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CAT Mock Test - 12 (November 14) - CAT MCQ


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30 Questions MCQ Test Daily Test for CAT Preparation - CAT Mock Test - 12 (November 14)

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CAT Mock Test - 12 (November 14) - Question 1

Directions: The passage below is accompanied by a set of questions. Choose the best answer to each question.

We tend to experience the olfactory realm as a shapeless suffusion, forever shifting, eluding description the way fog eludes the grasp of one's hand. Smell does not produce objects in our minds so much as auras, but these can be the most vivid of our sensory experiences. Smell is the sense most deeply entangled with memory and emotion. It functions as a kind of psychic mortar, binding together all the richness of past experience, such that a familiar scent can instantly overwhelm us with remembrance and feeling. And yet we strain to describe even the simplest odours; we retreat into simile and metaphor, or cadge the terminology of other senses, or designate smells, rather prosaically, by their source. The scent of a rose is "soft," or "rosy," or perhaps "evocative of decorous passion," but none of these descriptions would let you imagine it if you didn't know it already. Nor does smell lend itself to quantification. Sound and light fall along well-defined spectra of wavelength and frequency, but we have no such scale for odour, no metric by which to relate the aroma of cinnamon, say, to that of burnt rubber, or that of old books.
Nor can we say with certainty why anything smells the way it does. Lucretius, the Epicurean polymath, believed that odour was a function of geometry. "You cannot suppose that atoms of the same shape are entering our nostrils when stinking corpses are roasting," he wrote, "as when the stage is freshly sprinkled with saffron of Cilicia and a nearby altar exhales the perfumes of the Orient." A number of alternative theories have since been advanced. Some have imagined odours as chemical reactions between the nose and the molecules that enter it. According to "vibrational" theories, a molecule's scent depends upon its infrared or ultraviolet emissions. Shape-based theories are still the most prevalent, though, and Lucretius is thought to have been basically right, apart from the correlation he imagined between harmoniousness of form and loveliness of smell. The scent of a rose is the combined effect of about 260 volatile compounds, some as jagged as the flower's thorns.
If shape does indeed account for smell, however, we are far from knowing exactly how. Molecules of widely divergent structure can smell nearly identical. Muscone and Helvetolide, for instance, both smell of musk, but one is shaped like a ring, the other a kinked chain. Conversely, molecules of nearly identical structure produce odours that are completely distinct. The compound L-carvone smells of spearmint, while its mirror image, D-carvone, smells of caraway seed. Certain substances have unrelated smells at different concentrations. Gamma-undecalactone generally smells fatty and aversive. Heavily diluted, it smells of ripened peach.
We speak of scent as if it were a property intrinsic to a given substance, but odour is not simply "out there." It is a co-creation of the nose. At the very top of the nasal cavity, up between the eyes, sits mucosal tissue known as the olfactory epithelium. It is dense with neurons, and embedded in these neurons are proteins known as odourant receptors. Odourant receptors bind the volatile compounds we inhale, converting them into electric signals that will, eventually, register in our consciousness as smell. The nature of these receptors—how many kinds there are, which molecules they respond to—is central to our experience of scent. It is also, for the most part, a mystery.

Q. In the phrase 'Lucretius is thought to have been basically right ... and loveliness of smell', which of the following statements is the author trying to imply?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 1

The author is affirmative that form does influence the scent, however, whether the scent is repulsive or not is not stated in the passage to be dependent upon the form. Hence, Lucretius, although was right in determining that form influences the scent, was wrong in determining that a better form leads to a pleasant smell and vice-versa.
Option 1: This includes the extraneous 'repulsiveness' which is not indicated in the passage.
Option 2: This accurately highlights the purpose of the sentence.
Option 3: This is not inferable or implied in the passage.
Option 4: Although stated, it does not help explain the implication of the sentence mentioned.

CAT Mock Test - 12 (November 14) - Question 2

Directions: The passage below is accompanied by a set of questions. Choose the best answer to each question.

We tend to experience the olfactory realm as a shapeless suffusion, forever shifting, eluding description the way fog eludes the grasp of one's hand. Smell does not produce objects in our minds so much as auras, but these can be the most vivid of our sensory experiences. Smell is the sense most deeply entangled with memory and emotion. It functions as a kind of psychic mortar, binding together all the richness of past experience, such that a familiar scent can instantly overwhelm us with remembrance and feeling. And yet we strain to describe even the simplest odours; we retreat into simile and metaphor, or cadge the terminology of other senses, or designate smells, rather prosaically, by their source. The scent of a rose is "soft," or "rosy," or perhaps "evocative of decorous passion," but none of these descriptions would let you imagine it if you didn't know it already. Nor does smell lend itself to quantification. Sound and light fall along well-defined spectra of wavelength and frequency, but we have no such scale for odour, no metric by which to relate the aroma of cinnamon, say, to that of burnt rubber, or that of old books.
Nor can we say with certainty why anything smells the way it does. Lucretius, the Epicurean polymath, believed that odour was a function of geometry. "You cannot suppose that atoms of the same shape are entering our nostrils when stinking corpses are roasting," he wrote, "as when the stage is freshly sprinkled with saffron of Cilicia and a nearby altar exhales the perfumes of the Orient." A number of alternative theories have since been advanced. Some have imagined odours as chemical reactions between the nose and the molecules that enter it. According to "vibrational" theories, a molecule's scent depends upon its infrared or ultraviolet emissions. Shape-based theories are still the most prevalent, though, and Lucretius is thought to have been basically right, apart from the correlation he imagined between harmoniousness of form and loveliness of smell. The scent of a rose is the combined effect of about 260 volatile compounds, some as jagged as the flower's thorns.
If shape does indeed account for smell, however, we are far from knowing exactly how. Molecules of widely divergent structure can smell nearly identical. Muscone and Helvetolide, for instance, both smell of musk, but one is shaped like a ring, the other a kinked chain. Conversely, molecules of nearly identical structure produce odours that are completely distinct. The compound L-carvone smells of spearmint, while its mirror image, D-carvone, smells of caraway seed. Certain substances have unrelated smells at different concentrations. Gamma-undecalactone generally smells fatty and aversive. Heavily diluted, it smells of ripened peach.
We speak of scent as if it were a property intrinsic to a given substance, but odour is not simply "out there." It is a co-creation of the nose. At the very top of the nasal cavity, up between the eyes, sits mucosal tissue known as the olfactory epithelium. It is dense with neurons, and embedded in these neurons are proteins known as odourant receptors. Odourant receptors bind the volatile compounds we inhale, converting them into electric signals that will, eventually, register in our consciousness as smell. The nature of these receptors—how many kinds there are, which molecules they respond to—is central to our experience of scent. It is also, for the most part, a mystery.

Q. '...odour is not simply out there. It is a co-creation of the nose'. It can be inferred from this that the author is trying to imply which of the following?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 2

The author implies that 'odour' as a distinct entity is non-existent. What exists around us are only fumes generated by different things. These fumes, when inhaled through the nose, become odour or smell that our brain then perceives. Hence, not only the form, but also the nose is an important factor in the process of odour perception.
Option 1: This is what author implies; however, it is not the essence of the phrase mentioned. Odour is simply not out there, which can be perceived by the nose.
Option 2: Odour does not persist around us. We experience it in our brain through sensory organs.
Option 3: The statement accurately highlights the implication of the author in the phrase.
Option 4:The statement can be inferred; however, it does not explain the essence of the phrase.

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CAT Mock Test - 12 (November 14) - Question 3

Directions: Read the following passage carefully and answer the given question.

Claude Lorrain and Carle Vernet are considered by the Impressionists as precursors from the point of view of decorative landscape arrangement, and particularly of the predominance of light in which all objects are bathed. Ruysdael and Poussin are, in their eyes, for the same reasons precursors who observed so frankly the blue colouring of the horizon and the influence of blue upon the landscape. It is known that Turner worshipped Claude for the very same reasons. The Impressionists in their turn consider Turner as one of their mighty geniuses, a visionary. Notably in the famous Entry of the Crusaders into Constantinople, the fair woman kneeling in the foreground is painted in accordance with the principles of the division of tones: the nude back is furrowed with blue, green and yellow touches, the juxtaposition of which produces, at a certain distance, an admirable flesh-tone.
And now I must speak at some length of a painter who, together with the luminous and sparkling landscapist Félix Ziem, was the most direct initiator of Impressionist technique. Monticelli is one of those singular men of genius who are not connected with any school, and whose work is an inexhaustible source of applications. He lived at Marseilles, where he was born, made a short appearance at the Salons, and then returned to his native town, where he died poor, ignored, paralysed and mad.
In order to live he sold his small pictures at the cafés, where they fetched ten or twenty francs at the most. Today they sell for considerable prices. The mysterious power of these paintings secures him a fame which is, alas! posthumous. Many Monticellis have been sold by dealers as Diaz's; now they are more eagerly looked for than Diaz, and collectors have made fortunes with these small canvases bought formerly, to use a colloquial expression which is here only too literally true, ''for a piece of bread.''
Monticelli painted landscapes, romantic scenes, and still-life pictures: one could not imagine a more inspired sense of colour than shown by these works which seem to be painted with crushed jewels, with powerful harmony, and beyond all with an unheard-of delicacy in the perception of fine shades. There are tones which nobody had ever invented yet, a richness, a profusion, a subtlety which almost vie with the resources of music. The fairyland atmosphere of these works surrounds a very firm design of charming style, but, to use the words of the artist himself, ''in these canvases the objects are the decoration, the touches are the scales, and the light is the tenor.'' Monticelli has created for himself an entirely personal technique which can only be compared with that of Turner; he painted with a brush so full, fat and rich, that some of the details are often truly modelled in relief, in a substance as precious as enamels, jewels, ceramics - a substance which is a delight in itself. Every picture by Monticelli provokes astonishment; constructed upon one colour as upon a musical theme, it rises to intensities which one would have thought impossible. His pictures are magnificent bouquets, bursts of joy and colour, where nothing is ever crude, and where everything is ruled by a supreme sense of harmony.

Q. According to the passage, in which of the following ways was the work of early Impressionist masters significantly different in style?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 3

1. Correct. Refer to the part: 'particularly of the predominance of light in which all objects are bathed'. They laid emphasis on 'predominance of light' on objects and could achieve it with colours alone on the canvas. Therefore, option 1 is correct.
2. Incorrect. Illumination of paintings with sunlight or artificial light is not what the passage states about their style. This takes meaning of 'light' to mean 'sunlight' which is not what the passage implies. The paintings had their own light through the use of colours.
3. Incorrect. This does not answer the question. Hence, incorrect. If they followed their own pedigree, how will they be 'different' in style?
4. Incorrect. Decorative landscape arrangement cannot be taken to mean that "only" their works used landscapes. Otherwise how will their style be 'different'?

CAT Mock Test - 12 (November 14) - Question 4

Directions: Read the following passage carefully and answer the given question.

Claude Lorrain and Carle Vernet are considered by the Impressionists as precursors from the point of view of decorative landscape arrangement, and particularly of the predominance of light in which all objects are bathed. Ruysdael and Poussin are, in their eyes, for the same reasons precursors who observed so frankly the blue colouring of the horizon and the influence of blue upon the landscape. It is known that Turner worshipped Claude for the very same reasons. The Impressionists in their turn consider Turner as one of their mighty geniuses, a visionary. Notably in the famous Entry of the Crusaders into Constantinople, the fair woman kneeling in the foreground is painted in accordance with the principles of the division of tones: the nude back is furrowed with blue, green and yellow touches, the juxtaposition of which produces, at a certain distance, an admirable flesh-tone.
And now I must speak at some length of a painter who, together with the luminous and sparkling landscapist Félix Ziem, was the most direct initiator of Impressionist technique. Monticelli is one of those singular men of genius who are not connected with any school, and whose work is an inexhaustible source of applications. He lived at Marseilles, where he was born, made a short appearance at the Salons, and then returned to his native town, where he died poor, ignored, paralysed and mad.
In order to live he sold his small pictures at the cafés, where they fetched ten or twenty francs at the most. Today they sell for considerable prices. The mysterious power of these paintings secures him a fame which is, alas! posthumous. Many Monticellis have been sold by dealers as Diaz's; now they are more eagerly looked for than Diaz, and collectors have made fortunes with these small canvases bought formerly, to use a colloquial expression which is here only too literally true, ''for a piece of bread.''
Monticelli painted landscapes, romantic scenes, and still-life pictures: one could not imagine a more inspired sense of colour than shown by these works which seem to be painted with crushed jewels, with powerful harmony, and beyond all with an unheard-of delicacy in the perception of fine shades. There are tones which nobody had ever invented yet, a richness, a profusion, a subtlety which almost vie with the resources of music. The fairyland atmosphere of these works surrounds a very firm design of charming style, but, to use the words of the artist himself, ''in these canvases the objects are the decoration, the touches are the scales, and the light is the tenor.'' Monticelli has created for himself an entirely personal technique which can only be compared with that of Turner; he painted with a brush so full, fat and rich, that some of the details are often truly modelled in relief, in a substance as precious as enamels, jewels, ceramics - a substance which is a delight in itself. Every picture by Monticelli provokes astonishment; constructed upon one colour as upon a musical theme, it rises to intensities which one would have thought impossible. His pictures are magnificent bouquets, bursts of joy and colour, where nothing is ever crude, and where everything is ruled by a supreme sense of harmony.

Q. From the passage, it can be inferred that the painting 'Entry of the Crusaders into Constantinople' is truly symbolic of Impressionist art due to:

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 4

1. Incorrect. The painting is considered as a work of genius at least in part due to its being "in accordance with the principles of the division of tones". "True inspiration" does not catch the idea.
2. Correct. Impressionist is described as decorative art with predominance of light and colour. The last line of the first paragraph which states "the juxtaposition of colors" could achieve "an admirable flesh-tone" leads us to (2) as the answer.
3. Incorrect. Romanticism or sensuality cannot be inferred from what is stated in the passage. Hence, incorrect.
4. Incorrect. Predominance of blue color is only incidental. This does not make it symbolic.

CAT Mock Test - 12 (November 14) - Question 5

Directions: Read the following passage carefully and answer the given question.

Claude Lorrain and Carle Vernet are considered by the Impressionists as precursors from the point of view of decorative landscape arrangement, and particularly of the predominance of light in which all objects are bathed. Ruysdael and Poussin are, in their eyes, for the same reasons precursors who observed so frankly the blue colouring of the horizon and the influence of blue upon the landscape. It is known that Turner worshipped Claude for the very same reasons. The Impressionists in their turn consider Turner as one of their mighty geniuses, a visionary. Notably in the famous Entry of the Crusaders into Constantinople, the fair woman kneeling in the foreground is painted in accordance with the principles of the division of tones: the nude back is furrowed with blue, green and yellow touches, the juxtaposition of which produces, at a certain distance, an admirable flesh-tone.
And now I must speak at some length of a painter who, together with the luminous and sparkling landscapist Félix Ziem, was the most direct initiator of Impressionist technique. Monticelli is one of those singular men of genius who are not connected with any school, and whose work is an inexhaustible source of applications. He lived at Marseilles, where he was born, made a short appearance at the Salons, and then returned to his native town, where he died poor, ignored, paralysed and mad.
In order to live he sold his small pictures at the cafés, where they fetched ten or twenty francs at the most. Today they sell for considerable prices. The mysterious power of these paintings secures him a fame which is, alas! posthumous. Many Monticellis have been sold by dealers as Diaz's; now they are more eagerly looked for than Diaz, and collectors have made fortunes with these small canvases bought formerly, to use a colloquial expression which is here only too literally true, ''for a piece of bread.''
Monticelli painted landscapes, romantic scenes, and still-life pictures: one could not imagine a more inspired sense of colour than shown by these works which seem to be painted with crushed jewels, with powerful harmony, and beyond all with an unheard-of delicacy in the perception of fine shades. There are tones which nobody had ever invented yet, a richness, a profusion, a subtlety which almost vie with the resources of music. The fairyland atmosphere of these works surrounds a very firm design of charming style, but, to use the words of the artist himself, ''in these canvases the objects are the decoration, the touches are the scales, and the light is the tenor.'' Monticelli has created for himself an entirely personal technique which can only be compared with that of Turner; he painted with a brush so full, fat and rich, that some of the details are often truly modelled in relief, in a substance as precious as enamels, jewels, ceramics - a substance which is a delight in itself. Every picture by Monticelli provokes astonishment; constructed upon one colour as upon a musical theme, it rises to intensities which one would have thought impossible. His pictures are magnificent bouquets, bursts of joy and colour, where nothing is ever crude, and where everything is ruled by a supreme sense of harmony.

Q. Which of the following is stated by the author as Monticelli's contribution to the world of art?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 5

1. Incorrect. "Ultimate" is too far-fetched. "Scenic beauty" does not represent his contribution.
2. Incorrect. "Romance" and "festivity" are both extraneous to the passage.
3. Correct. Lines: "One could not imagine a more inspired sense of color..., with powerful harmony, and beyond all with an unheard-of delicacy in the perception of fine shades", lead us to the answer.
4. Incorrect. "Fantasy" is extraneous to the passage.

CAT Mock Test - 12 (November 14) - Question 6

Directions: The passage below is followed by a question based on its content. Answer the question on the basis of what is stated or implied in the passage.

The incisive observations entrenched in Parmenides' Eleatic as we know it may actually have originated in Parmenides' lecture notes, or even those of one of his students. Regardless of the origin, Kepler refers to Eleatic, written prior to 323 B.C., as "one of the most enlightening and dominant books ever produced by the human intellect".
Even though it cannot be disputed that translations of Parmenides' work were available at other places also, no proof exists demonstrating that European scholars had access to it between the fifth and ninth centuries. Parmenides was known in Turkey, and a Nestorian monk of the ninth century translated the Eleatic into Turkish from a complete Greek manuscript that is now lost. The work was translated from the Turkish in Arabic in the year 935; from this translation Altamsh of Kardaba, an Islamic philosopher, fashioned a condensed translation in the 12th century projected to "determine how much of Parmenides' book on poetry is concerned with universal rules common to all nations or to most; for most of what is found in this book consists either of rules proper to their poetry and their usage, or they are found in Arabian poetry, or they are found in other languages." Altamsh replaced Arabic examples for the Greek, possessed no notion of literature being a simulation of life, and failed to realise much of the sense of the treatise. It was, however, Altamsh's translation, translated into Latin by Herart Eledir in the thirteenth century, published in Venice in 1481 and reprinted in 1515, that was the first medium enabling Renaissance scholars to judge the content of Eleatic. This version of Eleatic circulated freely, leaving no signs that it influenced critical literature. The practice of translations into Latin (1498), into Greek by Erasmus in 1532, and into Italian by Guini in 1594 has been documented.
When the Italian Renaissance scholars were able to consider the work of Parmenides, the result was twisted not only by the number of quality of translation, but also by the nature of the Italian Renaissance itself, questions of the wished-for meaning of main words and phrases, and the enveloping influence of Horace and the ancient.
The Italians' particular ardour for form established the groundwork for the propagation of Parmenidian "rules," which evolved from faultily construed principles of the Eleatic and incorporated the add-ons of unity of place, elucidation of "nobility" to denote noticeable nobility, the Quintian five acts, and a subjective segregation of a fourth person in dialogue. In Gihhin Jinthos's work, Parmenides's prerequisite that the poet, in contrast to the historian, relate what could happen is interpreted as a requirement that the poetry represents things as they should occur. Other scholars freely amplified Parmenides' work, completing his statements by adding much of the collection of medieval guidelines and a heavy amount of Christian contemplation.
Parmenides is generally understood to have wanted that the tragic hero be "noble." Italian scholars interpreted that the tragic hero be highly famed and affluent, and the status of the actors became such a significant deliberation in the Renaissance that it was sensed to be the distinctive factor between comedy and tragedy. Other facets of drama – scheme, vista, number of players, and poetry – were caste by this construal.

Q. Which of the following statements best summarises the central idea of the passage?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 6

Choice (1) blankets both the historical background of the passage of Eleatic from oblivion into the Italian Renaissance and the influence it had upon the Italian Renaissance. The passage itself expands upon these two ideas.
Choice (2) ignores the historical passage of Eleatic into Italy and passes a value judgment upon scholars who considered it.
Choice (3) is too general since this passage discusses literary criticism of only one work, Eleatic.
Choice (4) is a good summary of the second half of the passage, but not an accurate summary of the whole passage.

CAT Mock Test - 12 (November 14) - Question 7

Directions: Read the passage and answer the following question.

Since the dawn of recorded law, Western societies have recognised that some people shouldn't be held liable for their acts because they are non compos mentis – not in their right mind. This exemption from criminal sanctions was seen as an act of mercy required by basic morality. This principle was well-established in the English common law, and from there into the law of the United States. In the scenario of ever-rising criminal instances, the question has always been 'the kind and degree of insanity that would excuse its victim from punishment for an act which if done by a sane person would bring upon him the sanctions of the law', as put in the House of Lords in 1843. Until the 20th century, little was known about mental illness. Judging whether a person was deranged—seriously mentally ill and irrational—was seen as a matter for common knowledge. It was a case of 'I know it when I see it.'
The courts tried to codify and standardise the construct of criminal insanity. By the 18th century, the commonly applied legal test in England was that a man should be found not guilty by reason of insanity (NGRI) if he is 'totally deprived of his understanding and memory, and doth not know what he is doing, no more than an infant, than a brute, or a wild beast, such a one is never the object of punishment'. Animals 'know' what they are doing, of course, but they don't know the moral dimension of it. Courts continued to waiver between holding any person guilty who 'knew' what he was doing, and holding to account only those who were morally aware of the wrongness of their action. The problem with this formula is that we tend to measure the wickedness of an actor by our degree of outrage over the act. This allows room for bias, moral condemnation, and the impulse for retribution to enter the process.
The current legal definition of insanity also has no psychiatric correlate; it is a pure creature of law, owing nothing to psychiatry and the sciences of brain and behaviour. The lack of a psychiatric correlate makes it look like psychiatrists and psychologists are unreliable or that mental illness is purely subjective; the fact is, mental health experts often can't agree on whether a defendant fits into the legal definition of insanity, even though they agree about the defendant's diagnosis and degree of psychiatric impairment.
If jurors don't identify with the defendant, perhaps because of ethnic, racial, gender or demographic (status) differences, and if they fear the defendant's criminal act is one that particularly shocks their conscience, acquittal is unlikely, no matter how mentally ill, delusional or irrational the defendant was at the time of commission of the crime. I believe this accounts in part for defence attorneys' hesitation to raise an insanity defence. Approximately 15 per cent of those incarcerated in US prisons have serious mental health disorders. But only 1 per cent of all felony defendants plead not guilty by reason of insanity, and only a quarter of those are found NGRI, in spite of strong psychiatric evidence. As Nygaard said, the legal definition of insanity is in such 'nebulous and often psychologically meaningless terms', it results in 'almost wholly arbitrary decision[s] as to who knows "right" from "wrong"'. These numbers suggest that, to paraphrase Shakespeare, the insanity defence is more honoured in its breach than in its observance.

Q. Which of the following, if true, would weaken the author's argument for insanity defence on the basis of non compos mentis?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 7

The author argues that some people shouldn't be held liable for their acts because they are not in their right mind (non compos mentis). But he also mentions that criminal cases are ever increasing - 'scenario of ever rising criminal instances'. So, if it is true that punishment can deter even the insane people from criminal acts, the author's argument will be weakened. Option 3 is the best choice.
Option 1 does not weaken the argument of the author. If the propotion of criminal acts done by insane people is negligible as compared to sane people, then the author's case of insanity defence on the basis of non compos mentis is upheld since the criminal act can then be treated as an exception and the insanity defence would work.
Option 2 does not weaken the author's argument. Insane people become fearless because of lack of judgement, but it can not be taken as a ground to oppose the argument that they should be held liable.
Option 4 is also not against the author's argument. It also conveys that morality should be considered when dealing with criminal acts, and so says the author.

CAT Mock Test - 12 (November 14) - Question 8

Directions: Read the passage and answer the following question.

Since the dawn of recorded law, Western societies have recognised that some people shouldn't be held liable for their acts because they are non compos mentis – not in their right mind. This exemption from criminal sanctions was seen as an act of mercy required by basic morality. This principle was well-established in the English common law, and from there into the law of the United States. In the scenario of ever-rising criminal instances, the question has always been 'the kind and degree of insanity that would excuse its victim from punishment for an act which if done by a sane person would bring upon him the sanctions of the law', as put in the House of Lords in 1843. Until the 20th century, little was known about mental illness. Judging whether a person was deranged—seriously mentally ill and irrational—was seen as a matter for common knowledge. It was a case of 'I know it when I see it.'
The courts tried to codify and standardise the construct of criminal insanity. By the 18th century, the commonly applied legal test in England was that a man should be found not guilty by reason of insanity (NGRI) if he is 'totally deprived of his understanding and memory, and doth not know what he is doing, no more than an infant, than a brute, or a wild beast, such a one is never the object of punishment'. Animals 'know' what they are doing, of course, but they don't know the moral dimension of it. Courts continued to waiver between holding any person guilty who 'knew' what he was doing, and holding to account only those who were morally aware of the wrongness of their action. The problem with this formula is that we tend to measure the wickedness of an actor by our degree of outrage over the act. This allows room for bias, moral condemnation, and the impulse for retribution to enter the process.
The current legal definition of insanity also has no psychiatric correlate; it is a pure creature of law, owing nothing to psychiatry and the sciences of brain and behaviour. The lack of a psychiatric correlate makes it look like psychiatrists and psychologists are unreliable or that mental illness is purely subjective; the fact is, mental health experts often can't agree on whether a defendant fits into the legal definition of insanity, even though they agree about the defendant's diagnosis and degree of psychiatric impairment.
If jurors don't identify with the defendant, perhaps because of ethnic, racial, gender or demographic (status) differences, and if they fear the defendant's criminal act is one that particularly shocks their conscience, acquittal is unlikely, no matter how mentally ill, delusional or irrational the defendant was at the time of commission of the crime. I believe this accounts in part for defence attorneys' hesitation to raise an insanity defence. Approximately 15 per cent of those incarcerated in US prisons have serious mental health disorders. But only 1 per cent of all felony defendants plead not guilty by reason of insanity, and only a quarter of those are found NGRI, in spite of strong psychiatric evidence. As Nygaard said, the legal definition of insanity is in such 'nebulous and often psychologically meaningless terms', it results in 'almost wholly arbitrary decision[s] as to who knows "right" from "wrong"'. These numbers suggest that, to paraphrase Shakespeare, the insanity defence is more honoured in its breach than in its observance.

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

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 8

Option 1 can be inferred from the second-last paragraph, 'The current legal definition of insanity also has no psychiatric correlate ... mental illness is purely subjective.'
Option 2 does not get support from the passage. It, in fact, implies that even the mentally ill are rational which is contradictory to what is stated in the text.
Option 3 cannot be inferred as the author states that it is not because of the erosion of human conscience but the lack of a reliable legal definition of insanity that insanity defence is partly not considered. Also, this option is extreme as it states 'no more considered a moral support'. The author states that '1 per cent of all felony defendants [do] plead not guilty by reason of insanity.'
Option 4 is contrary to what is mentioned in the passage: 'Animals know what they are doing, of course, but they don't know the moral dimension of it.'

*Answer can only contain numeric values
CAT Mock Test - 12 (November 14) - Question 9

Directions: The four sentences (labelled 1, 2, 3, 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.

1. It is expected not only to determine the results of an experiment but also to provide some understanding of the physical events that are presumed to underline the observed results.

2. Apart from experimental confirmations, however, something more is generally demanded of a theory.

3. When one seeks information of this kind in the quantum theory, certain conceptual difficulties arise.

4. In other words, a theory should not only give the position of a pointer on dial but also explain why the pointer takes up that position.


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 9

All the statements, except 2, start explaining a previous statement. So 2, which starts the topic under discussion - expectations from 'a theory' - comes first. It is followed by statement 1 ('it' in 1 refers to 'theory' in 2), which highlights the importance of explanation of 'results' in theory followed by an example on it which is mentioned in 4. Thus leaving us with 3 as the concluding statement. The sequence is 2143.

CAT Mock Test - 12 (November 14) - Question 10

Directions: The passage given below is followed by four alternative summaries. Choose the option that best captures the essence of the passage.

The longing not to die but to persist forever cannot arise in the mind which is locked up in time. Thus it is that man is not limited by time, really speaking. Otherwise, this desire to live long cannot arise in the mind. He is not even limited to space; otherwise, the desire to break the limitations of the world outside and probe into the corners of creation cannot arise in him. The longing to possess the whole world is not possible if it is locked up in a little space.

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 10

The author mentions about human mind that is not bound by the physical boundaries of space and is not locked up in time. He states that only this kind of mind can think about the possibilities that are beyond the scope of time and space (persist forever, the desire to break the limitations of the world outside, longing to possess the whole world). Hence, option 2 is the correct answer.
Option 1 is incorrect because a mind with no idea of limits of time is not removed, instead he has the idea to surpass time and space.

CAT Mock Test - 12 (November 14) - Question 11

Directions: These questions are based on the given charts.

In which of the following years, was the number of employees of company XYZ, the highest?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 11

Hence, in 2009 the number of employees of company XYZ was highest.

CAT Mock Test - 12 (November 14) - Question 12

Directions: These questions are based on the given charts.

The total assets of company XYZ continuously decreased (with respect to the previous year) in the four years from 2007 to 2010 by 20%, 10%, 5%, 10% respectively. Of these four years, in which year, was the ratio of revenue to assets the highest?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 12
From year 2007 to 2010, revenue is highest in year 2009 As assets of the company is continuously decreasing.

∴ Assets in 2009 is lesser than that in 2007 and 2008

∴ Ratio of revenue to assets in 2009 is higher than that in 2007 and 2008 Now in 2010 assets decreased by 10% when compared to 2009 and revenue in 2010 is 442 crores.

Let assets in 2009 be x

Then ratio of revenue to assets

In 2009 = 500/x

In 2010 = 4420.9x = 491.11/x

∴ Ratio is highest in 2009

CAT Mock Test - 12 (November 14) - Question 13

Directions: These questions are based on the given charts.

In which year during the period 2007-10 was the ratio of expenses to profit the lowest?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 13
The ratio of expenses to profit

The ratio is lowest in 2007.

CAT Mock Test - 12 (November 14) - Question 14

The following table shows data of lipsticks, please refer to the table to answer the questions that follow

Brand C’s sales in March 2009 account for what percentage of Brand C’s cumulative sales from April 2008 to August 2008?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 14
Brand ‘C’s April, 2008 to August, 2008 sales

= Rs 14850000

March sales are Rs 3137000.

Required percentage = 21%

CAT Mock Test - 12 (November 14) - Question 15

The following table shows data of lipsticks, please refer to the table to answer the questions that follow

What is the total market sales of brand ‘C’ (in Rs ’000) in March 2009?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 15
Since 5.7% of total market sales = 3137

= 55035 appx.

*Answer can only contain numeric values
CAT Mock Test - 12 (November 14) - Question 16

Directions: Read the following information and answer the question the follows:
Exactly three persons Hari, Krish, and Ram participated in a weightlifting competition, comprising three rounds, in which each person lifts a weight exactly once in each of the three rounds. After the three persons participate in the three rounds the combined total weight, which is defined as the sum of the heaviest two weights lifted in any round by a person, is calculated for each of the three persons. The three persons are ranked from 1 to 3, in the descending order of their combined total weights. No person lifted the same weight across any two rounds and the combined Total weight for each person was distinct. Further, the weight (in kg) that each person lifted was an integer.
Ram lifted 17 kg more in the first round than Krish did in that round, while Hari lifted the same weight in the second round as Krish did in the third round. Also, the round in which a person lifted his least weight was distinct for the three persons. The difference in the weight lifted by Krish in the first round and that by Ram in the third round was 20 kg, while the difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. Krish lifted 25 kg more in the second round than Hari did in the first round. The combined total weight for Hari was the sum of the weights that he lifted in the first and second rounds. Further, Ram lifted 15 kg more in the second round than Krish did in the third round.
 

Q. If Krish was ranked first in the competition, what is the minimum difference (in kg) between the highest weight that any person lifted in any round and the lowest weight that any person lifted in any round?


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 16

Given that Ram lifted 17 kg more than Krish in the first round. Let the weight that Krish lifted in the first round be X. Weight lifted by Ram lifted in the first round will be X + 17. Let the weight that Hari lifted in the second round be Y which is the same as the weight lifted by Krish in the third round.
Given that the difference in the weights lifted by Krish in the first round and that by Ram in the third round was 20 kg hence the weight that Ram lifted in the third round can be X ± 20.
The difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. And the weight that Hari lifted in the third round will be X + 17 ± 18 = X–1 or X+35.
Krish lifted 25 kg more in the second round than Hari did in the first round. Let Hari lift Z kg in the first round hence Krish lifted Z + 25 kg in the second round.
Also, Ram lifted 15 kg more in the second round than Krish did in the third round. Since Krish lifted Y kg in the third round Ram must lift Y + 15 kg in the second round. For Hari, the weights that he lifted in the first and second rounds were the top weight. In the three rounds. Hari lifted Z, Y, and X–1/ X+35 kgs. Both Z and Y must definitely be greater than X – 1. So, the wait for Hari in 3rd round will be X + 35.
Since Krish lifted X, Z+25, and Y in the three rounds, Z + 25 must be in the top 2, this is because Z is greater than X – 1 and hence Z + 25 will be greater than X. Each person lifted the least weight in a different round. Hence Krish could not have lifted the least weight in the third round.  Krish must have lifted the least weight in the first round. For Krish, the weight in the second and third rounds would have been considered.
For Ram, the weight in the first and third rounds will be considered. This means that the weight Ram lifted in the third round must be greater than that in the second round. Therefore Y + 15 < X ± 20. But Y > X – 1. 
So, Y + 15 cannot be less than X–20. This implies that the weight lifted by Ram in the third round is X + 20. Ram Limited X + 17, Y + 15, and X + 20 in the three rounds X + 17 must be greater than Y + 15 = >Y < X + 2.
For, Hari the weight that he lifted in the third round cannot be X + 35(Y < X + 2) and if Hari lifted X + 35 in the third round it will definitely be greater than Y. Hence, Hari lifted Z, Y, and X –1 in the three rounds. Since the weight in the first and second rounds was considered Y > X – 1.
Hence X – 1 < Y < X + 2. Since X, Y, and Z are all integers Y can be equal to X or X + 1. But if X = Y, Krish would have lifted the same weight in the first and third rounds. Hence Y cannot be equal to X. So, Y=X+1.
The following table provides the weight that each person lifted and combines the Total weight in terms of X and Z.


If Krish was ranked first in the competition, then X+Z+26>2X+37=>Z<X+11. Since Z is greater than X+11, Z+25 will be greater than X+36. Hence the highest weight that anyone lifted must be Z+25 and the least weight is X-1. We need to minimize the difference between the highest and lowest weights that any person lifted in any attempt, i.e., we need to minimize the value of Z+25 - (X-1). The minimum value of Z=X+12. Hence the minimum difference =X+12+25-X+1=38kg.
Answer: 38

*Answer can only contain numeric values
CAT Mock Test - 12 (November 14) - Question 17

Directions: Read the following information and answer the question the follows:
Exactly three persons Hari, Krish, and Ram participated in a weightlifting competition, comprising three rounds, in which each person lifts a weight exactly once in each of the three rounds. After the three persons participate in the three rounds the combined total weight, which is defined as the sum of the heaviest two weights lifted in any round by a person, is calculated for each of the three persons. The three persons are ranked from 1 to 3, in the descending order of their combined total weights. No person lifted the same weight across any two rounds and the combined Total weight for each person was distinct. Further, the weight (in kg) that each person lifted was an integer.
Ram lifted 17 kg more in the first round than Krish did in that round, while Hari lifted the same weight in the second round as Krish did in the third round. Also, the round in which a person lifted his least weight was distinct for the three persons. The difference in the weight lifted by Krish in the first round and that by Ram in the third round was 20 kg, while the difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. Krish lifted 25 kg more in the second round than Hari did in the first round. The combined total weight for Hari was the sum of the weights that he lifted in the first and second rounds. Further, Ram lifted 15 kg more in the second round than Krish did in the third round.
 

Q. If Hari was ranked second in the competition what is the minimum difference (in kg) between the weight that Krish lifted in the second round and the weight that Ram lifted in the second round?


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 17

Given that Ram lifted 17 kg more than Krish in the first round. Let the weight that Krish lifted in the first round be X. Weight lifted by Ram lifted in the first round will be X + 17. Let the weight that Hari lifted in the second round be Y which is the same as the weight lifted by Krish in the third round.
Given that the difference in the weights lifted by Krish in the first round and that by Ram in the third round was 20 kg hence the weight that Ram lifted in the third round can be X ± 20.
The difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. And the weight that Hari lifted in the third round will be X + 17 ± 18 = X–1 or X+35.
Krish lifted 25 kg more in the second round than Hari did in the first round. Let Hari lift Z kg in the first round hence Krish lifted Z + 25 kg in the second round.
Also, Ram lifted 15 kg more in the second round than Krish did in the third round. Since Krish lifted Y kg in the third round Ram must lift Y + 15 kg in the second round. For Hari, the weights that he lifted in the first and second rounds were the top weight. In the three rounds. Hari lifted Z, Y, and X–1/ X+35 kgs. Both Z and Y must definitely be greater than X – 1. So, the wait for Hari in 3rd round will be X + 35.
Since Krish lifted X, Z+25, and Y in the three rounds, Z + 25 must be in the top 2, this is because Z is greater than X – 1 and hence Z + 25 will be greater than X. Each person lifted the least weight in a different round. Hence Krish could not have lifted the least weight in the third round.  Krish must have lifted the least weight in the first round. For Krish, the weight in the second and third rounds would have been considered.
For Ram, the weight in the first and third rounds will be considered. This means that the weight Ram lifted in the third round must be greater than that in the second round. Therefore Y + 15 < X ± 20. But Y > X – 1. 
So, Y + 15 cannot be less than X–20. This implies that the weight lifted by Ram in the third round is X + 20. Ram Limited X + 17, Y + 15, and X + 20 in the three rounds X + 17 must be greater than Y + 15 = >Y < X + 2.
For, Hari the weight that he lifted in the third round cannot be X + 35(Y < X + 2) and if Hari lifted X + 35 in the third round it will definitely be greater than Y. Hence, Hari lifted Z, Y, and X –1 in the three rounds. Since the weight in the first and second rounds was considered Y > X – 1.
Hence X – 1 < Y < X + 2. Since X, Y, and Z are all integers Y can be equal to X or X + 1. But if X = Y, Krish would have lifted the same weight in the first and third rounds. Hence Y cannot be equal to X. So, Y=X+1.
The following table provides the weight that each person lifted and combines the Total weight in terms of X and Z.


If Hari was ranked second in the competition, Kris must have been ranked first and Ram must have been ranked last. Hence, 2X + 37 < X+Z+1= > Z > X + 36. We need to minimize the value of Z+25–(X+16). The minimum possible value of Z=X+37. Hence, the minimum possible difference = X + 37 + 25 – (X+16) = 46 kg
Answer: 46

*Answer can only contain numeric values
CAT Mock Test - 12 (November 14) - Question 18

Directions: Read the following information and answer the question the follows:
Exactly three persons Hari, Krish, and Ram participated in a weightlifting competition, comprising three rounds, in which each person lifts a weight exactly once in each of the three rounds. After the three persons participate in the three rounds the combined total weight, which is defined as the sum of the heaviest two weights lifted in any round by a person, is calculated for each of the three persons. The three persons are ranked from 1 to 3, in the descending order of their combined total weights. No person lifted the same weight across any two rounds and the combined Total weight for each person was distinct. Further, the weight (in kg) that each person lifted was an integer.
Ram lifted 17 kg more in the first round than Krish did in that round, while Hari lifted the same weight in the second round as Krish did in the third round. Also, the round in which a person lifted his least weight was distinct for the three persons. The difference in the weight lifted by Krish in the first round and that by Ram in the third round was 20 kg, while the difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. Krish lifted 25 kg more in the second round than Hari did in the first round. The combined total weight for Hari was the sum of the weights that he lifted in the first and second rounds. Further, Ram lifted 15 kg more in the second round than Krish did in the third round.
 

Q. If the weights lifted by each person in the second round were all distinct integral multiples of 15 what is the minimum combined Total weight (in kg) of the person who was ranked first?


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 18

Given that Ram lifted 17 kg more than Krish in the first round. Let the weight that Krish lifted in the first round be X. Weight lifted by Ram lifted in the first round will be X + 17. Let the weight that Hari lifted in the second round be Y which is the same as the weight lifted by Krish in the third round.
Given that the difference in the weights lifted by Krish in the first round and that by Ram in the third round was 20 kg hence the weight that Ram lifted in the third round can be X ± 20.
The difference in the weights lifted by Ram in the first round and Hari in the third round was 18 kg. And the weight that Hari lifted in the third round will be X + 17 ± 18 = X–1 or X+35.
Krish lifted 25 kg more in the second round than Hari did in the first round. Let Hari lift Z kg in the first round hence Krish lifted Z + 25 kg in the second round.
Also, Ram lifted 15 kg more in the second round than Krish did in the third round. Since Krish lifted Y kg in the third round Ram must lift Y + 15 kg in the second round. For Hari, the weights that he lifted in the first and second rounds were the top weight. In the three rounds. Hari lifted Z, Y, and X–1/ X+35 kgs. Both Z and Y must definitely be greater than X – 1. So, the wait for Hari in 3rd round will be X + 35.
Since Krish lifted X, Z+25, and Y in the three rounds, Z + 25 must be in the top 2, this is because Z is greater than X – 1 and hence Z + 25 will be greater than X. Each person lifted the least weight in a different round. Hence Krish could not have lifted the least weight in the third round.  Krish must have lifted the least weight in the first round. For Krish, the weight in the second and third rounds would have been considered.
For Ram, the weight in the first and third rounds will be considered. This means that the weight Ram lifted in the third round must be greater than that in the second round. Therefore Y + 15 < X ± 20. But Y > X – 1. 
So, Y + 15 cannot be less than X–20. This implies that the weight lifted by Ram in the third round is X + 20. Ram Limited X + 17, Y + 15, and X + 20 in the three rounds X + 17 must be greater than Y + 15 = >Y < X + 2.
For, Hari the weight that he lifted in the third round cannot be X + 35(Y < X + 2) and if Hari lifted X + 35 in the third round it will definitely be greater than Y. Hence, Hari lifted Z, Y, and X –1 in the three rounds. Since the weight in the first and second rounds was considered Y > X – 1.
Hence X – 1 < Y < X + 2. Since X, Y, and Z are all integers Y can be equal to X or X + 1. But if X = Y, Krish would have lifted the same weight in the first and third rounds. Hence Y cannot be equal to X. So, Y=X+1.
The following table provides the weight that each person lifted and combines the Total weight in terms of X and Z.


For X+1 and X+16 to be multiples of 15, X must be of the form 15k–1. The minimum possible value of X=14. Since Z+25 must be a distinct integral multiple of 15, Z+25 can be a minimum of 45. Hence, Z=20. In this case, Ram would be ranked first and the combined total weight for Ram=65kg. If we take Z=5(to minimize the value of Z+25), then X must be at least 44(X cannot be 14 because X+16 will be equal to Z+25 first. But the combined total weight= 125kg. Hence, the minimum combined total weight =65kg.
Answer : 65

CAT Mock Test - 12 (November 14) - Question 19

Directions: – Answer the questions on the basis of the information given below.
A group of X students applied to three colleges– A, B, and C to pursue their post–graduation such that each student applied to at least one college. Further, it is known that the number of students who applied only to A is one–third the number of students who applied only to C. The number of students who applied to exactly two colleges is the same as the number of students who applied to only C. The number of students who applied to at least two colleges is the same as the number of students who applied to A. The number of students who applied to B is equal to the number of students who applied only to A.

Q. If exactly 100 students applied only to A, what is the value of X?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 19


From the given Venn diagram
3a = c    
d + e + f  = c = 3a
d + e + f + g = a + d + e + g 
=> f = a
a = b + d + f + g
as, a = f so b + d + g = 0 i.e., b = d = g = 0
Hence, d + e + f  = c = 3a, d = 0, f = a
Than e = 2a

Total number of student – a + b + c + d + e + f + g 
=> a + 0 + 3a + 0 + 2a + a + 0  => 7a
Given a = 100, Total number of students is 7a 
= 7 × 100 
= 700

CAT Mock Test - 12 (November 14) - Question 20

Directions: – Answer the questions on the basis of the information given below.
A group of X students applied to three colleges– A, B, and C to pursue their post–graduation such that each student applied to at least one college. Further, it is known that the number of students who applied only to A is one–third the number of students who applied only to C. The number of students who applied to exactly two colleges is the same as the number of students who applied to only C. The number of students who applied to at least two colleges is the same as the number of students who applied to A. The number of students who applied to B is equal to the number of students who applied only to A.

Q. Which of the following can be the number of students who applied to C?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 20


From the given Venn diagram
3a = c    
d + e + f  = c = 3a
d + e + f + g = a + d + e + g 
=> f = a
a = b + d + f + g
as, a = f so b + d + g = 0 i.e., b = d = g = 0
Hence, d + e + f  = c = 3a, d = 0, f = a
Than e = 2a

Since a has to be an integer, the number of students who applied for college C must be divisible by 6.
The answer option is B.

CAT Mock Test - 12 (November 14) - Question 21

If f(y) = x2 + (2p + 1)x + p2 −1 and x is a real number, for what values of ' p′ the function becomes 0?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 21
The function f(y) is a quadratic equation.

It is given that x is real.

So the discriminant of f(y) ≥ 0

i.e. D = b2 − 4ac ≥ 0 or

(2p + 1)2 − 4(p2 − 1) ≥ 0

4p2 + 4p + 1 − 4(p2 − 1) ≥ 0

4p + 5 ≥ 0

Or p ≥ -5/4

CAT Mock Test - 12 (November 14) - Question 22

A factory has 80 workers and 3 machines. Each worker knows to operate at least 1 machine. If there are 65 persons who knows to operate machine 1,60 who knows to operate machine 2 and 55 who knows to operate machine 3, what can be the minimum number of persons who knows to operate all the three machines?


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 22
Let's start with taking a random value for all three category. So let's first take 40 for the all three category. Now 65 + 60 + 55 = 180, this means there is

an extra count of 180−80=100.

Now as we know that the extra count occurs in the in the exactly two area and the all three area.

So let's try put the extra count in these area.

Trial 1− since 40 is already assumed to be in the all three area, it takes care of extra count of 40 × 2 = 80.

Thus we are left with 20 as extra count which we have to place at the exactly two area.

Thus in the above case our venn diagram will look as:

A close look in the figure tells us that we can further decrease the value of all the three area. A bit of logical thinking will bring us to the value 20. No value less than 20 can satisfy the conditions of the question. As there is no scope left for reallocating numbers left from one area to another in this case.

Hence the final venn diagram will look as:

CAT Mock Test - 12 (November 14) - Question 23

If cos ⁡A + cos2⁡A = 1 and a sin12⁡A + b sin10 ⁡A + c sin8⁡A + d sin6 ⁡A − 1 = 0. Find the value of a + b/c + d

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 23
Given,

cos⁡A = 1 − cos2⁡A

⇒ cos⁡ A = sin2 ⁡A

⇒ cos2⁡A = sin4⁡A

⇒ 1−sin2 ⁡A = sin4 ⁡A

⇒ 1 = sin4⁡A + sin2⁡A

⇒ 13 =(sin4⁡A + sin2⁡A)3

⇒ 1 = sin12⁡A + sin6⁡A + 3 sin8⁡A + 3sin10⁡A

⇒ sin12⁡A + sin6⁡A + 3sin8⁡A + 3sin10⁡A−1 = 0

On comparing,

a = 1, b = 3, c = 3, d = 1

∴ b/c + d = 3

Always look out for Pythagorean triplets, we know that (8, 15, 17) is one

CAT Mock Test - 12 (November 14) - Question 24

A train 150m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 24
D = 72 × 5/18 = 25 = 500 - 150 = 350
CAT Mock Test - 12 (November 14) - Question 25

A bike costs Rs.48000. Its value depreciates by 30% in the first year and in each subsequent year the depreciation is 20% of the value at the beginning of that year. The value of the bike after 3 years will be


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 25
The required value of the bike after 3 years = 48000 (70/100) (80/100)2= Rs. 21504
CAT Mock Test - 12 (November 14) - Question 26

The cost of diamond varies directly as the square of its weight. Once, this diamond broke into four pieces with weights in the ratio 1:2:3:4. When the pieces were sold, the merchant got Rs. 70,000 less. Find the original price of the diamond.


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 26
Let the original weight of the diamond be 10x. Hence, its original price will be k(100x2), where k is a constant. The weights of the pieces after breaking are x,2x,3x and 4x. Therefore, their prices will be kx2, 4kx2, 9kx2 and 16kx2. So the total price of the pieces = (1 + 4 + 9 + 16)kx2 = 30kx2

Hence, the difference in the price of the original diamond and its pieces

= 100kx2 − 30kx2 = 70kx2 = 70000. Hence, kx2 = 000 and the original price

= 100kx2 = 100 × 1000 = 100000

CAT Mock Test - 12 (November 14) - Question 27

If two of the sides of a right triangle are 10cm and 10.5cm and its inradius is 3cm, what is its circumradius?

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 27
The hypotenuse is the longest side of a right-angled triangle. Given that two of the sides of a right triangle are 10cm and 10.5cm.

If hypotenuse =10.5cm, then the sides containing the right angle are and But the inradius of the triangle is given as 3cm. The smallest of the sides is more than 6cm long. Therefore, the 10.5cm side is not the hypotenuse. Hence the lengths of the sides containing the right angle are 10cm and 10.5cm. 80, hypotenuse

The circumradius of the right triangle = 14.5/2 = 7.25cm

CAT Mock Test - 12 (November 14) - Question 28

The number of distinct pairs of integers (m,n), satisfying ∣1+mn∣ < ∣m+n∣ < 5 is

 


Detailed Solution for CAT Mock Test - 12 (November 14) - Question 28

Let us break this up into 2 inequations [ Let us assume x as m and y as n ]

| 1 + mn | < | m + n |

| m + n | < 5

Looking at these expressions, we can clearly tell that the graphs will be symmetrical about the origin.

Let us try out with the first quadrant and extend the results to the other quadrants.

We will also consider the +X and +Y axes along with the quadrant.

So, the first inequality becomes,

1 + mn < m + n

1 + mn - m - n < 0

1 - m + mn - n < 0

(1-m) + n(m-1) < 0

(1-m)(1-n) < 0

(m - 1)(n - 1) < 0

Let us try to plot the graph.

If we consider only mn < 0, then we get 

But, we have (m - 1)(n - 1) < 0, so we need to shift the graphs by one unit towards positive x and positive y.

So, we have,

But, we are only considering the first quadrant and the +X and +Y axes. Hence, if we extend, we get the following region.

So, if we look for only integer values, we get

(0,2), (0,3),.......

(0,-2), (0, -3),......

(2,0), (3,0), ......

(-2,0), (-3,0), .......

Now, let us consider the other inequation as well, in which |x + y| < 5

Since one of the values is always zero, the modulus of the other value is less than or equal to 4.

Hence, we get 

(0,2), (0,3), (0,4)

(0,-2), (0, -3), (0, -4)

(2,0), (3,0), (4,0)

(-2,0), (-3,0), (-4,0)

Hence, a total of 12 values.

CAT Mock Test - 12 (November 14) - Question 29

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 29

CAT Mock Test - 12 (November 14) - Question 30

Side AB of a triangle ABC is 80 cm long, whose perimeter is 170cm. If angle ABC = 60 degrees, the shortest side of triangle ABC measures (cm)

Detailed Solution for CAT Mock Test - 12 (November 14) - Question 30
a + b = 90cm. cosine rule gives

Solving a = 17 and b = 73

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