed after the 2008 crisis, hitting a decade low in 2012-2013. But if anything, this provided the country with the opportunity to rethink its policies and engage more firmly in the reforms necessary to improve its competitiveness. Growth rebounded in 2014, and in 2015 surpassed that of China.

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

In other areas, India has not yet recovered to 2007 levels, with the biggest shortfall coming in financial market development - this pillar taking 0.03 points off India’s 2016 score in comparison to 2007 (a reduced pillar score of 0.52 points, multiplied by a pillar weight of 6%). The Reserve Bank of India has helped increase financial market transparency, shedding light on the large amounts of non-performing loans previously not reported on the balance sheets of Indian banks. However, the banks have not yet found a way to sell these assets, and in some cases need large recapitalizations.

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. The statement- “Growth rebounded in 2014, and last year surpassed that of China.” implies:*

Solution:

Solution: The word “rebounded” means ‘recover in value, amount, or strength after a decrease or decline.’ If India’s growth rebounded in 2014, it means after a decline in growth in the previous years, India saw recovery in 2014 and then went on to surpass China’s growth. This does not mean that India suffered from a recession prior to 2015. Thus, eliminate options 1 and 4. Option 2 cannot be deduced from the statement or passage. Hence, the correct answer is option 3.

QUESTION: 6

India’s GDP per capita (in terms of purchasing power parity) almost doubled between 2007 and 2016, from $3,587 to $6,599. Growth slowed after the 2008 crisis, hitting a decade low in 2012-2013. But if anything, this provided the country with the opportunity to rethink its policies and engage more firmly in the reforms necessary to improve its competitiveness. Growth rebounded in 2014, and in 2015 surpassed that of China.

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

In other areas, India has not yet recovered to 2007 levels, with the biggest shortfall coming in financial market development - this pillar taking 0.03 points off India’s 2016 score in comparison to 2007 (a reduced pillar score of 0.52 points, multiplied by a pillar weight of 6%). The Reserve Bank of India has helped increase financial market transparency, shedding light on the large amounts of non-performing loans previously not reported on the balance sheets of Indian banks. However, the banks have not yet found a way to sell these assets, and in some cases need large recapitalizations.

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. According to the passage, which of the following is true with regards to the Reserve Bank of India?*

Solution:

Solution: Options 1 and 3 are contextually misleading.Although option 2 is factually true, it bears no semblance to the context of the passage and thus can be eliminated.Option 4 is corroborated from the penultimate paragraph that states “The Reserve Bank of India has helped increase ...nonperforming loans previously not reported on the balance sheets of Indian banks.” Hence, the correct answer is option 4.

QUESTION: 7

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. Which of the following questions would be apt if you were to interview the author?*

Solution:

Solution: The passage mentions “Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other.” Thus, option 1 would be a valid question to ask the author.

Options 2 and 3 are out of context.

Option 4 is already answered in the third paragraph “Improvements in health, primary education and infrastructure contributed most to this improvement..., each accounting for 15% of the final score.”. Hence, the correct answer is option 1.

QUESTION: 8

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. Based on the passage, what can be said about the author’s style? *

*1. Abstract *

*2. Data driven *

*3. Analytical *

*4. Argumentative *

Solution:

Solution: As abstract passage highlights hypothetical ideas and opinions.

In analytical passages, the author presents the reader with an analysis on the subject.

Data driven passages are generally statistical in nature and may consist of numerical analysis.

In argumentative passages, the subject is usually an issue that has two sides to it.

The author’s style is a combination of an analytical and data driven writing. Thus, option 2 is correct.

Hence, the correct answer is option 2.

QUESTION: 9

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. The passage mentions all of the following, except:*

Solution:

Solution: Option 1, 2 and 3 are mentioned in the passage, except option 4 which is not contextually supported.

Hence, the correct answer is option 4.

QUESTION: 10

Group Question

Answer the questions based on the passage given below.

He who wishes to decide whether man is the modified descendant of some pre-existing form, would probably first enquire whether man varies, however slightly, in bodily structure and in mental faculties; and if so, whether the variations are transmitted to his offspring in accordance with the laws which prevail with the lower animals. Again, are the variations the result, as far as our ignorance permits us to judge, of the same general causes, and are they governed by the same general laws, as in the case of other organisms; for instance, by correlation, the inherited effects of use and disuse, etc.? Is man subject to similar malconformations, the result of arrested development, of reduplication of parts, etc., and does he display in any of his anomalies reversion to some former and ancient type of structure? It might also naturally be enquired whether man, like so many other animals, has given rise to varieties and sub-races, differing but slightly from each other, or to races differing so much that they must be classed as doubtful species? How are such races distributed over the world; and how, when crossed, do they react on each other in the first and succeeding generations? And so with many other points.

The enquirer would next come to the important point, whether man tends to increase at so rapid a rate, as to lead to occasional severe struggles for existence; and consequently to beneficial variations, whether in body or mind, being preserved, and injurious ones eliminated. Do the races or species of men, whichever term may be applied, encroach on and replace one another, so that some finally become extinct? We shall see that all these questions, as indeed is obvious in respect to most of them, must be answered in the affirmative, in the same manner as with the lower animals. But the several considerations just referred to may be conveniently deferred for a time: and we will first see how far the bodily structure of man shows traces, more or less plain, of his descent from some lower form.

It is notorious that man is constructed on the same general type or model as other mammals. All the bones in his skeleton can be compared with corresponding bones in a monkey, bat, or seal. So it is with his muscles, nerves, blood-vessels and internal viscera. The brain, the most important of all the organs, follows the same law, as shown by Huxley and other anatomists. The conclusions of this author, as well as those of Gratiolet and Aeby, concerning the brain, will be discussed by Prof. Huxley in the Appendix alluded to in the Preface to this edition, who is a hostile witness, admits that every chief fissure and fold in the brain of man has its analogy in that of the orang; but he adds that at no period of development do their brains perfectly agree; nor could perfect agreement be expected, for otherwise their mental powers would have been the same. But it would be superfluous here to give further details on the correspondence between man and the higher mammals in the structure of the brain and all other parts of the body.

*Q. All of the following can be inferred from the passage except: *

Solution:

Solution: Option 1 can be inferred from the following, “Do the races or species of men, whichever term may be applied, encroach on and replace one another, so that some finally become extinct? We shall see that all these questions, as indeed is obvious in respect to most of them, must be answered in the affirmative...” Option 2 can be inferred from the following extract, “Again, are the.... of structure?” The author answers these questions in the affirmative in the second paragraph.

Option 3 can be inferred from the following, “The enquirer would ...ones eliminated.” The author answers these queries once again in the affirmative.

The following extract, “The enquirer would next come to the important point, whether man tends to increase at so rapid a rate, as to lead to occasional severe struggles for existence...” repudiates option 4. Note the word “occasional” in the extract which contradicts “constant and unremitting” is mentioned in option 4.

Hence, the correct answer is option 4.

QUESTION: 11

Group Question

Answer the questions based on the passage given below.

He who wishes to decide whether man is the modified descendant of some pre-existing form, would probably first enquire whether man varies, however slightly, in bodily structure and in mental faculties; and if so, whether the variations are transmitted to his offspring in accordance with the laws which prevail with the lower animals. Again, are the variations the result, as far as our ignorance permits us to judge, of the same general causes, and are they governed by the same general laws, as in the case of other organisms; for instance, by correlation, the inherited effects of use and disuse, etc.? Is man subject to similar malconformations, the result of arrested development, of reduplication of parts, etc., and does he display in any of his anomalies reversion to some former and ancient type of structure? It might also naturally be enquired whether man, like so many other animals, has given rise to varieties and sub-races, differing but slightly from each other, or to races differing so much that they must be classed as doubtful species? How are such races distributed over the world; and how, when crossed, do they react on each other in the first and succeeding generations? And so with many other points.

The enquirer would next come to the important point, whether man tends to increase at so rapid a rate, as to lead to occasional severe struggles for existence; and consequently to beneficial variations, whether in body or mind, being preserved, and injurious ones eliminated. Do the races or species of men, whichever term may be applied, encroach on and replace one another, so that some finally become extinct? We shall see that all these questions, as indeed is obvious in respect to most of them, must be answered in the affirmative, in the same manner as with the lower animals. But the several considerations just referred to may be conveniently deferred for a time: and we will first see how far the bodily structure of man shows traces, more or less plain, of his descent from some lower form.

It is notorious that man is constructed on the same general type or model as other mammals. All the bones in his skeleton can be compared with corresponding bones in a monkey, bat, or seal. So it is with his muscles, nerves, blood-vessels and internal viscera. The brain, the most important of all the organs, follows the same law, as shown by Huxley and other anatomists. The conclusions of this author, as well as those of Gratiolet and Aeby, concerning the brain, will be discussed by Prof. Huxley in the Appendix alluded to in the Preface to this edition, who is a hostile witness, admits that every chief fissure and fold in the brain of man has its analogy in that of the orang; but he adds that at no period of development do their brains perfectly agree; nor could perfect agreement be expected, for otherwise their mental powers would have been the same. But it would be superfluous here to give further details on the correspondence between man and the higher mammals in the structure of the brain and all other parts of the body.

*Q. Which of the following is NOT TRUE according to the passage?*

Solution:

Solution: The following extract, “All the bones in his skeleton can be compared with corresponding bones in a monkey, bat, or seal” establishes option 2 to be true.The following extract, “Prof. Huxley in the Appendix alluded to in the Preface to this edition, who is a hostile witness, admits that every chief fissure and fold in the brain of man has its analogy in that of the orang...” determines options 3 and 4 to be true statements.The following extract, “and we will first see how far the bodily structure of man shows traces, more or less plain, of his descent from some lower form” determines option 1 to be a false statement.Hence, the correct answer is option 1.

QUESTION: 12

India’s overall competitiveness score was rather stagnant between 2007 and 2014, and the country slipped down the rankings in the Global Competitiveness Report as others made improvements.

However, improvements since 2014 have seen it climb to 39th in this year’s edition of the report - up from 48th in 2007-2008. Its overall score improved by 0.19 points in that time.

Improvements in health, primary education and infrastructure contributed most to this improvement - although this is partly explained by the relatively large weight these “basic requirements” components have until now been given in factor-driven economies, each accounting for 15% of the final score.

Improvements in infrastructure were small and faltering until 2014, when the government increased public investment and accelerated approval procedures to attract private resources. Macroeconomic conditions - the third-biggest positive contributor - followed a similar path: the recent slump in commodity prices has helped India to keep inflation below its target of 5%, while rebalancing its current account and decreasing its public deficit. Another improvement over the past decade has been increased market size (the adoption of new PPP estimates by the IMF in 2014 also contributed to the upward increase in the measure of market size used in the GCI).

The efficiency of the goods market has also deteriorated, as India failed to address long-running problems such as different local sales and value added taxes (this is set to finally change as of 2017 if the Central GST and Integrated GST bills currently in parliament are fully implemented). Another area of concern is India’s stagnating performance in technological readiness, a pillar on which it scores one full point lower than any other. These three pillars will be key for India to prosper in its next stage of development, when it will no longer be possible to base its competitiveness on low-cost, abundant labour. Higher education and training has also shown no improvement.

*Q. In the context of the passage what could be the possible meaning of the word “notorious?”*

Solution:

Solution: The word has been used in the following context, “It is notorious that man is constructed on the same general type or model as other mammals.” We can eliminate “obvious” because the author does not go on to add details of why we should consider the fact that man's bones are similar to that of other mammals to be “obvious” or self-evident. “Obvious” is too categorical to be true. “Not worth mentioning”, like obvious implies that this fact (of man's bones being similar to that of mammals) is so clearly self-evident as to be not worth mentioning. This would not be a true inference. “Widely and unfavourably known” can also be eliminated since we do not know the cause of this fact being considered “unfavourable” in any way. “Widely known” is the only sensible answer option that best describes the meaning of the word “notorious” contextually. Hence, the correct answer is option 2.

QUESTION: 13

Group Question

Answer the questions based on the passage given below.

The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations.

According, therefore, as this produce, or what is purchased with it, bears a greater or smaller proportion to the number of those who are to consume it, the nation will be better or worse supplied with all the necessaries and conveniencies for which it has occasion.

But this proportion must in every nation be regulated by two different circumstances: first, by the skill, dexterity, and judgment with which its labour is generally applied; and, secondly, by the proportion between the number of those who are employed in useful labour, and that of those who are not so employed. Whatever be the soil, climate, or extent of territory of any particular nation, the abundance or scantiness of its annual supply must, in that particular situation, depend upon those two circumstances.

The abundance or scantiness of this supply, too, seems to depend more upon the former of those two circumstances than upon the latter. Among the savage nations of hunters and fishers, every individual who is able to work is more or less employed in useful labour, and endeavours to provide, as well as he can, the necessaries and conveniencies of life, for himself, and such of his family or tribe as are either too old, or too young, or too infirm, to go a-hunting and fishing.

Such nations, however, are so miserably poor, that, from mere want, they are frequently reduced, or at least think themselves reduced, to the necessity sometimes of directly destroying, and sometimes of abandoning their infants, their old people, and those afflicted with lingering diseases, to perish with hunger, or to be devoured by wild beasts. Among civilized and thriving nations, on the contrary, though a great number of people do not labour at all, many of whom consume the produce often times, frequently of a hundred times, more labour than the greater part of those who work; yet the produce of the whole labour of the society is so great, that all are often abundantly supplied; and a workman, even of the lowest and poorest order, if he is frugal and industrious, may enjoy a greater share of the necessaries and conveniencies of life than it is possible for any savage to acquire.

The causes of this improvement in the productive powers of labour, and the order according to which its produce is naturally distributed among the different ranks and conditions of men in the society, make the subject of the first book of this Inquiry.

Whatever be the actual state of the skill, dexterity, and judgment, with which labour is applied in any nation, the abundance or scantiness of its annual supply must depend, during the continuance of that state, upon the proportion between the number of those who are annually employed in useful labour, and that of those who are not so employed. The number of useful and productive labourers, it will hereafter appear, is everywhere in proportion to the quantity of capital stock which is employed in setting them to work, and to the particular way in which it is so employed. The second book, therefore, treats of the nature of capital stock, of the manner in which it is gradually accumulated, and of the different quantities of labour which it puts into motion, according to the different ways in which it is employed.

Nations tolerably well advanced as to skill, dexterity, and judgment, in the application of labour, have followed very different plans in the general conduct or direction of it; and those plans have not all been equally favourable to the greatness of its produce. The policy of some nations has given extraordinary encouragement to the industry of the country; that of others to the industry of towns. Scarce any nation has dealt equally and impartially with every sort of industry. Since the down-fall of the Roman empire, the policy of Europe has been more favourable to arts, manufactures, and commerce, the industry of towns, than to agriculture, the Industry of the country. The circumstances which seem to have introduced and established this policy are explained in the third book.

Though those different plans were, perhaps, first introduced by the private interests and prejudices of particular orders of men, without any regard to, or foresight of, their consequences upon the general welfare of the society; yet they have given occasion to very different theories of political economy; of which some magnify the importance of that industry which is carried on in towns, others of that which is carried on in the country. Those theories have had a considerable influence, not only upon the opinions of men of learning, but upon the public conduct of princes and sovereign states. I have endeavoured, in the fourth book, to explain as fully and distinctly as I can those different theories, and the principal effects which they have produced in different ages and nations.

*Q. The wealth or the necessaries and conveniences of nations is most dependent on which of the following?*

Solution:

Solution: The following extract, “The abundance or scantiness of this supply, too, seems to depend more upon the former of those two circumstances than upon the latter” implies that the skill, dexterity and the way labour is applied is the most critical factor in the wealth of nations. The author reinforces this concept of his with examples immediately after this extract. Options 1, 2 and 3 are also reasons for the wealth of nations but they are not the most important ones.

Hence, the correct answer is option 4.

QUESTION: 14

The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations.

According, therefore, as this produce, or what is purchased with it, bears a greater or smaller proportion to the number of those who are to consume it, the nation will be better or worse supplied with all the necessaries and conveniencies for which it has occasion.

But this proportion must in every nation be regulated by two different circumstances: first, by the skill, dexterity, and judgment with which its labour is generally applied; and, secondly, by the proportion between the number of those who are employed in useful labour, and that of those who are not so employed. Whatever be the soil, climate, or extent of territory of any particular nation, the abundance or scantiness of its annual supply must, in that particular situation, depend upon those two circumstances.

The abundance or scantiness of this supply, too, seems to depend more upon the former of those two circumstances than upon the latter. Among the savage nations of hunters and fishers, every individual who is able to work is more or less employed in useful labour, and endeavours to provide, as well as he can, the necessaries and conveniencies of life, for himself, and such of his family or tribe as are either too old, or too young, or too infirm, to go a-hunting and fishing.

Such nations, however, are so miserably poor, that, from mere want, they are frequently reduced, or at least think themselves reduced, to the necessity sometimes of directly destroying, and sometimes of abandoning their infants, their old people, and those afflicted with lingering diseases, to perish with hunger, or to be devoured by wild beasts. Among civilized and thriving nations, on the contrary, though a great number of people do not labour at all, many of whom consume the produce often times, frequently of a hundred times, more labour than the greater part of those who work; yet the produce of the whole labour of the society is so great, that all are often abundantly supplied; and a workman, even of the lowest and poorest order, if he is frugal and industrious, may enjoy a greater share of the necessaries and conveniencies of life than it is possible for any savage to acquire.

The causes of this improvement in the productive powers of labour, and the order according to which its produce is naturally distributed among the different ranks and conditions of men in the society, make the subject of the first book of this Inquiry.

Whatever be the actual state of the skill, dexterity, and judgment, with which labour is applied in any nation, the abundance or scantiness of its annual supply must depend, during the continuance of that state, upon the proportion between the number of those who are annually employed in useful labour, and that of those who are not so employed. The number of useful and productive labourers, it will hereafter appear, is everywhere in proportion to the quantity of capital stock which is employed in setting them to work, and to the particular way in which it is so employed. The second book, therefore, treats of the nature of capital stock, of the manner in which it is gradually accumulated, and of the different quantities of labour which it puts into motion, according to the different ways in which it is employed.

Nations tolerably well advanced as to skill, dexterity, and judgment, in the application of labour, have followed very different plans in the general conduct or direction of it; and those plans have not all been equally favourable to the greatness of its produce. The policy of some nations has given extraordinary encouragement to the industry of the country; that of others to the industry of towns. Scarce any nation has dealt equally and impartially with every sort of industry. Since the down-fall of the Roman empire, the policy of Europe has been more favourable to arts, manufactures, and commerce, the industry of towns, than to agriculture, the Industry of the country. The circumstances which seem to have introduced and established this policy are explained in the third book.

Though those different plans were, perhaps, first introduced by the private interests and prejudices of particular orders of men, without any regard to, or foresight of, their consequences upon the general welfare of the society; yet they have given occasion to very different theories of political economy; of which some magnify the importance of that industry which is carried on in towns, others of that which is carried on in the country. Those theories have had a considerable influence, not only upon the opinions of men of learning, but upon the public conduct of princes and sovereign states. I have endeavoured, in the fourth book, to explain as fully and distinctly as I can those different theories, and the principal effects which they have produced in different ages and nations.

*Q. Nations following different methods of employing labour have done so out of: *

Solution:

Solution: The following extract, “Though those different plans were, perhaps, first introduced by the private interests and prejudices of particular orders of men, without any regard to, or foresight of, their consequences upon the general welfare of the society” points directly to option 2 as being the most suitable answer. Options 1 and 4 do not give the reason as to why nations had different methods of employing labour - in short they do not answer the question asked. Option 3 has not been mentioned in the passage. In fact it contradicts the extract given above.Hence, the correct answer is option 2.

QUESTION: 15

The annual labour of every nation is the fund which originally supplies it with all the necessaries and conveniencies of life which it annually consumes, and which consist always either in the immediate produce of that labour, or in what is purchased with that produce from other nations.

According, therefore, as this produce, or what is purchased with it, bears a greater or smaller proportion to the number of those who are to consume it, the nation will be better or worse supplied with all the necessaries and conveniencies for which it has occasion.

But this proportion must in every nation be regulated by two different circumstances: first, by the skill, dexterity, and judgment with which its labour is generally applied; and, secondly, by the proportion between the number of those who are employed in useful labour, and that of those who are not so employed. Whatever be the soil, climate, or extent of territory of any particular nation, the abundance or scantiness of its annual supply must, in that particular situation, depend upon those two circumstances.

The abundance or scantiness of this supply, too, seems to depend more upon the former of those two circumstances than upon the latter. Among the savage nations of hunters and fishers, every individual who is able to work is more or less employed in useful labour, and endeavours to provide, as well as he can, the necessaries and conveniencies of life, for himself, and such of his family or tribe as are either too old, or too young, or too infirm, to go a-hunting and fishing.

Such nations, however, are so miserably poor, that, from mere want, they are frequently reduced, or at least think themselves reduced, to the necessity sometimes of directly destroying, and sometimes of abandoning their infants, their old people, and those afflicted with lingering diseases, to perish with hunger, or to be devoured by wild beasts. Among civilized and thriving nations, on the contrary, though a great number of people do not labour at all, many of whom consume the produce often times, frequently of a hundred times, more labour than the greater part of those who work; yet the produce of the whole labour of the society is so great, that all are often abundantly supplied; and a workman, even of the lowest and poorest order, if he is frugal and industrious, may enjoy a greater share of the necessaries and conveniencies of life than it is possible for any savage to acquire.

The causes of this improvement in the productive powers of labour, and the order according to which its produce is naturally distributed among the different ranks and conditions of men in the society, make the subject of the first book of this Inquiry.

Whatever be the actual state of the skill, dexterity, and judgment, with which labour is applied in any nation, the abundance or scantiness of its annual supply must depend, during the continuance of that state, upon the proportion between the number of those who are annually employed in useful labour, and that of those who are not so employed. The number of useful and productive labourers, it will hereafter appear, is everywhere in proportion to the quantity of capital stock which is employed in setting them to work, and to the particular way in which it is so employed. The second book, therefore, treats of the nature of capital stock, of the manner in which it is gradually accumulated, and of the different quantities of labour which it puts into motion, according to the different ways in which it is employed.

Nations tolerably well advanced as to skill, dexterity, and judgment, in the application of labour, have followed very different plans in the general conduct or direction of it; and those plans have not all been equally favourable to the greatness of its produce. The policy of some nations has given extraordinary encouragement to the industry of the country; that of others to the industry of towns. Scarce any nation has dealt equally and impartially with every sort of industry. Since the down-fall of the Roman empire, the policy of Europe has been more favourable to arts, manufactures, and commerce, the industry of towns, than to agriculture, the Industry of the country. The circumstances which seem to have introduced and established this policy are explained in the third book.

Though those different plans were, perhaps, first introduced by the private interests and prejudices of particular orders of men, without any regard to, or foresight of, their consequences upon the general welfare of the society; yet they have given occasion to very different theories of political economy; of which some magnify the importance of that industry which is carried on in towns, others of that which is carried on in the country. Those theories have had a considerable influence, not only upon the opinions of men of learning, but upon the public conduct of princes and sovereign states. I have endeavoured, in the fourth book, to explain as fully and distinctly as I can those different theories, and the principal effects which they have produced in different ages and nations.

*Q. The phrase, “savage nations of hunters and fishers” would imply which of the following? *

Solution:

Solution: The phrase “savage” when used to refer to nations is being politically incorrect. We do not know from the passage whether it was alright to be politically incorrect in the olden days. Eliminate option 1. Option 2 becomes the correct answer. Option 3 gives a literal meaning - we need an implication of this phrase. Option 4 cannot be inferred from the passage.

Hence, the correct answer is option 2.

QUESTION: 16

**Group Question **

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

The Balkan peninsula, which had been raised to a high level of security and prosperity during the Roman dominion, gradually relapsed into barbarism as a result of these endless invasions. The process continued unabated throughout the three following centuries. It is impossible to count the number of times the tide of invasion and devastation swept southwards over the unfortunate peninsula. In the sixth century the Slavs appear for the first time. From their original homes which were immediately north of the Carpathians, in Galicia and Poland, but may also have included parts of the modern Hungary, they moved southwards and south-eastwards. They were presumably in Dacia, north of the Danube, in the previous century, but they are first mentioned as having crossed that river during the reign of the Emperor Justin I (518-27 A.D.). They were a loosely-knit congeries of tribes without any single leader or central authority; some say they merely possessed the instinct of anarchy, others that they were permeated with the ideals of democracy. The Eastern Slavs, the ancestors of the Russians, were only welded into anything approaching unity by the comparatively much smaller number of Scandinavian (Varangian) adventurers who came and took charge of their affairs at Kiev. Similarly the Southern Slavs were never of themselves able to form a united community, conscious of its aim and capable of persevering in its attainment.

The Slavs did not invade the Balkan peninsula alone but in the company of the Avars, a terrible and justly dreaded nation, who, like the Huns, were of Asiatic (Turkish or Mongol) origin. These invasions became more frequent during the reign of the Emperor Justinian I (527-65 A.D.), and culminated in 559 A.D. in a great combined attack of all the invaders on Constantinople under a certain Zabergan, which was brilliantly defeated by the veteran Byzantine general Belisarius.

The Avars were a nomad tribe, and the horse was their natural means of locomotion. The Slavs, on the other hand, moved about on foot, and seem to have been used as infantry by the more masterful Asiatics in their warlike expeditions. Generally speaking, the Avars, who must have been infinitely less numerous than the Slavs, were settled in Hungary, where Attila and the Huns had been settled a little more than a century previously; that is to say, they were north of the Danube, though they were always overrunning into Upper Moesia, the modern Serbia. The Slavs, whose numbers were without doubt very large, gradually settled all over the country south of the Danube, the rural parts of which, as a result of incessant invasion and retreat, had become waste and empty. During the second half of the sixth century all the military energies of Constantinople were diverted to Persia, so that the invaders of the Balkan Peninsula had the field very much to themselves. It was during this time that the power of the Avars reached its height. They were masters of all the country up to the walls of Adrianople and Salonika, though they did not settle there. The peninsula seems to have been colonized by Slavs, who penetrated right down into Greece; but the Avars were throughout this time, both in politics and in war, the directing and dominating force. During another Persian war, which broke out in 622 A.D. and entailed the prolonged absence of the emperor from Constantinople, the Avars, not satisfied with the tribute extorted from the Greeks, made an alliance against them with the Persians, and in 626 A.D. collected a large army of Slavs and Asiatics and attacked Constantinople both by land and sea from the European side, while the Persians threatened it from Asia. But the walls of the city and the ships of the Greeks proved invincible, and, quarrels breaking out between the Slavs and the Avars, both had to save themselves in ignominious and precipitate retreat.

*Q. What can be correctly inferred about the Balkan Peninsula?*

*A. It did not deteriorate easily.
B. The people are held responsible for the countries desolation.
C. The southern-Slavs appeared first in the sixth century.
D. After their pillage the Huns settled themselves in the place of the Slavs.
E. Belisarius drove back the Avars.*

Solution:

Solution: Statement B is correct because, the author writes that the people were busy in theological disputes and circus; and also in defence of the emperor and the generals, the author writes, “same time to defend...from Armenia to Spain...not more successful”.

Statement C is correct because, the author writes; “In...sixth century... Slavs appear...first time...homes which...in Galicia and Poland...moved southwards and south-eastwards”. After which the author writes that; “They...Dacia...first mentioned as having crossed that river...Justin I (518-27).” Statement D is correct because, according to the passage, the Slavs settled in the Balkan Peninsula. To the north of this was Dacia, where the Huns had settled prior to the Avars. Slavs originated in Dacia.

Statement E is correct because, the author writes that; “The Slavs.. .company of the Avars.. .These invasions.. .great combined attack...defeated... general Belisarius. Statement A is incorrect because, the author writes about the conclusions given in the passage, “what is more probable...accounts of enormous.. .booty.. .exaggerated”.

Hence, the correct answer is option 4.

QUESTION: 17

The Balkan peninsula, which had been raised to a high level of security and prosperity during the Roman dominion, gradually relapsed into barbarism as a result of these endless invasions. The process continued unabated throughout the three following centuries. It is impossible to count the number of times the tide of invasion and devastation swept southwards over the unfortunate peninsula. In the sixth century the Slavs appear for the first time. From their original homes which were immediately north of the Carpathians, in Galicia and Poland, but may also have included parts of the modern Hungary, they moved southwards and south-eastwards. They were presumably in Dacia, north of the Danube, in the previous century, but they are first mentioned as having crossed that river during the reign of the Emperor Justin I (518-27 A.D.). They were a loosely-knit congeries of tribes without any single leader or central authority; some say they merely possessed the instinct of anarchy, others that they were permeated with the ideals of democracy. The Eastern Slavs, the ancestors of the Russians, were only welded into anything approaching unity by the comparatively much smaller number of Scandinavian (Varangian) adventurers who came and took charge of their affairs at Kiev. Similarly the Southern Slavs were never of themselves able to form a united community, conscious of its aim and capable of persevering in its attainment.

The Slavs did not invade the Balkan peninsula alone but in the company of the Avars, a terrible and justly dreaded nation, who, like the Huns, were of Asiatic (Turkish or Mongol) origin. These invasions became more frequent during the reign of the Emperor Justinian I (527-65 A.D.), and culminated in 559 A.D. in a great combined attack of all the invaders on Constantinople under a certain Zabergan, which was brilliantly defeated by the veteran Byzantine general Belisarius.

The Avars were a nomad tribe, and the horse was their natural means of locomotion. The Slavs, on the other hand, moved about on foot, and seem to have been used as infantry by the more masterful Asiatics in their warlike expeditions. Generally speaking, the Avars, who must have been infinitely less numerous than the Slavs, were settled in Hungary, where Attila and the Huns had been settled a little more than a century previously; that is to say, they were north of the Danube, though they were always overrunning into Upper Moesia, the modern Serbia. The Slavs, whose numbers were without doubt very large, gradually settled all over the country south of the Danube, the rural parts of which, as a result of incessant invasion and retreat, had become waste and empty. During the second half of the sixth century all the military energies of Constantinople were diverted to Persia, so that the invaders of the Balkan Peninsula had the field very much to themselves. It was during this time that the power of the Avars reached its height. They were masters of all the country up to the walls of Adrianople and Salonika, though they did not settle there. The peninsula seems to have been colonized by Slavs, who penetrated right down into Greece; but the Avars were throughout this time, both in politics and in war, the directing and dominating force. During another Persian war, which broke out in 622 A.D. and entailed the prolonged absence of the emperor from Constantinople, the Avars, not satisfied with the tribute extorted from the Greeks, made an alliance against them with the Persians, and in 626 A.D. collected a large army of Slavs and Asiatics and attacked Constantinople both by land and sea from the European side, while the Persians threatened it from Asia. But the walls of the city and the ships of the Greeks proved invincible, and, quarrels breaking out between the Slavs and the Avars, both had to save themselves in ignominious and precipitate retreat.

*Q. According to the author, which of the following is/are true relating to the Slavs?*

*A. They dominated the peninsula.
B. They moved southwards and westwards to entirely cover Greece.
C. Moving southwards into Southern Thrace they made a great difference.
D. They always remained in the peninsula.
E. They were useful instruments in the rise of Constantinople.
F. They coined the term 'the Slavonias'.*

Solution:

Solution: Statement D is correct because, along the entire length of the passage, it mentions the Slavs staying in the Peninsula; it also mentions that even the language was influenced by the Slavs; and unlike the Avars there is no mention of their extinction from the Peninsula.

Statement A is incorrect because the passage mentions that although the Slavs “colonized” the peninsula, it was the Avars who were politically and militarily the “dominant” force. Statement B is incorrect as the passage mentions that they “filtered” into Greece. That means they were present in some numbers but they did not cover the entire country.

Statement C is not mentioned in the passage.

Statement E is incorrect since there is no mention of it in the passage.

Statement F is incorrect because it was the Greeks who coined the term, “the Slavonias” and not the Slavs themselves.

Hence, the correct answer is option 2.

QUESTION: 18

The Balkan peninsula, which had been raised to a high level of security and prosperity during the Roman dominion, gradually relapsed into barbarism as a result of these endless invasions. The process continued unabated throughout the three following centuries. It is impossible to count the number of times the tide of invasion and devastation swept southwards over the unfortunate peninsula. In the sixth century the Slavs appear for the first time. From their original homes which were immediately north of the Carpathians, in Galicia and Poland, but may also have included parts of the modern Hungary, they moved southwards and south-eastwards. They were presumably in Dacia, north of the Danube, in the previous century, but they are first mentioned as having crossed that river during the reign of the Emperor Justin I (518-27 A.D.). They were a loosely-knit congeries of tribes without any single leader or central authority; some say they merely possessed the instinct of anarchy, others that they were permeated with the ideals of democracy. The Eastern Slavs, the ancestors of the Russians, were only welded into anything approaching unity by the comparatively much smaller number of Scandinavian (Varangian) adventurers who came and took charge of their affairs at Kiev. Similarly the Southern Slavs were never of themselves able to form a united community, conscious of its aim and capable of persevering in its attainment.

The Slavs did not invade the Balkan peninsula alone but in the company of the Avars, a terrible and justly dreaded nation, who, like the Huns, were of Asiatic (Turkish or Mongol) origin. These invasions became more frequent during the reign of the Emperor Justinian I (527-65 A.D.), and culminated in 559 A.D. in a great combined attack of all the invaders on Constantinople under a certain Zabergan, which was brilliantly defeated by the veteran Byzantine general Belisarius.

The Avars were a nomad tribe, and the horse was their natural means of locomotion. The Slavs, on the other hand, moved about on foot, and seem to have been used as infantry by the more masterful Asiatics in their warlike expeditions. Generally speaking, the Avars, who must have been infinitely less numerous than the Slavs, were settled in Hungary, where Attila and the Huns had been settled a little more than a century previously; that is to say, they were north of the Danube, though they were always overrunning into Upper Moesia, the modern Serbia. The Slavs, whose numbers were without doubt very large, gradually settled all over the country south of the Danube, the rural parts of which, as a result of incessant invasion and retreat, had become waste and empty. During the second half of the sixth century all the military energies of Constantinople were diverted to Persia, so that the invaders of the Balkan Peninsula had the field very much to themselves. It was during this time that the power of the Avars reached its height. They were masters of all the country up to the walls of Adrianople and Salonika, though they did not settle there. The peninsula seems to have been colonized by Slavs, who penetrated right down into Greece; but the Avars were throughout this time, both in politics and in war, the directing and dominating force. During another Persian war, which broke out in 622 A.D. and entailed the prolonged absence of the emperor from Constantinople, the Avars, not satisfied with the tribute extorted from the Greeks, made an alliance against them with the Persians, and in 626 A.D. collected a large army of Slavs and Asiatics and attacked Constantinople both by land and sea from the European side, while the Persians threatened it from Asia. But the walls of the city and the ships of the Greeks proved invincible, and, quarrels breaking out between the Slavs and the Avars, both had to save themselves in ignominious and precipitate retreat.

*Q. Which of the following statements would the author definitely agree on?*

Solution:

Solution: Option 1 is incorrect because the passage mentions that the Balkan peninisula experienced endless invasions and lapsed into Barbarism.Option 2 is incorrect because; the author writes that; “they are first mentioned...reign of the Emperor Justin I ... loosely-knit congeries of tribes”. This implies that the Slavs were a weak force; and the first mention of an attempt of pillage is along with the Avars.Option 3 is incorrect because the passage mentions that the Slavs covered the whole of Russia, overflowed into Macedonia and then “filtered” down into Greece.Option 4 can be implied because they survived and went on to occupy the entire peninsula while the Avars perished. Therefore the Slavs proved to be more ‘clever’ than the Avars. Hence, the correct answer is option 4.

QUESTION: 19

The Balkan peninsula, which had been raised to a high level of security and prosperity during the Roman dominion, gradually relapsed into barbarism as a result of these endless invasions. The process continued unabated throughout the three following centuries. It is impossible to count the number of times the tide of invasion and devastation swept southwards over the unfortunate peninsula. In the sixth century the Slavs appear for the first time. From their original homes which were immediately north of the Carpathians, in Galicia and Poland, but may also have included parts of the modern Hungary, they moved southwards and south-eastwards. They were presumably in Dacia, north of the Danube, in the previous century, but they are first mentioned as having crossed that river during the reign of the Emperor Justin I (518-27 A.D.). They were a loosely-knit congeries of tribes without any single leader or central authority; some say they merely possessed the instinct of anarchy, others that they were permeated with the ideals of democracy. The Eastern Slavs, the ancestors of the Russians, were only welded into anything approaching unity by the comparatively much smaller number of Scandinavian (Varangian) adventurers who came and took charge of their affairs at Kiev. Similarly the Southern Slavs were never of themselves able to form a united community, conscious of its aim and capable of persevering in its attainment.

*Q. As per the passage, which of the following can be correctly inferred from the passage?*

Solution:

Solution: Option 4 is correct because, the author writes that; “Avars were a nomad tribe” and “They were masters...and Salonika”. Thus the author would agree to this statement.Option 1 is incorrect because, the author writes that; “The few Slavs...assimilated by the inhabitants...who were the descendants of the Roman soldiers”. Therefore the inhabitants were descendents of the Romans and not the Slavs.Option 2 is incorrect because, the author writes that; “the Avars...an alliance...Persians...and attacked...while the Persians threatened it from Asia. But the walls...proved invincible...quarrels...between the Slavs and the Avars”. Therefore Persian alliance was not a curse to the Avars.Option 3 is incorrect because, the author mentions that only the Southern Slavs were ready for persevering for an alliance whereas the affairs of the Eastern Slavs were checked by the Scandinavian’s. Therefore the author may not agree to this statement because it is not completely true.Hence, the correct answer is option 4.

QUESTION: 20

*Q. Which of the following descriptions does not apply to Slavs?*

Solution:

Solution: All the options except 2 have been mentioned verbatim in the passage.Option 2 is true of Avars and not Slavs.Hence, the correct answer is option 2.

QUESTION: 21

*Q. Which of the following statements would the author most likely agree with?*

Solution:

Solution: Option 1 should have been “gradually relapsed into barbarism” instead of “gradually grew out of barbarism”.Option 2 is contrary to the data mentioned in the passage- they were never able to form a united community amongst themselves.Option 3 should have been “rural parts” instead of “urban parts”.Option 4 is clearly stated in the passage.Hence, the correct answer is option 4.

*Answer can only contain numeric values

QUESTION: 22

The question below consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from the options.

1. The inherently erratic behaviour of the major renewable energy technologies presents serious problems for power system planners.

2. Ask any power system engineer about renewable energy and you are likely to be told that it doesn’t deliver “base-load” power.

3. It limits how much of these types of renewable power can usefully be fed into the world’s electricity grids; after all, consumers expect power always to be available.

4. In other words, renewable energy can’t be relied upon to provide power 24 hours a day, seven days a week: wind doesn’t always spin the turbines on the hill, the sun cannot shine on solar power stations at night, and even hydroelectricity can run short if the rains don’t come.

Solution:

Solution: At first glance, it is obvious that 4 cannot be the opening statement since “in other words” signifies a summing up or a paraphrase of a previously introduced idea.

The idea of renewable energy’s “base load power” is introduced in 2, which is elaborated upon in 4- “...the sun cannot shine on solar power stations at night...”. Therefore, 4 will follow 2. 1 immediately follows 4 since the shortcomings of solar energy, wind energy and hydroelectricity are all instances of “erratic behaviour” as is stated in 1.

Finally, the pronouns “it” and “these” in 3 are derived from 1 (“it” refers to the erratic behaviour and “these” refers to the major renewable energy technologies).

Hence, the correct answer is option 2413.

*Answer can only contain numeric values

QUESTION: 23

Carefully read the statements in the questions below and arrange them in a logical order.

1. It is not the differentness that worries Conrad but the lurking hint of kinship, of common ancestry.

2. The book opens on the River Thames, tranquil, resting, peacefully "at the decline of day after ages of good service done to the race that peopled its banks.”

3. As though if the Thames were to visit its primordial relative, the Congo, it would run the terrible risk of hearing grotesque echoes of its own forgotten darkness, and falling victim to an avenging recrudescence of the mindless frenzy of the first beginnings.

4. The River Congo is quite decidedly not a River Emeritus as it has rendered no service and enjoys no old-age pension; we are told that “going up that river was like traveling back to the earliest beginnings of the world.”

5. Joseph Conrad's Heart of Darkness projects the image of Africa as "the other world,” the antithesis of Europe and therefore of civilization, a place where man's vaunted intelligence and refinement are finally mocked by triumphant beastiality.

Solution:

Solution: The paragraph details upon the difference in the portrayal of Africa and Europe through the example of the Thames and the Congo in Joseph Conrad's Heart of Darkness. It does so by putting forth the idea of the contrast between Africa and Europe as presented in the book and then presenting examples from the book to support the same. This makes statement 5 a better choice for beginning the sequence than statement 1 which elaborates on the distinction rather than introducing it.

Statement 5 must be followed by statement 2 which elaborates on the Heart of Darkness by mentioning its beginning which is about the river Thames.

Statement 4 follows statement 2 by introducing the river Congo and highlighting the contrast between the Congo and the Thames.

From the remaining statements, we notice that statement 3 elaborates on the “kinship” and “common ancestry” referred to in statement 1 and presents a possible reason for Conrad's worries. Therefore, statement 1 follows statement 4 and statement 3 concludes the paragraph.

Hence, the correct sequence is 52413.

*Answer can only contain numeric values

QUESTION: 24

Carefully read the statements in the questions below and arrange them in a logical order.

1. As he had left Joseph ready to mount his horse, he didn’t think any misfortune might have befallen him, neither did he worry that he might miss the road as it was too plain.

2. He therefore decided to ride slowly ahead, thinking that he would be overtaken shortly.

3. When he reached the top of the hill, Parson Adams looked back and wondered why he couldn’t see Joseph anywhere.

4. The most probable reason that he believed was that Joseph had met with a friend or an acquaintance and their discourse might have taken place for a longer time, causing this delay.

5. He soon arrived at a large puddle of water which had filled the entire road; there was no way to pass, unless one waded through.

Solution:

Solution: Statement 3 is the first statement. Adams has to reach the top of the hill first before he starts guessing why Joseph is not following him.

Statements 1,2, and 4 speak about what Adams thinks could have happened to Joseph. Thus, logically statement 3 goes before any of them.

Statement 1 is where Adams begins to surmise, “...most probable reason” in Statement 4 shows the 1-4 link.

Statement 2 is where Adams decides upon a course of action. The 4-2 link is clear.

Statement 5 can only fit last into the sequence. The 2-5 link is clear. Thus, the correct order is 31425.

*Answer can only contain numeric values

QUESTION: 25

Select the odd man out from the given alternatives.

1. Welcome to the world of food entrepreneurship.

2. Today being known as a chef or a restaurateur is a social compliment.

3. And to cater to the steadily rising need for competent and trained hospitality personnel, catering institutes mushroomed everywhere.

4. The world looks up to the two occupations as something between a wizard or some practitioner of magic with secret ingredients and recipes, and a suave person of the world who can patronise the food connoisseurs.

Solution:

Solution: In these statements, it is easy to establish a link between statements 2 and 4, since 2 talks about how being a “chef’ or “restaurateur” is a social compliment, while 4 elaborates on this by referring to them as “....the two occupations...”.

Therefore, the odd statement has to be decided between sentence 3 and sentence 1.

Sentence 1 is a general statement about “food entrepreneurship”, which refers to ‘carrying out a business in the food sector’. Being either a “chef or “restaurateur” can be considered as a form of entrepreneurship in the food sector. Therefore, this statement has a definite link to the others.

Statement 3 talks about the training of “hospitality personnel” in “catering institutes”. “Personnel” is a broad term that covers all kinds of staff in the hospitality industry, and is not restricted merely to chefs. Also, their education and training is not discussed in any of the other statements. Therefore, this is the odd statement. 2, 4 and 1 form a sequence.

Hence, the correct answer is 3.

*Answer can only contain numeric values

QUESTION: 26

Select the odd man out from the given alternatives.

1. This may or may not turn out to be correct.

2. The possibility of survival after death cannot be considered without taking into account the nature of the human person.

3. When we pose this question with regard to the persistence of immaterial souls, what we find is that there is no problem that needs a solution.

4. A natural way of thinking would seem to be that mind-body dualism is a “survival-friendly” metaphysical view, whereas materialism is inimical to survival.

Solution:

Solution: 2-4-1 follows a logical train of thought - 2 talks about the possibility of survival after death, 4 mentions mind-body dualism, and 1 says that this may or may not be true. “...the persistence of immaterial souls...” in statement 3 is completely disconnected.

Hence, the correct answer is 3.

*Answer can only contain numeric values

QUESTION: 27

Choose the odd one out from the sentences given below.

1. For disinvestment to happen, it remains necessary to work on structural changes in how public sector companies are managed.

2. India needs to prepare its markets and prepare the companies for disinvestment.

3. Public sector companies must be freed of the all-encompassing control of their nodal ministries.

4. Disinvestment remains entirely a political decision and not a decision taken by a disinvestment commission.

Solution:

Solution: All of the statements discuss disinvestment and what needs to be done in-order for disinvestment to take place. However, only three statements among the four form a logical sequence.

From all the statements given, only statement 2 puts forth the main purpose of the other statements.

Statement 1 then goes on to explain how disinvestment can happen and statement 3 elaborates on how the managing of public sector companies needs to change. Thus, statements 2-1-3 form a logical sequence.

Though statement 4 mentions the term “disinvestment”, which may make it seem connected to the other statements, what is being discussed in it about disinvestment being a political decision has nothing to do with the other three statements.

Hence, the correct answer is 4.

QUESTION: 28

Fill in the blanks with the most appropriate pair of words from the given options.

The Indian traditional habit of marrying within one’s caste or community leads to genetic mutations, thus explaining why certain diseases are ______ only in a particular pocket of the _______ in India.

Solution:

Solution: Since according to the context, genetic mutations take place within the community through marriages that happen only within the community, certain diseases are inherent and passed on from one generation of the community to another. The context thus, tells us that these diseases are generally found or prevalent only in that particular pocket of the people belonging to that community. “ Pocket o f eliminates the word ‘community’ as it will further restrict the number of people within the community.

Pocket of “people” will refer to a community, and will be more correctly put as a pocket of “population”. Therefore, we can eliminate options 1, 2 and 4. “Prevalent” is better than “found” and communicates the occurrence and continuity of diseases in a more appropriate manner.

Hence, the correct answer is option 3.

QUESTION: 29

Each of the questions below contains a paragraph followed by alternative summaries. Choose the option that best captures the essence of the paragraph.

Since the beginning of the development of microwave wireless transmission equipment, manufacturers and operators have tried to mitigate the effects of reflected signals associated with signal propagation. These reflections are called multipath. In real-world situations, microwave systems involve careful design to overcome the effects of multipath. Most existing multipath mitigation approaches fall well short of the full reliable information rate potential of many wireless communications systems.

Solution:

Solution: The gist of the passage is: Effects of multipath (reflected signals) are a problem in microwave systems. Design (done carefully) and operation try to overcome these effects. But most approaches are unable to do away with this.

Option 1 is eliminated because it states: “Most systems are inadequate.” Which is not a fact - inadequate in what?

Option 2 is eliminated due to the categorical statement of ‘none’. Option 3 states ‘to overcome multiplepaths’ - changes the terminology and the meaning.

Option 4 captures the essence of the text. One may object to “to achieve the full reliable information rate”. This is not wrong.

Besides, one needs to choose the best and not the ideal.

Hence, the correct answer is option 4.

QUESTION: 30

Each of the questions below contains a paragraph followed by alternative summaries. Choose the option that best captures the essence of the paragraph.

The Great Depression (also known in the U.K. as the Great Slump) was a dramatic, worldwide economic downturn beginning in some countries as early as 1928. The beginning of the Great Depression in the United States is associated with the stock market crash on October 29, 1929, known as Black Tuesday. The depression had devastating effects in both the industrialized countries and those, which exported raw materials. International trade declined sharply, as did personal incomes, tax revenues, prices, and profits. Cities all around the world were hit hard, especially those dependent on heavy industry. Construction was virtually halted in many countries. Farming and rural areas suffered as crop prices fell by 40 to 60 percent. Facing plummeting demand with few alternate sources of jobs, areas dependent on primary sector industries such as farming, mining and logging suffered the most. At the time, Herbert Hoover was President of the United States.

Solution:

Solution: The main points in the paragraph are: 1. What was the Great Depression? 2. Where did it start? 3. What were the effects of the Great Depression?

Option 1 does not mention what the Great Depression was.

Option 2 summarizes the effects of the Great Depression but fails to mention what the Great Depression was and where it started.

In option 3 all the points are covered and are in the right order. The logic of the summary is also right: the start in the USA and the worldwide effects.

Option 4 states that a decline in the farming and construction sectors in the non-industrialized countries started the Great Depression, which is not true as can be inferred from the passage. Hence, the correct answer is option 3.

*Answer can only contain numeric values

QUESTION: 31

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Identify the total number of sentences that are grammatically incorrect.

1. Accustomed as we are to think of China as greatest peace-loving nation on earth, we are in some danger of forgetting her experience of war.

2. Her long military annals stretch back to point at which they are lost in the mists of time.

3. The perpetual collisions of the ancient feudal states accompanied the overthrow of many dynasties.

4. No less remarkable is the succession of illustrious captains to who China can point with pride.

Solution:

Solution: When we use the superlative, we need to precede it with the definite article ‘the’. Statement 1 should read as ‘the greatest peace-loving nation...’.

The phrase “to point” means ‘to show specifically’ or ‘show direction of. In statement 2, it should be ‘to a point’, which means a certain point in the history or past.

In statement 4, the pronoun should be ‘whom’ (objective) and not “who” (subjective) as it follows the preposition “to”.

Therefore, there are total 3 grammatically incorrect sentences. Hence, the correct answer is 3.

*Answer can only contain numeric values

QUESTION: 32

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Identify the total number of sentences that are grammatically correct and appropriate.

1. Now this is virtually the predicament of the body we call a sun when in the immediate presence of another body of similar great mass.

2. The component gases are held in a state of rigidity by the tremendous gravitational force of its own aggregate mass.

3. At the surface of such a body is enveloped in a shell of relatively cool matter.

4. The consequence will be a tidal deformation of the whole body.

Solution:

Solution: In sentence 2, the antecedent (noun which the pronoun refers to) of the pronoun “its” is “gases”, which is plural and should take the pronoun “their”.

There is no need for the preposition “of’ (the first one) in sentence 3. It should be written as, ‘At the surface, such a body is enveloped in a shell of relatively cool matter’ to be correct.

The other sentences are grammatically correct.

Hence, the correct answer is 2.

QUESTION: 33

Fill in the blanks with the most appropriate pair of words from the given options.

A virtually ___________ problem facing the translator of Franz Kafka is how to deal with the author's intentional use of ___________ terms or of words that have several meanings.

Solution:

Solution: Option 1 is eliminated because of “versatile”. For the second blank we need a word that describes terms or words that have several meanings (which is the reason why Kafka is so difficult to translate). “Ambiguous” in option 3 is a better word to use in this context than “versatile”.

Option 2 is eliminated because “virtually simple” does not make sense with “problem”.

Option 4 is eliminated because of “simple”. Simple terms are not likely to have several meanings.

Option 3 makes perfect sense logically.

Hence, the correct answer is option 3.

QUESTION: 34

The following question has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

Last month Soozlon-acquired Hunksen Transmissions International, a maker of gearboxes for wind turbines, was listed on the London Stock Exchange. Nothing noteworthy about that, you might say, despite the jump in the share price on the first day of trading and the handsome gain since: green technology is all the rage, is it not? But Hunksen exemplifies another trend too, which should prove every bit as durable: the rise of multinational companies from emerging econom ies._______________ .

Solution:

Solution: Option 1 makes the content of the paragraph an exception, hence will go against “the trend” mentioned in the paragraph.

Option 2 will require quite a lot of clarification/assumptions about “Economic theory” to make it the concluding sentence.

Option 3 dilutes “another trend” - if the world is replete with such examples we cannot call it a mere trend.

However, someone has to begin “another trend”. Its parent (of the trend) brings us back to Soozlon, hence option 4 is correct.

Hence, the correct answer is option 4.

*Answer can only contain numeric values

QUESTION: 35

Group Question

Answer the following question based on the information given below.

A company wants to recruit a group of five people — one expert each for Java, C, C++, SQL and ERP. There are 12 probable candidates. The following is known about them.

A. Akash and Preeti are experts in C and C++ only.

B. Mohit and Chandni know only SQL very well.

C. Of Ashish, Swati, Neha and Khushi, exactly two know Java and the other two know ERP.

D. Aradhana does not want to work with Vikas. However both of them are experts in all the five fields. Hence one of them has to be necessarily selected.

E. Kashika and Dripto who are twins and good only in ERP and C++, will work only if both of them are selected.

*Q. In how many ways can a team of 5 be formed (for various combinations i.e., person and field) if Kashika is not part of the team?*

Solution:

Solution: If Kashika is not part of the team then Dripto is also not there in the team.

One of Vikas or Aradhana has to be selected. This can be done in 2 ways.

We need to select remaining 4 people from the list.

Among the 8 remaining people two are experts in C as well as C++. There are two experts each for Java, ERP and SQL.

We will first consider Vikas or Aradhana to be an expert in C (or C++).

Then we can choose one expert for C++ (or C) in 2 ways, one expert for ERP in 2 ways, one expert for Java in 2 ways and one expert for SQL in 2 ways.

Thus, when Vikas or Aradhana is an expert of C , we can choose a team of 5 in 2 * 2 x 2 x 2 x 2 = 32 ways.

When Vikas or Aradhana is an expert of C++ we can choose a team 0f 5 in 2 x 2 x 2 x 2 x 2 = 32 ways.

Hence, Vikas or Aradhana is an expert of C or C++ we can choose a team of 5 in 2 x 32 ways.

Now, we consider that Vikas or Aradhana is an expert of Java.

One of them can be selected in 2 ways.

Then, both Akash and Preeti have to be selected as they are the only ones who are expert in C and C++.

One expert for SQL can be selected in 2 ways and one expert for ERP can be selected in another 2 ways.

Thus, when Vikas or Aradhana is an expert of Java, we can choose a team 0f 5 in 2x2x2x2 = 2 x 8 ways.

Similarly, when Vikas or Aradhana is an expert of SQL and ERP, we can choose a team of 5 in 2 x 8 ways.

Thus, total number of ways to choose a team of 5, when Kashika is not a part of team = 2 x (32 + 8 + 8 + 8)= 112 Answer: 112

*Answer can only contain numeric values

QUESTION: 36

A company wants to recruit a group of five people — one expert each for Java, C, C++, SQL and ERP. There are 12 probable candidates. The following is known about them.

A. Akash and Preeti are experts in C and C++ only.

B. Mohit and Chandni know only SQL very well.

C. Of Ashish, Swati, Neha and Khushi, exactly two know Java and the other two know ERP.

D. Aradhana does not want to work with Vikas. However both of them are experts in all the five fields. Hence one of them has to be necessarily selected.

E. Kashika and Dripto who are twins and good only in ERP and C++, will work only if both of them are selected.

*Q. If it is known that Ashish and Neha know Java while Swati and Khushi know ERP, then in how many ways can a team of 5 be formed with Ashish and Swati in it?*

Solution:

Solution: If two members are present in the team with one of them knowing ERP, we cannot take Kashika and Dripto in the team as one of them will have to be an ERP expert.

We consider three cases.

Case i: Aradhna/Vikas are selected for C in 2 ways.

Akash/Preeti are selected for C++ in 2 ways.

Mohit/Chandni are selected for SQL in 2 ways.

Total number o f ways = 2 x 2 x 2 = 8 Case ii: AradhnaA/ikas are selected for C++ in 2 ways.

Akash/Preeti are selected for C in 2 ways.

Mohit/Chandni are selected for SQL in 2 ways.

Total number o f ways = 2 x 2 x 2 = 8 Case iii: Aradhna/Vikas are selected for SQL in 2 ways.

Akash and Preeti are selected for C and C++ in 2 ways.

Total number of ways = 4

Thus the team of five can be formed in 8 + 8 + 2 = 20 ways. Answer: 20

*Answer can only contain numeric values

QUESTION: 37

A company wants to recruit a group of five people — one expert each for Java, C, C++, SQL and ERP. There are 12 probable candidates. The following is known about them.

A. Akash and Preeti are experts in C and C++ only.

B. Mohit and Chandni know only SQL very well.

C. Of Ashish, Swati, Neha and Khushi, exactly two know Java and the other two know ERP.

D. Aradhana does not want to work with Vikas. However both of them are experts in all the five fields. Hence one of them has to be necessarily selected.

E. Kashika and Dripto who are twins and good only in ERP and C++, will work only if both of them are selected.

*Q. If Akash is selected for C and Neha for Java, then in how many ways can the remainder be selected?*

Solution:

Solution: Case 1: Dripto and Kashika are selected for ERP and C++ One of Aradhana and Vikas has to be selecetd for SQL.

Thus the team can be selected in 4 ways.

Case 2: Dripto and Kashika are not selected.

We assume (without loss of generality) that Ashish and Neha are Java experts and Swati and Khushi are ERP experts.

This case has three subcases.

Subcase /: One out of Aradhna and Vikas is selected for C++ in 2 ways. (Preeti is not selected.) One out of Swati and Khushi is selected for ERP in 2 ways. One out of Mohit and Chandni is selected for SQL in 2 ways. Total number o f ways = 2 x 2 x 2 = 8 Subcase //: One out of Aradhna and Vikas is selected for ERP in 2 ways. Preeti is selected for C++ in 1 way.

One out of Mohit and Chandni is selected for SQL in 2 ways. Total number of ways = 2 x 1 x 2 = 4

Subcase ///: One out of Aradhna and Vikas is selected for SQL in 2 ways.

Preeti is selected for C++ in 1 way.

One out of Swati and Khushi is selected for ERP in 2 ways.

Total number o f ways = 2 x 1 x 2 = 4 The total number of ways in which the team can be selected = 4 + 8 + 4 + 4 = 20

Answer: 20

*Answer can only contain numeric values

QUESTION: 38

A company wants to recruit a group of five people — one expert each for Java, C, C++, SQL and ERP. There are 12 probable candidates. The following is known about them.

B. Mohit and Chandni know only SQL very well.

C. Of Ashish, Swati, Neha and Khushi, exactly two know Java and the other two know ERP.

D. Aradhana does not want to work with Vikas. However both of them are experts in all the five fields. Hence one of them has to be necessarily selected.

E. Kashika and Dripto who are twins and good only in ERP and C++, will work only if both of them are selected.

*Q. If Dripto, Mohit and Chandni are definitely not selected, then probability that Aradhana is selected. (Note: Round off your answer upto one decimal place.)*

Solution:

Solution: Since one among Aradhana and Vikas is selected, the required probability =1/2 Answer: 0.5

QUESTION: 39

Group Question

Answer the following question based on the information given below.

Eight friends: A, B, C, D, E, F, G and H have among them Apple, Banana, Orange, Guava, Papaya, Mango, Pomegranate and Carrot in that order. The total number of fruits between them is 36 and further no two of the friends have the same number of fruits with them and each friend has fruits of that type only and atleast one unit of the type of fruit they have.

Further, the following information regarding the distribution of fruits is known:

I. The total number of Apples and Papayas is the same as number of Pomegranates that G has.

II. Oranges and Guavas put together are 10 in number.

III. The total number of Papaya and Mangoes is 8.

IV. Apples and oranges together are 6 in number.

V. If the number of fruits that F has is not equal to 6, then H will have more fruits than F.

VI. If the number of Papayas is not equal to 1, then the number of carrots is greater than Bananas.

VII. If the number of fruits with G is not 8, then the number of fruits with F will be greater than the number of fruits with B.

VIII. If the number of Bananas is not 5, then the number of Pomegranates is also not 5.

IX. If E does not have 3 fruits with him, then C does not have 4 fruits with him.

*Q. Who among the following has got the largest number of units of fruits with him?*

Solution:

Solution: For the sake of simplicity lets consider that the number of apples that A has is a.

Total number of fruits that A has and the total number of apples will be a.

Similarly, let the number of Bananas be b, Oranges be c, Guavas be d, Papayas be e, Mangoes be f, Pomegranates be g and Carrots be h.

Now since the total number of fruits with them is 36 and none of the two friends have the same number of fruits with them, it implies that they have between them 1,2,3, 4, 5, 6, 7 and 8 fruits.

From the given conditions we have: From (I), a + e = g ...(i) From (II), c + d = 10 ...(ii) From (III), e + f = 8 ...(iii) From (IV), a + c = 6 ...(iv)

From (V), If f 6 then h > f ...(v) From (VI), If e 1 then h > b ...(vi) From (VII), If g 8 then f > b ...(vii) From (VIII), If b 5 then g 5 ...(viii) From (IX), If e 3 then c 4 ...(ix) From (ii) and (iv), we have: d = a + 4 ...(x) This implies that d __>__ 5 If d = 5, then from (ii) we have c = 5, which is not possible,

of d 5

Similarly, from the above equations the possible values for variables can be as shown:

From (iii) we have the possible set of values for e and f as follows:

For the values of d, c and a there are only two cases possible. Consider Case 1: d = 6, c = 4 and a = 2 We have from (i), the possible values of g for corresponding values of e:

From (ix), if e 3 then c 4 , In this case since e = 1 or 5, and c = 4, it would mean a contradiction.

This case is not possible.

Consider Case 2: d = 8, c = 2 and a = 4

Case 2a: d = 8 , c = 2, a = 4, e = 1, g = 5 and f = 7. So b and h should be from 3 and 6.

From (v): If f 6 then h > f, in this case f = 7, implies that h < f and hence a contradiction.

This case is not valid.

Case 2b: d =8, c = 2, a = 4, e = 5, g = 9 and f = 3 From (i) we have, a + e = g But g cannot be 9.

This case is not valid.

Case 2c: d = 8, c = 2, a = 4, e = 3, g = 7 and f = 5

This case doesnot violate any of the conditions and hence is valid. From (vi) we get that, If e 1 then h > b. h = 6 and b = 1 The final set of corresponding values would then be:

From the table we get that D has the maximum number of units of fruits with him.

Hence, option 4.

QUESTION: 40

Eight friends: A, B, C, D, E, F, G and H have among them Apple, Banana, Orange, Guava, Papaya, Mango, Pomegranate and Carrot in that order. The total number of fruits between them is 36 and further no two of the friends have the same number of fruits with them and each friend has fruits of that type only and atleast one unit of the type of fruit they have.

Further, the following information regarding the distribution of fruits is known:

I. The total number of Apples and Papayas is the same as number of Pomegranates that G has.

II. Oranges and Guavas put together are 10 in number.

III. The total number of Papaya and Mangoes is 8.

IV. Apples and oranges together are 6 in number.

V. If the number of fruits that F has is not equal to 6, then H will have more fruits than F.

VI. If the number of Papayas is not equal to 1, then the number of carrots is greater than Bananas.

VII. If the number of fruits with G is not 8, then the number of fruits with F will be greater than the number of fruits with B.

VIII. If the number of Bananas is not 5, then the number of Pomegranates is also not 5.

IX. If E does not have 3 fruits with him, then C does not have 4 fruits with him.

*Q. Who among the following has the number of units of a fruit that is a perfect square?*

Solution:

Solution: Only 4 among these numbers is a perfect square and A has 4 apples.

Hence, option 2.

QUESTION: 41

Eight friends: A, B, C, D, E, F, G and H have among them Apple, Banana, Orange, Guava, Papaya, Mango, Pomegranate and Carrot in that order. The total number of fruits between them is 36 and further no two of the friends have the same number of fruits with them and each friend has fruits of that type only and atleast one unit of the type of fruit they have.

Further, the following information regarding the distribution of fruits is known:

I. The total number of Apples and Papayas is the same as number of Pomegranates that G has.

II. Oranges and Guavas put together are 10 in number.

III. The total number of Papaya and Mangoes is 8.

IV. Apples and oranges together are 6 in number.

V. If the number of fruits that F has is not equal to 6, then H will have more fruits than F.

VI. If the number of Papayas is not equal to 1, then the number of carrots is greater than Bananas.

VII. If the number of fruits with G is not 8, then the number of fruits with F will be greater than the number of fruits with B.

VIII. If the number of Bananas is not 5, then the number of Pomegranates is also not 5.

IX. If E does not have 3 fruits with him, then C does not have 4 fruits with him.

*Q. What is the difference in the number of Oranges and Apples?*

Solution:

Solution: From the table given in the solution of the first question of the set we get that: Number of apples = 4 and number of oranges = 2 The required difference is 4 - 2 = 2 Hence, option 3.

QUESTION: 42

Eight friends: A, B, C, D, E, F, G and H have among them Apple, Banana, Orange, Guava, Papaya, Mango, Pomegranate and Carrot in that order. The total number of fruits between them is 36 and further no two of the friends have the same number of fruits with them and each friend has fruits of that type only and atleast one unit of the type of fruit they have.

Further, the following information regarding the distribution of fruits is known:

II. Oranges and Guavas put together are 10 in number.

III. The total number of Papaya and Mangoes is 8.

IV. Apples and oranges together are 6 in number.

V. If the number of fruits that F has is not equal to 6, then H will have more fruits than F.

VI. If the number of Papayas is not equal to 1, then the number of carrots is greater than Bananas.

VII. If the number of fruits with G is not 8, then the number of fruits with F will be greater than the number of fruits with B.

VIII. If the number of Bananas is not 5, then the number of Pomegranates is also not 5.

IX. If E does not have 3 fruits with him, then C does not have 4 fruits with him.

*Q. Which pair of the following has got the least number of units of fruits between them?*

Solution:

Solution: Referring the table given in the solution of the first question of the set we get that: a + d= 12

e + f = 8

f + g= 12

d + h = 14

d + f = 13 From these e + f is the least.

Hence, option 1.

QUESTION: 43

Group Question

Answer the following question based on the information given below.

Amar and Ajit play a mathematical game with each other. The rules are as follows

1. A player gives a name to the other player and the other player has to tell the sum of the position of the letters of the name in the alphabetical list.

2. If the name given is denoted by X, then the sum is denoted by S(X). For example, S(AMAR) = 1 + 13 + 1 + 18 = 33

Answer the following questions based on the information above.

*Q. If S(X) = 100, and X is of 10 letters, how many A’s can X contajn at the maximum?*

Solution:

Solution: We have to maximize the occurrence of A’s. A holds a value of 1 and the name is of 10 characters. Having all the 10 A’s would give us a total of 10 but S(X) =10 Thus we have to occupy the remaining letters with Z.

If Z occupies 4 places, then total due to Z is 26 * 4 = 104 which exceeds 100.

Thus Z occupies 3 places giving a total of 78.

One of the places has to be occupied by P giving the total to be 78 + 16 = 94 Thus the remaining 6 places have to be occupied by A giving the total of 100 Hence, option 4.

QUESTION: 44

Amar and Ajit play a mathematical game with each other. The rules are as follows

1. A player gives a name to the other player and the other player has to tell the sum of the position of the letters of the name in the alphabetical list.

2. If the name given is denoted by X, then the sum is denoted by S(X). For example, S(AMAR) = 1 + 13 + 1 + 18 = 33

Answer the following questions based on the information above.

*Q. X and Y are two 10 lettered names having at least 5 vowels. What is the largest value of S(X) - S(Y)?*

Solution:

Solution: S(X) - S(Y) is largest when S(X) is largest and S(Y) is smallest The largest value of S(X) occurs when there are 5 U’s and the remaining places are occupied by Z.

The smallest value of S(Y) occurs when all the letters are A’s.

Thus S(X) = 235 and S(Y) = 10 S(Y) - S(X) = 225

Hence, option 1.

QUESTION: 45

Group Question

Answer the following question based on the information given below.

Certain set of scientist device a robot. They have trained it such that it moves according to the color in the command issued. The speed (in m/s) with which it moves is fed together with the command. The various color symbols are as follows:

1. WHITE - START (Starts moving towards North with a speed of 5 m/s)

2. YELLOW - TURN North West

3. GREEN - TURN towards North

4. BLUE - TURN North East

5. ORANGE - TURN towards East

6. BROWN - TURN South East

7. BLACK - TURN towards South

8. PURPLE - TURN South West

9. MAGENTA - TURN towards West

10. RED-STOP

For example: The robot keeps moving once it has got a particular direction and speed. A typical instruction to the robot for example is YELLOW, 12 which means it has to go at a speed of 12 m/s after turning North West till the next instruction is issued.

Answer the following questions based on the information below.

*Q. The robot is given following instruction where T indicates the 3Marks time the robot gets the instruction.
T = 0: WHITE*

*T= 1: YELLOW, 4*

*T = 3: MAGENTA, 6*

*T = 5: RED*

*Find the shortest distance (in m) of the robot from its start position.*

*T = 1: YELLOW, 4 means as soon as the first second ends, the robot turns North West and moves at speed of 4 m/s till he gets the next instruction.*

Solution:

Solution: START is for 1 s which means that it moves 5 m North.

YELLOW is for 2 s which means it turns North West and moves for 8 m which is

MAGENTA is for 2 s which means it turns West and moves for 12 m.

Thus, totally it has moved North and West.

Hence, option 1.

QUESTION: 46

Certain set of scientist device a robot. They have trained it such that it moves according to the color in the command issued. The speed (in m/s) with which it moves is fed together with the command. The various color symbols are as follows:

1. WHITE - START (Starts moving towards North with a speed of 5 m/s)

2. YELLOW - TURN North West

3. GREEN - TURN towards North

4. BLUE - TURN North East

5. ORANGE - TURN towards East

6. BROWN - TURN South East

7. BLACK - TURN towards South

8. PURPLE - TURN South West

9. MAGENTA - TURN towards West

10. RED-STOP

For example: The robot keeps moving once it has got a particular direction and speed. A typical instruction to the robot for example is YELLOW, 12 which means it has to go at a speed of 12 m/s after turning North West till the next instruction is issued.

Answer the following questions based on the information below.

*Q. How many minimum commands does a robot need to move with a constant speed of 5 m/s and reach a point 30 m towards South and 40 m towards West?*

Solution:

Solution: To move to 30 m South and 40 m West, he needs to move 50 m South West. So, it has to have the following commands: T = 0: WHITE

T = 0: PURPLE, 10

T= 10: RED

Hence, option 2.

QUESTION: 47

Group Question

Answer the following question based on the information given below.

A + B means A is the uncle of B.

A - B means A is the nephew of B.

A * B means A is the brother of B.

*Q. A * B + C means: *

Solution:

Solution: A * B means that A is the brother of B, and B + C means B is the uncle of C.

Hence A is either C’s father or C’s uncle.

Hence C is A’s son or daughter or nephew or niece.

Hence statement 1 is not definitely true.

Similarly statement 2 is also not definitely true. Option 2 can be considered if C can only be A’s son or nephew.

However, C can be A’s daughter or niece as well. Hence option 4.

QUESTION: 48

A + B means A is the uncle of B.

A - B means A is the nephew of B.

A * B means A is the brother of B.

*Q. P - Q + R means:*

Solution:

Solution: P is the nephew of Q and Q is the uncle of R.

Thus, P can be the brother or cousin of R. The same applies to R.

Thus, P has a sibling if R is his brother, but has no sibling if R is his cousin.

Thus, P (as well as R) may or may not have a sibling.

Hence, options 1 and 3 can be eliminated.

Now, if P and R are cousins, it means that Q has two siblings who are the parents of P and R.

If P and R are siblings, it means that Q has a sibling who is the father or mother of P and R. Thus, “Q has a sibling” or “Q has two siblings”.

Therefore, the statement in option 2 may or may not be true. Hence, option 4.

QUESTION: 49

Group Question

Answer the following question based on the information given below.

The hostels in a management institute are named after rivers. One can reach the destination hostel, only via the intermediate hostel specified in the table below, which also gives the least time required to move from the intermediate hostel to destination hostel.

*Q. If Vikram starts from hostel Tapti and has to come back to it after crossing all the hostels at least once, then what is the minimum possible time that he would take?*

Solution:

Since Vikram starts from Tapti and has to come back to it, note that he can go from Tapti to either Narmada or Sarayu but he can come to Tapti only through Saravathi.

Therefore, work backwards and trace his route.

The only way to reach Tapti is through Saravathi.

Similarly, the only way to reach Saravathi is through Brahmnaputra.

Therefore, Vikram definitely travels along Brahmaputra- Saravathi-Tapti i.e. 4 + 10 = 14 minutes.

Now, Vikram can reach Brahmaputra through either Cauvery or Narmada.

Also, note that Vikram can reach Narmada only in one way but can reach Sarayu in two ways (either from Tapti or from Krishna).

Therefore, Vikram definitely goes from Tapti to Narmada and takes 10 minutes in doing so.

Thus, Vikram definitely spend 14 + 10 = 24 minutes.

Only the remaining time can be minimised.

Since Vikram can reach Brahmaputra in 2 ways.

Case 1 : Vikram reaches Brahmaputra directly through Narmada.

The only route possible satisfying all these conditions is: Narmada - Brahmaputra - Krishna - Sarayu - Cauvery - Brahmaputra.

This route takes 6 + 4 + 5 + 5 + 3 = 23 minutes Case 2 : Vikram reaches Brahmaputra through Cauvery.

The shortest route possible satisfying all these conditions is: Narmada - Cauvery - Krishna - Sarayu - Cauvery - Brahmaputra.

This route takes 6 + 3 + 5 + 5 + 3 = 22 minutes Thus, to minimise the time, the route that Vikram should take is:

Tapti —> Narmada —> Cauvery —> Krishna —► Sarayu —► Cauvery -> Brahmaputra -> Saravathi —> Tapti The minimum time taken by Vikram = 10 + 2 2 + 14 = 46 minutes Hence, option 2.

QUESTION: 50

A school has four sections A, B, C, D of Class IX students.

The results of half yearly and annual examinations are shown in the table given below.

Q. If the number of students passing an examination be considered a criteria for comparison of difficulty level of two examinations, which of the following statements is true in this context?

Solution:

Number of students who passed half-yearly exams in the school

= (Number of students passed in half-yearly but failed in annual exams) + (Number of students passed in both exams)

= (6 + 17 + 9 + 15) + (64 + 55 + 46 + 76)

= 288.

Also, Number of students who passed annual exams in the school

= (Number of students failed in half-yearly but passed in annual exams) + (Number of students passed in both exams)

= (14 + 12 + 8 + 13) + (64 + 55 + 46 + 76) = 288.

Since, the number of students passed in half-yearly = the number of students passed in annual exams. Therefore, it can be inferred that both the examinations had almost the same difficulty level.

Thus Statements (a), (b) and (d) are false and Statement (c) is true.

*Answer can only contain numeric values

QUESTION: 51

Group Question

Answer the following question based on the information given below.

The chart below gives the number of female students as a percentage of the total number of students getting mentored at a particular institute:

If the sum total of the various combinations shown in the pie chart is 15000 and the number of female students getting mentored at Career Setters, Adept Trainers, Real Insight and Dreamz Academy is represented as A, B, C and D respectively, then the graph below depicts the combination of female students of various institutes as apercentage of the sum total of the various combinations shown in the pie chart.

*Q. What is the number of male students studying at Adept Trainers?*

Solution:

Solution: From the chart we get that: A + B + C = 37% of 15000 = 5550 ...(i) B + C + D = 42% of 15000 = 6300 ...(ii) B - C = 4% of 15000 = 600 ...(iii) A + D = 17% of 15000 = 2550 .. .(iv) Adding (i) and (ii) we get: A + 2(B + C ) + D = 11850 ...(v) From (iv), A + D = 2550 B + C = 4650 ...(vi)

Solving (vi) and (iii) we get, B = 2625 C = 2025

Substituting the value of B and C in (i) we get,

A = 900

Substituting the value of D in (iv) we get, Now from the first chart given we know that A = 900 represents 10% of the total students at Career Setters.

Total students at Career setters will be 9000 Number of male students at Career Setters = 8100 Similarly we can calculate the number of male and female students for other institutes also.

The data for total students and break up of students can be tabulated as shown below,

From the table we can see that the number of male students studying at Adept Trainers is 6125.

ANSWER: 6125.

*Answer can only contain numeric values

QUESTION: 52

The chart below gives the number of female students as a percentage of the total number of students getting mentored at a particular institute:

If the sum total of the various combinations shown in the pie chart is 15000 and the number of female students getting mentored at Career Setters, Adept Trainers, Real Insight and Dreamz Academy is represented as A, B, C and D respectively, then the graph below depicts the combination of female students of various institutes as apercentage of the sum total of the various combinations shown in the pie chart.

*Q. The number of male students in Career Setters is more or less than the number of female students at Dreamz Academy by what percentage? *

Solution:

Solution: Number of male students at Career Setters = 8100 Number of female students at Dreamz Academy = 1650

The number of Male students at Career setters is more than number of female students by: 8100- 1650 = 6450

The required percentage =

ANSWER : 390.9%.

*Answer can only contain numeric values

QUESTION: 53

The chart below gives the number of female students as a percentage of the total number of students getting mentored at a particular institute:

If the sum total of the various combinations shown in the pie chart is 15000 and the number of female students getting mentored at Career Setters, Adept Trainers, Real Insight and Dreamz Academy is represented as A, B, C and D respectively, then the graph below depicts the combination of female students of various institutes as apercentage of the sum total of the various combinations shown in the pie chart.

*Q. 2000 additional students seek admission in Career Setters, Adept Trainers, Real Insight and Dreamz Academy in the ratio of 4 : 3 : 2 : 1 Which institute has the maximum percentage of male students of the total students of that institute if all the new students who take admission are females?*

Solution:

Solution: The split up of 2000 students among these four institutes would be in ratio: 4 : 3 : 2 : 1, i.e. 800, 600, 400 and 200 in that order in Career Setters, Adept Trainers, Real Insight and Dreamz Academy respectively.And it is given that all the new students who take admission are females.

∴ The percentage of male students in Career Setters

Percentage of male students in adept Trainers =

Percentage of male students in real Insight =

Percentage of male students in Dreamz Academy =

The maximum percentage of male students would be at Career Setters.

ANSWER: 1

*Answer can only contain numeric values

QUESTION: 54

The chart below gives the number of female students as a percentage of the total number of students getting mentored at a particular institute:

*Q. 2000 additional students seek admission in Career Setters Adept Trainers, Real Insight and Dreamz Academy in the ratio of 4 : 3 : 2 : 1. If the total number of female students that have been added is the same as the number of female students that are mentored at Career Setters after the addition, then the total number of male students that have been added cannot be less than:*

Solution:

Solution: It is given that 2000 students have been added in the ratio 4 : 3 : 2 : 1

Number of students added in Career Setters will be 800. v The total number of female students that have been added is same as the number of female students that are mentored at Career Setters after the addition, Maximum number of females that can be at Career Setters = 900 + 800 = 1700

Now this would also be the maximum number of female students that could have been added.

Number of male students that have been added cannot be less than = 2000 - 1700 = 300 ANSWER : 300.

QUESTION: 55

Group Question

Answer the following question based on the information given below.

The following figure shows the number of accidents and the number of survivors for the months of January to May of the year 2014 in a sub-area of a district. Safety ratio = No. of Survivors / No. of Accidents

*Q. On an average, how many accidents took place per month considering the period between February and May (both months included)? *

Solution:

Solution: Required average = (25 + 35 + 15 + 20) / 4 = 23.75 Hence, option 2.

QUESTION: 56

The following figure shows the number of accidents and the number of survivors for the months of January to May of the year 2014 in a sub-area of a district. Safety ratio = No. of Survivors / No. of Accidents

*Q. The maximum safety ratio among all the months was: *

Solution:

Hence, option 3.

QUESTION: 57

Group Question

Answer the following question based on the information given below.

The performance of a certain cricket team Shaka Laka when playing against its rival Jhinga Lala is shown by the 2 graphs below.

While batting, the following chart is applicable.

Here, the x-axis represents the strike rate (runs scored per 100 balls faced) while the y-axis represents the number of balls faced.

While bowling, the following chart applies.

Here, the x-axis represents the runs per over by a bowler and the y- axis represents the number of overs bowled.

Apart from the runs given in the graph, there are no more runs scored. Shaka Laka batted first.

*Q. What is the total number of runs scored by Shaka Laka?*

Solution:

Solution: Total number of runs scored by a player = Strike Rate (per 100 balls) x Number of Balls Faced Total number of runs scored by Shaka Laka = Sum of runs scored by each player.

Here, for instance, Mehwag has a strike rate of 125 and has faced 40 balls, thus he scored 1.25 x 40 = 50 runs.

Similarly, the number of runs scored by each player can be calculated.

Exam Reports

Mehwag : 1.25 x 40 = 50 Fendulkar: 0.8 x 15 = 12 Sarthik : 0.7 x 50 = 35 Bhoni: 0.9 x 30 = 27 Tohli: 0.7 x 50 = 35 Baina : 0.9 x 60 = 54 Hathan: 1.4x30 = 42 Radeja : 1.1 x 20 = 22 Sumar: 1 x 5 = 5 Thus, total number of runs scored = 282 Hence, option 2.

QUESTION: 58

The performance of a certain cricket team Shaka Laka when playing against its rival Jhinga Lala is shown by the 2 graphs below.

While batting, the following chart is applicable.

Here, the x-axis represents the strike rate (runs scored per 100 balls faced) while the y-axis represents the number of balls faced.

While bowling, the following chart applies.

Here, the x-axis represents the runs per over by a bowler and the y- axis represents the number of overs bowled.

Apart from the runs given in the graph, there are no more runs scored. Shaka Laka batted first.

*Q. How many runs did Jhinga Lala lose by? *

Solution:

Solution: It is given that Shaka Laka batted first.Margin of Shaka Laka’s victory = Runs scored by Shaka Laka - Runs conceded by Shaka Laka From the solution to the previous question, total number of runs scored by Shaka Laka = 282 The runs scored by Jhinga Lala (or conceded by Shaka Laka) = Sum of runs given by all the bowlers.

The runs given by a particular bowler = runs per over for the bowler * number of overs bowled by that bowler.

The runs conceded by each bowler can be calculated as shown in the table below.

Thus, the total number of runs scored by Jhinga Lala = 280 Thus, Jhinga Lala lost by 2 runs Hence, option 1.

QUESTION: 59

Group Question

Answer the following question based on the information given below.

A multi-locational shoe manufacturing company has four plants, one in each of the following cities: Mumbai, Delhi, Hyderabad and Bangalore.

The graph below gives the break-up of the revenue earned by the company from each of the four plants in terms of percentage of the total revenue for two different years.

The revenue earned from each plant grew by atleast 10% in Year 2 when compared to Year 1.

*Q. If the total revenue earned by the company in Year 1 was Rs.50 crores, then what could be the possible revenue (in Rs. crores) of the company in Year 2? *

Solution:

Solution: Except for the Mumbai plant, all other plants had shown an increase in contribution to the total revenue in Year 2 as compared to Year 1.

So it can be concluded that Mumbai plant had grown the least from Year 1 to Year 2.

To find the least possible revenue of the company in Year 2, consider the increase in revenue of the Mumbai plant in Year 2 to be the least i.e. 10% Now, the revenue in Year 1 was Rs. 50 Crores.

Contribution of the Mumbai plant in revenue of Year 1 = 90% of 50 = 90 x 50/100 = 45 crores Contribution of the Mumbai plant in revenue of Year 2 = 1.1 x 45 = 49.5 crores This represents 60% of the revenue in Year 2.

So, the minimum revenue in Year 2 = 100 x 49.5/60 = 82.5 crores.

All the options except option 3 are less than this value.

So the possible revenue is 90 crores.

Hence, option 3.

QUESTION: 60

A multi-locational shoe manufacturing company has four plants, one in each of the following cities: Mumbai, Delhi, Hyderabad and Bangalore.

The graph below gives the break-up of the revenue earned by the company from each of the four plants in terms of percentage of the total revenue for two different years.

The revenue earned from each plant grew by atleast 10% in Year 2 when compared to Year 1.

*Q. If the growth in revenue from the Delhi plant in Year 2 is 100% more than that of the Mumbai plant, then what is the percentage increase in the total revenue of the company?*

Solution:

Solution: Let the revenue of company in Year 1 and Year 2 be x and y respectively.

Then, we have, Growth of Delhi plant = 2 x Growth of Mumbai plant 0.3y - 0.05x = 2(0.6y - 0.9x) 0.3y - 0.05x = 1.2y - 1.8x 1.75x = 0.9y y = 1.75/0.9x = 1.94x So, the growth is close to 94%.

Hence, option 4.

QUESTION: 61

Group Question

Answer the following question based on the information given below.

The price to earnings ratio (P/E) of 5 companies for 5 working days is shown below. However, the names of the companies have got jumbled.

The graph below shows the earnings per share (EPS) of each company for each of the five working days.

Also, share price on a given day = P/E(Given day) x EPS 61.

*Q. What can be the highest share price on any given day in the given period? *

Solution:

Solution: Max share price for any day = Max P/E value for a certain day x Max EPS for a company.

Since Girla has the highest EPS i.e. 9, consider Girla.

If Girla corresponds to company Y or W, Girla can have a share price of 108 (i.e. 9 x 12) on day 1 or day 3.

Hence, the highest share price on any given day =108 Hence, option 2.

QUESTION: 62

The price to earnings ratio (P/E) of 5 companies for 5 working days is shown below. However, the names of the companies have got jumbled.

The graph below shows the earnings per share (EPS) of each company for each of the five working days.

Also, share price on a given day = P/E(Given day) x EPS 61.

*Q. The company that shows the highest growth rate in its share price over the given period is said to give the best returns. What can be the best returns that an investor can get in this period?*

Solution:

Solution: Share Price = (P/E) x EPS For any company, the EPS is constant throughout the week.So, the company that shows the best growth rate in its P/E value will also give the best returns.Note that the company that gives the best returns is not required. Only the maximum value of returns is required.Only companies W and X show positive growth in this period.

Returns for company X

Returns for company W = Hence, option 3.

QUESTION: 63

Group Question

Answer the following question based on the information given below.

It is year 1211 and Genghis Khan has attacked the outpost to the Chinese Empire with Trebuchets. Trebuchets fire gunpowder hundreds of meters away and a single shot can destroy the outpost with all its inhabitants. The commander of the outpost Kim Chee realized that there is no way to stop the trebuchets. They would be lucky if they could somehow run away from the outpost and escape the attack. So he tells all his 10 team members to escape. The outpost is in the middle and there are four ways to escape from the outpost. Assume that the individual speeds of all men in the outpost are the same.

North: To the north, there is a flowing river. A man can swim underwater in the river at a speed of 10.8 km/hr. However after swimming for 20 seconds, he has to stop for one-sixth of a minute to breathe, or else he will drown.

East: To the east, there is a hilly area. A man can run in the hilly area at a speed of 3.6 km/hr. However, after running for 20 meters, he has to stop for 10 seconds to catch his breathe.

West: To the west, there is a forest. Here a man can run at a speed of 7.2 km/hr. But since the forest is dense, a man has to stop for 2 seconds after running for 10 seconds to find the way through the dense undergrowth.

South: To the south, there are tall grasses. A man can run at a speed of 5.4 km/hr here. But since there are poisonous snakes in this area, after running for 15 meters, a man has to stop for 5 seconds to ensure that there are no snakes in the next 15 meters lest he may be bitten.

*Q. Assuming that in 60 seconds the outpost will be hit, in which 3 direction should Kim Chee and his men move to have the maximum chances of survival? Chances of survival depend upon the distance from the place of impact. *

Solution:

Solution: The men will have maximum chances of survival in the direction where they cover the maximum distance in 60 seconds. Consider each direction.

North: Speed of travel = 10.8 km/hr = 3 m/s So, distance travelled in 20 seconds = 60 m At this stage, the men rest for one-sixth of a minute, they rest for 10 seconds.

So, effectively, 60 m is covered in 30 seconds.

Therefore, distance covered in 60 seconds = 60 x 2 = 120 m

East: Speed of travel = 3.6 km/hr = 1 m/s So, distance travelled in 20 seconds = 20 m At this stage, the men rest for 10 seconds.

So, effectively, 20 m is covered in 30 seconds.

Therefore, distance covered in 60 seconds = 20 x 2 = 40 m West: Speed of travel = 7.2 km/hr = 2 m/s So, distance travelled in 10 seconds = 20 m At this stage, the men rest for 2 seconds.

So, effectively, 20 m is covered in 12 seconds.

Therefore, distance covered in 60 seconds = 20 x 5 = 100 m South: Speed of travel = 5.4 km/hr =1.5 m/s So, time required for 15 m = 10 m At this stage, the men rest for 5 seconds.

So, effectively, 15 m is covered in 15 seconds.

Therefore, distance covered in 60 seconds = 1 5 x 4 = 60 m Thus, the maximum distance he can travel in 60 seconds is in the North direction.

So, the chances of survival are the maximum if Kim Chee and his men move towards North.

Hence, option 1.

QUESTION: 64

It is year 1211 and Genghis Khan has attacked the outpost to the Chinese Empire with Trebuchets. Trebuchets fire gunpowder hundreds of meters away and a single shot can destroy the outpost with all its inhabitants. The commander of the outpost Kim Chee realized that there is no way to stop the trebuchets. They would be lucky if they could somehow run away from the outpost and escape the attack. So he tells all his 10 team members to escape. The outpost is in the middle and there are four ways to escape from the outpost. Assume that the individual speeds of all men in the outpost are the same.

North: To the north, there is a flowing river. A man can swim underwater in the river at a speed of 10.8 km/hr. However after swimming for 20 seconds, he has to stop for one-sixth of a minute to breathe, or else he will drown.

East: To the east, there is a hilly area. A man can run in the hilly area at a speed of 3.6 km/hr. However, after running for 20 meters, he has to stop for 10 seconds to catch his breathe.

West: To the west, there is a forest. Here a man can run at a speed of 7.2 km/hr. But since the forest is dense, a man has to stop for 2 seconds after running for 10 seconds to find the way through the dense undergrowth.

South: To the south, there are tall grasses. A man can run at a speed of 5.4 km/hr here. But since there are poisonous snakes in this area, after running for 15 meters, a man has to stop for 5 seconds to ensure that there are no snakes in the next 15 meters lest he may be bitten.

*Q. A man travelled towards the West for 70 seconds. How much time would he take to cover the same distance if he were travelling towards the East?*

Solution:

Solution: While travelling towards the West, he covers 20 m in 10 seconds and then rests for 2 seconds, i.e., in 12 seconds he travels for 20 m. 70 = 12 x 5 + 10 So, in 70 seconds, he must have travelled (20 x 5) + 20 = 120 m

While travelling towards the East, he covers 20 m in 20 seconds and then rests for 10 seconds, i.e., in 30 seconds he travels for 20 m So, in 30 x 5 = 150 seconds, he would have covered 100 m and to complete 120 m (i.e., to cover next 20 m) he must have taken 20 seconds.

Thus, 150 + 20 = 170 seconds Hence, option 3.

QUESTION: 65

It is year 1211 and Genghis Khan has attacked the outpost to the Chinese Empire with Trebuchets. Trebuchets fire gunpowder hundreds of meters away and a single shot can destroy the outpost with all its inhabitants. The commander of the outpost Kim Chee realized that there is no way to stop the trebuchets. They would be lucky if they could somehow run away from the outpost and escape the attack. So he tells all his 10 team members to escape. The outpost is in the middle and there are four ways to escape from the outpost. Assume that the individual speeds of all men in the outpost are the same.

North: To the north, there is a flowing river. A man can swim underwater in the river at a speed of 10.8 km/hr. However after swimming for 20 seconds, he has to stop for one-sixth of a minute to breathe, or else he will drown.

East: To the east, there is a hilly area. A man can run in the hilly area at a speed of 3.6 km/hr. However, after running for 20 meters, he has to stop for 10 seconds to catch his breathe.

West: To the west, there is a forest. Here a man can run at a speed of 7.2 km/hr. But since the forest is dense, a man has to stop for 2 seconds after running for 10 seconds to find the way through the dense undergrowth.

South: To the south, there are tall grasses. A man can run at a speed of 5.4 km/hr here. But since there are poisonous snakes in this area, after running for 15 meters, a man has to stop for 5 seconds to ensure that there are no snakes in the next 15 meters lest he may be bitten.

*Q. Assume that two men start running simultaneously, one towards East and the other towards South. At what time out of the options given below a person running towards east is at the same distance away from the outpost as a man running towards south?*

Solution:

Solution: Option 1:15 seconds Since a man running towards east runs 20 m in 20 seconds, he would cover 15 meters in 15 seconds.

Also a man running towards south covers 15 m in 10 seconds and stops for 5 seconds, he effectively covers 15 meters in 15 seconds.

Therefore after 15 seconds, both men would be at the same distance from the outpost.

Hence, option 1.

QUESTION: 66

It is year 1211 and Genghis Khan has attacked the outpost to the Chinese Empire with Trebuchets. Trebuchets fire gunpowder hundreds of meters away and a single shot can destroy the outpost with all its inhabitants. The commander of the outpost Kim Chee realized that there is no way to stop the trebuchets. They would be lucky if they could somehow run away from the outpost and escape the attack. So he tells all his 10 team members to escape. The outpost is in the middle and there are four ways to escape from the outpost. Assume that the individual speeds of all men in the outpost are the same.

*Q. What is the ratio of the distance covered by a man running towards west to the distance covered by a man swimming towards north in 40 seconds?*

Solution:

Solution: From the first question, while running towards west, a man covers a distance of 20 meters in 10 seconds and stops for 2 seconds, that is, he effectively covers 20 meters in 12 seconds.

Therefore he covers a distance of 60 meters in 36 seconds.

In 4 more seconds he can cover a distance of 8 meters.

Therefore, while running towards west, total distance covered is 68 meters in 40 seconds.

While running towards north, a man covers a distance of 60 meters in 20 seconds and stops for 10 seconds, that is, he effectively covers 60 meters in 30 seconds.

In 10 more seconds he can cover a distance of 30 meters.

Therefore, while running towards north, he in total covers a distance of 90 meters in 40 seconds. Required ratio = 68 : 90 = 34 : 45 Hence Option 2.

QUESTION: 67

S = {sin A, cos A, tan A, cosec A, sec A, cot A}

P, Q and R take values from S such that P, Q, R, 1/P, 1/Q, 1/R are all different. For how many ordered sets of the values of P, Q and R does f become zero?

Solution:

Since P, Q and R can take values of the basic trigonometric functions and /should be equal to zero, the three terms being added should be of the form 1, -1 and -1.

Consider R = tan A or cot A Then

= tan^{2}A + cot^{2}A + 1 = sec^{2}A + cosec^{2}A - 1 For f to be zero, P = sin A or cos A and Q = cos A or sin A Similarly, for R = cot A, we get 2 combinations of P and Q.

Thus, there are 4 such cases.

Hence, option 4.

QUESTION: 68

A cylindrical rubber tube is inflated such that the ratio of the radius and the lateral surface area of the inflated tube to that of the normal tube are 6 : 5 and 3 : 2 respectively. What is the ratio of the volume of the inflated tube to that of the normal tube, if the inflated tube is also a cylinder?

Solution:

Solution: Let,

r_{1}, h_{1} and V_{1}. Radius, height and volume of the cylindrical rubber tube.

r_{2}, h_{2} and V_{2 }Radius, height and volume of the inflated cylindrical rubber tube.

r_{2} :r_{1} = 6 : 5 and 2πr_{2}h_{2} : 2πr_{1}h_{1} = 3 : 2 ⇒ πr_{2}h_{2 }: πr_{1}h_{1 }= 3 :2

∴ V_{2} : V_{1} = 9 : 5

Hence, option 1.

QUESTION: 69

If (a_{1}, a_{2}, a_{3}, a_{4}, a_{5}) is a permutation of (2, 5, -4, -9, 6), then the equation, a_{1}x^{4} + a_{2}x^{3} + a_{3}x^{2} + a_{4}x + a_{5} = 0 has

Solution:

Solution: As a_{1} + a_{2} + a_{3} + a_{4} + a_{5} = 0, x = 1 is one of the real roots of the given equation.

Now, as the complex conjugate of any imaginary root of an equation is also a root, hence, imaginary roots always appear in pairs.

Hence the given equation can have a maximum of two imaginary roots.

Hence, the given equation has at least two real roots.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 70

The number of digits in 2^{250 }is: (Note: log 2 = 0.301)

Solution:

Solution: log 2^{250} = 250 x log 2 = 250 x 0.3010 = 75.25 Now, number of digits = characteristic of logarithm + 1 = 75 + 1 = 76

Answer: 76

QUESTION: 71

Which of the following statements cannot be true?

I. If the length of the sides of a right angled triangle are in arithmetic progression, the length of one of its sides can be 1809 units.

II. A primitive Pythagorean triplet is one where the GCD of the three numbers in the triplet is 1. If an integer greater than 25 belongs to a Pythagorean triplet, then that triplet is non-primitive.

III. The area of a right angled triangle will always be an odd integer.

Solution:

Solution: Statement I is correct: If (a, b, c) is a Pythagorean triplet then (ka, kb, kc) is also a Pythagorean triplet for any natural number k. (3, 4, 5) is a Pythagorean triplet. (3k, 4k, 5k) will also be a Pythagorean triplet for any natural number k.

(1809, 2412, 3015) is a Pythagorean triplet (for k = 603) and 1809, 2412 and 3015 are in A.P.

Statement II is incorrect: (28, 45, 53) is a primitive Pythagorean triplet with length of all the sides greater than 25.

Statement III is incorrect: For the right angled triangle with length of sides 3, 4 and 5, its area = 1/2 x 3 x 4 = 6 square units, which is even. Moreover, the area of a right triangle need not always be an integer value.

Hence, option 3.

QUESTION: 72

If one root is common between two quadratic equations, x^{2} + 4x + 6 and ax^{2} + bx+ c, then find the product of the roots of ax^{2} + bx+ c. (Given: a, b and c are natural numbers.)

Solution:

Solution: Discriminant of (x^{2} + 4x + 6) < 0 The equation will not have real roots. i.e., x^{2} + 4x + 6 has complex roots and they are conjugates of each other. One of the roots is also a root of ax^{2} + bx + c. Conjugate roots always occur in pairs.

So, the product of the roots of (ax^{2} + bx + c) is same as that of (x^{2} + 4x + 6). v a = 1 , b = 4 and c = 6 The product = c/a = 6 Hence, option 4.

QUESTION: 73

Pankaj, Raj and Suraj together invested Rs. 4 lakhs to open a mobile store. They earned a profit of 50% on the investment at the end of 1st year. They reinvested the profit back into the business and at the end of the second year, earned a profit of 100% on their investment for that year. If at the end of the second year, the share of Raj and Pankaj together in the profit earned is Rs. 4 lakhs, then what was Suraj’s share in the initial investment?

Solution:

Solution: Profit earned at the end of 1st year = 50% of Rs. 4 lakhs = Rs. 2 lakhs

Investment for 2nd year = Initial investment + Profit earned in the 1st year = 4 + 2 = Rs. 6 lakhs

Profit earned at the end of 2nd year = 100% of Rs. 6 lakhs = Rs. 6 lakhs

So, total profit earned in 2 years = 2 + 6 = Rs. 8 lakhs The share of Raj and Pankaj in the total profit earned = Rs. 4 lakhs Share of Suraj in the profit earned = 8 - 4 = Rs. 4 lakhs. % Share of Suraj in the profit = 50%

% Share of Suraj in the initial investment = 50% Hence, option 3.

QUESTION: 74

A shopkeeper sells a pen to a buyer at a loss of 12%. The same buyer sells the pen to another buyer at a loss of 11 % on the new price. The new buyer then sells it at a loss of 10% and so on. The value of the loss decreases by 1 percentage point for each transaction. After how many such transactions will the price of the pen be less than 60% of its original value?

Solution:

Solution: Let the initial price = Rs. X. Price after the third transaction = X x 0.88 x 0.89 x 0.9 » 0.7X > 0.6X

Price after the fourth transaction » X x 0.7 x 0.91 » 0.637X > 0.6X Price after the fifth transaction « X x 0.637 x 0.92 « 0.6X It is better to check exact value for the fifth transaction as the values above are approximate values.

QUESTION: 75

Saurabh has 3 coins such that the probability of getting a head on i^{th} coin is P_{i}. P_{1}= 0.25, P_{2} = 0.3, P_{3} = 0.5. Find the probability of not getting odd number of heads if these 3 coins are tossed.

Solution:

Solution: Required probability = P(0 Heads) + P(2 Heads) = (1 - 0.25) (1 - 0.3) (1 - 0.5) + 0.25 x 0.3 x (1 - 0.5) + 0.5 x 0.3 x (1 - 0.25) + 0.25 x 0.5 x (1 - 0 . 3 )

= 0.5

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 76

What is the numerator of A, if A is expressed in its simplest form?

Solution:

The numerator is 48.

Answer: 48 Alternatively,

*Answer can only contain numeric values

QUESTION: 77

Mean of six positive integers is 20. The difference between mean and mode is not more than 6. What is the maximum difference between the highest and the lowest number?

Solution:

Mean of six numbers is 20.

∴ Sum of six numbers = 120

| Mean - Mode | __<__ 6

| 20 - Mode | __<__ 6

∴ 14 __<__ Mode __<__ 26

To maximize the difference between the highest and the lowest number, the lowest number and mode should be minimized and the highest number should be maximized.

Mode = 14 and Lowest number = 1 The numbers are 1, 2, 3, 14, 14, 86.

Difference between the highest and the lowest number = 8 6 - 1 = 85

Answer: 85

QUESTION: 78

A certain amount is kept in a bank at 8% compound interest. An equal amount is kept in another bank at 10% simple interest. When the amount in the first bank gets doubled, by what percentage does the amount with the second bank increase? log 10^{2} = 0.3 & log10^{1.08} = 0.033

Solution:

Solution: Let the amount kept with the 1st bank be P. Thus, the amount kept with the 2nd bank is also P.

Now, we have

Or 2 = 1.08^{n}

Taking log on both the sides, we get, log_{10} 2 = log_{10} 1.08^{n}

log_{10} 2 = n log_{10} 1.08

∴ n = 0.3/0.033 ≌ 9

The amount gets doubled in 9 years.

Now, simple interest for 9 years is

Thus, increase % = 90%

Hence, option 4.

*Answer can only contain numeric values

QUESTION: 79

Find the maximum possible value of A, if A __<__ (49sin^{2}θ + 64cosec^{2}θ).

Solution:

(49sin^{2}θ + 64cosec^{2}θ)/ 2 __>__ √49sin^{2}θ x 64cosec^{2}θ ...(A.M. __>__ G.M.)

49sin^{2}θ + 64cosec^{2}θ __>__ 112

So, the maximum value of A is 112.

QUESTION: 80

What is the difference in the angles between the minute hand and the hour hand at 3:20 pm and 9:30 pm?

Solution:

Solution: At 3:20 pm, the distance travelled by the minute hand is one-third of the distance that it travels in an hour, which is 1/3 x 360° = 120° Similarly, the hour hand travels one-third of the distance that it travels in an hour, which is 1/3 x 30° = 10° At 3:20 pm, the minute hand points to 4 on the clock and the hour hand is between 3 and 4 and is 10° away from 3. The distance between the hour and the minute hand at 3:20 pm is 20°

Similarly, we can find that the distance between the hour and minute hands at 9:30 pm is 90 + 15 = 105°

Difference between the angles between the minute and the hour hand at 3:20 pm and 9:30 pm = 105° - 20° = 85° Hence, option 4.

QUESTION: 81

Rakesh and Vishal are running along a circular path of circumference 84 km in opposite directions. They start from point O_{1 }and meet for the first time at point O_{2}. After meeting they exchange their speeds as well as their directions and continue running around the track. They repeat this process every time they meet. Initially, Rakesh has a speed of 85 km/hr and Vishal has a speed of 17 km/hr. What is the distance along the track between the points where they meet for the 3rd and 6th time?

Solution:

Solution:

The initial speeds of Rakesh and Vishal is in ratio 5 : 1 .

The distance covered by Rakesh and Vishal before meeting would be in the ratio 5 : 1 .

i.e. Rakesh will cover 70 km and Vishal will cover 14 km before their 1st meeting.

Now they will exchange their speeds and their directions.

Rakesh will travel at speed of 17 km/hr and Vishal will travel at a speed of 85 km/hr.

The distance covered by Vishal and Rakesh before meeting would be in the ratio 5 : 1 . Rakesh will cover 14 km and Vishal will cover 70 km between their 1st and 2nd meeting.

The distance between their meeting points will be 14 km. As they repeat the same process the distance between their meeting points will be a multiple of 14.

We are required to find the distance between their 3rd and 6th meeting (6th meeting will be at starting point).

The distance must be 3 x 14 = 42 km Hence, option 4.

*Answer can only contain numeric values

QUESTION: 82

Instead of taking 37 as one of the multipliers, Disha took 73. As a result, the product went up by 612. What is the new product?

Solution:

Solution: Let the number to be multiplied be a. so 73a - 3 7 a = 612

a = 17

Required product = 17 x 73 = 1241

Answer: 1241

*Answer can only contain numeric values

QUESTION: 83

The lengths of three sides of a triangle are given by (x + 7), (9 - 2x) and (3x - 1). For how many integral values of x will the triangle be isosceles?

Solution:

Solution: An isosceles triangle has two sides equal. We have three cases:

Case (i): x + 7 = 9 - 2x

3x = 2. x = 2/3, which is not an integer.

Case (ii): x + 7 = 3x - 1

2x = 8, x = 4

The sides are 11,11 and 1

Case (iii): 9 - 2x = 3x - 1, 5x = 10, x = 2 The sides are 5, 5 and 9

The triangle is isosceles for two values of x.

Answer: 2

QUESTION: 84

f(x) is a linear function such that, f(1) __<__ f(2), f(3) __>__ f(4) and f(5) = 25. What is the value of f(7)?

Solution:

Since f(x) is a linear function we can express f(x) as, f(x) = ax + b, where a and b are real numbers.

∴ f(1) __<__ f(2)

a + b < 2a + b

∴ a __>__ 0 ...(i)

∵ f(3) __>__ f(4)

∴ 3a + b __>__ 4a + b

∴ a __<__ 0 ...(ii)

From (i) and (ii), we get a = 0

We know that f(5) = 25

∴ 5a + b = 25

Substituting the value of a in the above equation, we get b = 25 /(x) = 25, for all real numbers x. f(7) = 25 Hence, option 3.

QUESTION: 85

The pressure of a gas varies depends only on its volume & temperature. Increasing the volume by 50% increases the pressure by 125% (keeping other factors constant). Decreasing the temperature by 50% increases the pressure by 700% (keeping other factors constant). By what percent does the pressure increase/decrease if the temperature decreases by 50% and then volume increases by 50%? (Assume there is no addition/subtraction involved anywhere in the relationship)

Solution:

Solution: Let the original values for pressure, volume and temperature be P, V and T respectively.

Step 1: T decreases by 50% (keeping V constant): Since P increases by 700%, P_{1} = P + 7P = 8P

Step 2: V increases by 50% (keeping T constant): Since P_{1 }increases by 125%, P_{2 }= 8P + 8P(1.25) = 18P

An increase from P to 18P implies an increase of [(18 - 1) x 100]% i.e. 1700% Hence, option 3.

QUESTION: 86

For two natural numbers a and b, their geometric mean is 80% of their arithmetic mean. Also, 10 times their harmonic mean is the square of a. What is the sum of all possible numbers values of a and b?

Solution:

Solution: It is given that the geometric mean of a and b is 80% of the arithmetic mean.

∴ 25ab = 4a^{2} + 8ab + 4b^{2}

∴ 4a^{2 }- 17ab +4b^{2} = 0

On factorizing the above given equation,

(4a - b)(4b - a) = 0

∴ 4a = b r 4b = a

It is also given that 10 times the harmonic mean is equal to a^{2}.

20b = a^{2 }+ ab ...(i)

Substituting 4a = b in equation (i),

80a = a^{2} + 4a^{2}

∴ a = 16

∴ b = 64

Substituting a= 4b in equation (i),

20b = 16b^{2 }+ 4b^{2}

b = 1 and a = 4

Thus, the sum of all possible values of a and b is (1 + 4 + 16 + 64) = 85

Hence, option 3.

*Answer can only contain numeric values

QUESTION: 87

Total number of factors of a natural number N is 45. What is the maximum number of prime numbers by which N is exactly divisible?

Solution:

Solution: If can factorize the number N into its prime factors as follows N = a^{w} x b^{x} x c^{y} x d^{z} x... where a, b, c, d are prime numbers, Then, number of factors of N = (w + 1 )(x + 1 )(y + 1 )(z + 1)...

Here, the number of factors of N = 45 In order to maximize the number of prime factors of N, we express 45 such that it cannot be factorized any further. 45 = 3 x 3 x 5 N = a^{2} x b^{2} x c^{4} N can have a maximum of 3 prime factors.

Answer: 3

QUESTION: 88

A shop WSS sells two products - product A and product B. Due to a festive offer, the shop increases the selling price of product A by 50% and makes product B free along with product A. By doing this, it’s profit decreases by 40%. If the shopkeeper still earns 20% profit on the selling price, then the total percentage discount offered by him is:

Solution:

Solution: Let Rs. a be the selling price of A and Rs. b be the selling price of B.

Hence, the initial selling price of A and B together is Rs. a + b.

Now, he increases the selling price of product A by 50% and makes product B free along with product A.

So, the new selling price of A and B = Rs. 1.5a For this selling price, he makes a 20% profit on the selling price i.e. he makes a profit of 1.5a/5 i.e. Rs. 0.3a So, cost price of A and B together = 1.5a - 0.3a i.e. Rs. 1.2a

Now, the current profit of Rs. 0.3a is 60% of the initial profit.

Hence, initial profit = 0.3a/0.6 = Rs. a/2 But his initial profit = Rs. (a + b) - 1.2a Hence, a + b - 1.2a = a/2 Hence, b = 0.7a Hence, the initial selling price of both products = a + b = a + 0.7a = 1.7 a

Hence, total discount offered by him,

Hence, option 1.

QUESTION: 89

The number of sides in a regular polygon is 16. What is the value of any interior angle of the polygon?

Solution:

Solution: Since it is a regular polygon, hence the distances of all the vertices from the center of the polygon are equal. Therefore, the lines joining the center of the polygon to the vertices divide the polygon into 16 congruent isosceles triangles with the sides of the polygon as their bases.

Let the non-equal angle of any such triangle be a.

Therefore, 16a = 360° [since all these non-equal angles collectively form one full circle] or, a = 22.5°

Any interior angle of this polygon will be twice this base angle. Hence, interior angle = 157.5° Hence, option 3.

Alternatively, The sum of exterior angles of a regular polygon is 360° As the polygon has 16 sides, there are 16 exterior angles, each angle being equal to 360/16 = 22.5° Each interior angle is thus 180 - 22.5 = 157.5° Hence, option 3.

*Answer can only contain numeric values

QUESTION: 90

A shopkeeper marks up the cost of an item by 15% and then gives a discount of Rs. 94.5 and he achieves break-even by selling the item. What is the cost price of the item?

Solution:

Solution: Let ‘x_{1}' be the cost price of the item.

From the given conditions, 1.15x- 94.5 = x

x = 630 Answer: 630

QUESTION: 91

|x - 1| + |x - 2| + |x + 1| + |x + 2| = 4k If this equation has integral solutions, which of these values can k never take?

Solution:

Solution: Since the equation has integral solutions, consider different integral values of x and solve the equation.

For x = 0: |-1| + |-2| + |1| + |2| = 1 + 2 + 1 + 2 = 6

Since the terms are symmetrical about the number line, x = ±1 gives the same magnitude.

For x = ±1: |0| + |-11 + |2| + |3| = 1 +2 + 3 = 6

Similarly, for x = ±2: |11 + |0| + |3| + |4| = 1 + 3 + 4 = 8

Thus, as the magnitude of x increases, the magnitude of the LHS also increases.

4k __>__6 : . k > 1 Hence, k can never take 1 as a value.

Hence, option 1.

Alternatively, Since -2, -1, +1, +2 are the critical points for the given equation, divide the real number line into appropriate intervals such that the LHS of this equation behaves similarly within an interval.

The suitable intervals are: (-∞, -2], (-2, -1], (-1, 1], (1,2], (2, ∞). Call these intervals A, B, C, D and E respectively.

In interval A,

x - 1 < 0 ⇒ |x - 11 = -(x - 1) = -x + 1 = 1 - x

x-2<0 ⇒ |x-2| = -(x-2) = -x + 2 = 2- x

x + 1 < 0 ⇒ |x + 11 = -(x + 1) = -x - 1

x + 2 £ 0 ⇒ |x + 2| = -(x + 2) = -x - 2

Hence, L. H. S. = 1 - x + 2- x- x-1 - x - 2 = -4x = 4k

∴ k = - x

k = - x

k takes the values 2, 3 and 4 for x = -2, -3 and -4 respectively.

It can similarly be shown that k cannot take the value 1 in any of the other intervals.

Hence, option 1.

QUESTION: 92

Saradindu wrote five numbers a, b, c, d and e on a paper such that a = 4b = 8c, and 3b = 7d= 21e. Then he wrote the following 4 pairs and asked his friend to identify a pair containing a non-integer. If his friend chose the correct pair then which of the following pairs did he choose?

Solution:

Solution: Since a = 4b = 8c and 3b = 7d = 21e

a : b : c = 8 : 2 : 1 and b : d : e = 7 : 3 : 1

a : b : c : d : e = 56 : 14 : 7 : 6 : 2

so a = 56k; b = 14k; c = 7k; d = 6k and e = 2k, where k is an integer Evaluating the given options:

**Option 1:
Option 2: **

The second option contains 3.5, which is not an integer.

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 93

The time table of a certain class consists of six sessions. In each session, one of the five subjects is to be taught. How many different time tables are possible if each subject has to be taught at least once?

Solution:

Solution: Among the 6 sessions of the 5 subjects, one subject is repeated.

This can be arranged in ways.

A subject that is to be repeated can be selected in 5 ways.

∴ The total number of different possible time tables

Answer: 1800

QUESTION: 94

Sourav and Sachin invested Rs. 40,000 and Rs. 60,000 respectively to open a restaurant. Every month, one-third of the profit made by the restaurant was shared equally between the two, one-third of profit was retained for reinvestment and the remaining profit was shared by them in the ratio of their investments. If apart from the profit kept aside for reinvestment the rest of the profit was divided in the ratio of their individual investments then Sachin would have received Rs. 5,000 more in the month of November. What is the total profit made by the restaurant in the month of November?

Solution:

Solution: Let the profit for the month of November be Rs. x.

Ratio of investments of Sourav and Sachin = 2 : 3

∴ Sachin's share in profit

If the entire two-thirds of the profit was divided in the ratio of the investments then,

Sachin's share in profit =

By the condition given

By the condition given in the question,

∴ x = 1,50,000

Hence, option 3.

QUESTION: 95

Line L_{1} makes 30° with the x-axis and line L_{2} makes 60° with the x axis and both of them pass through the origin. A perpendicular from P(a, 0) to L_{1}, meets L_{1 }at B_{1}. The perpendicular from B_{1} to L_{2} , meets L_{2} at B. What is the area of quadrilateral OPB_{1}B?

Solution:

OP = a

As ΔOPB_{1} is a 30 - 60 - 90 triangle,

ΔOB_{1}B is a 30 - 60 - 90 triangle too.

Hence, Option 2.

*Answer can only contain numeric values

QUESTION: 96

A natural number P, when divided by K, leaves a remainder of 11. When K divides 2P, it leaves remainder 5. What is the remainder when K divides 4P?

Solution:

Solution: P = a K + 11

2P = 2Ka + 22 = 2Ka + 17 + 5

As 2P leaves remainder 5, when divided by K, 2Ka + 17 is divisible by K

17 is divisible by K=> K= 17 Now, 4P = 4(aK + 11) = 4 aK + 44 = 4 aK + 34 + 10 Thus, when K = 17 divides 4P. it leaves remainder 10.

Answer: 10

QUESTION: 97

ΔOBC is drawn on coordinate plane with O(0, 0) and B(2, 0) such that BC = 1 and m ∠OBC = 60°. The triangle is then rotated by 90°. What is the area covered by OC?

Solution:

OB = 2 units and CB = 1 unit and m ∠OBC=60°

ΔOCB is 30-60-90 triangle.

∴ OC = √3 units

∴ Area traced by OC = Hence, option 1.

QUESTION: 98

In the following figure, three circles C_{1}, C_{2} and C_{3} are shown. Three tangents are common to these three circles. What is the value of

Solution:

Let m ∠BAC = a, m ∠ABC = b, m ∠ACB = c, m ∠DEF = α, m ∠GHJ = β and m ∠MLK = θ.

We know that exterior angle of the triangle is equal to the sum of opposite interior angles.

∴ In AABC we have,

m ∠FBE = a + c

m ∠GBH = a + c

m ∠HCJ = a + b

m ∠LCK = a + b

m ∠MAL = b + c

m ∠DAE = b + c

Consider ABFE,

B is the external point through which the tangents BE and BF are drawn to the circle C_{1} BF = BE

Let m ∠BEF = m ∠BFE = x (say)

2x + m ∠FBE = 180°

2x = 180° - m ∠FBE

= 180° - a - c

= b (∵ a + t + c= 180°)

∴ x = b/2

Now consider ADAE,

Similarly,

Let m ∠ADE = m ∠AED = y

2y = 180° - m ∠DAE

y = a/2

α = 180° - x - y

= 180° - a/2 - b/2

Similarly, β = 180° - b/2 - c/2 and θ = 180° - a/2 - c/2

∴ α + β + θ = 180° - a/2 - b/2 + 180° - b/2 - c/2 + 180° - a/2 - c/2

= 540° - (a + b + c)

= 540° - 180° ...(∵ a + b + c = 180°)

= 360°

Hence, option 2.

*Answer can only contain numeric values

QUESTION: 99

Find m ∠ABP, such that m (arc XY) = 40°

m (arc AL) = 60°, Q is the centre.

Solution:

Draw QR such that QR is parallel to PC.

m∠AQR = zAPC = 90°

m∠ACL = (1/2) x m (arc AL) = 60/2 = 30°

m∠AQL = 60°

CL is diameter of the circle.

∴ m∠AQL + mz.AQR + mzCQR = 180°

∴ m∠CQR = 180-90-60

∴ m∠CQR = 30°

∴ m (arc RC) = 30°

m (arc AC) = 90 + 30 = 120°

m ∠ABP = m∠ABC = (1/2) x (120 - 40) = 40°

*Answer can only contain numeric values

QUESTION: 100

Let X be the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Nine bit strings made of 0s and 1s are used to represent subsets of X. The n-th bit from the right will be 1 if n is present in the subset and 0 if it is absent. For example, the sequence 100011011 represents {1, 2, 4, 5, 9}.

Let A, B and C be the subsets of X represented by 100011111, 011001111 and 100111001. If D is a set of those elements which appear in exactly two of A, B and C, then what is the sum of digits of the representation of D?

Solution:

Solution: The main part of the question is to understand that each 1 in the binary sequence represents an element of the set. If the nth bit is 1, n is there in the set, else not.

Hence, we have A = {1, 2, 3, 4, 5, 9} B = {1,2, 3, 4, 7, 8}

c = { 1,4, 5, 6, 9} Now, D is set of those elements which appear in exactly two of A, B and C.

Hence, D = {2, 3, 5, 9} Hence, D can be represented by 100010110.

Sum = 4 Answer: 4

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