1
What type of semi-conductor is obtained when silicon is doped with boron? (2 marks)
Having invested the whole of yesterday making notes on what he should be making notes on, instead of making the notes he should be making, Roll No. 27 did not want to use up another day in pre-preparatory mode, tuning his mental engine, so to speak, and motivating himself and building his self-confidence by oiling his cerebral cortex with the most powerful – literally, the V8s, you could say – of inspirational quotations by famous and powerful role models and dead people the whole world looked up to such as Benjamin Franklin and Swami Vivekananda and Abraham Lincoln that he had personally curated from Reader’s Digest and jotted down in his red diary for ready and regular reference, a sort of psychological vitamins that he gulped down a few mg of nine times a day as per the self-motivational alarm he’d set on his wristwatch with the option to also, alternatively, chant inside his skull silently (so as not to wake anyone, apart from himself, up), ‘YOU ARE A TOPPER, YOU ALWAYS HAVE BEEN A TOPPER, YOU ALWAYS WILL BE A TOPPER’ whenever he found the needle of his can-do spirit sliding toward empty and the avalanche of negativity threatened to bury him under. Sometimes the avalanche of negativity began as a tiny and innocuous wave-particle vibrating at a frequency of 80–400 MHz between and slightly above his eyebrows where his third eye would have been had he been Lord Shiva and this vibrating wave-particle gradually either metastasized or rippled outward across his temples and ear and neck and burrowed down his spine and, like a fighter jet, swooped back at the last minute away from his butt and up to his diaphragm and chest cavity and when this by now body-sized wave-particle swept over him and turned into the avalanche of negativity, he knew nothing was going to change and he would flunk again and be held up as a warning to others – as others had once been held up as a warning to him – because he just wasn’t good enough and the moment he knew he wasn’t good enough was the moment the urge to get up from his desk and leave his books and go somewhere else, anywhere else, became irrepressible.
And that’s when he sought the help of inspirational quotes, from Paul A. Hauck’s How to Do What You Want to Do, and from the proverbs from the Book of Proverbs that he’d been gifted for his fourteenth birthday by his male parent. The Book of Proverbs was a concentrated form of the inspiring real-life stories from Chicken Soup for the High School Student’s Soul that he’d picked up from the 32nd International Book Fair and been dipping into of late. They were self-belief-inducing, psychic momentum-generating capsules of motivational whey protein designed to make the reader believe – without the necessity of any intervention from his/her volitional apparatus – that s/he had it in himself/herself to tough it out because tough times never lasted while tough guys/girls did, and so he (Roll No. 27) needed to believe in himself enough to be able to motivate himself, to read out the riot act to his negativistic mind, show his negative-thinking self – his enemy and agent saboteur – who was boss, so he could prepare adequately this time, rather than end up repeating what had happened with the quarterlies and half-yearlies, where he’d exhausted all his prep time trying to get himself to believe that he still had it in him to study instead of actually studying.
But then, even now, though he knew he should be focusing his mind on semi-conductors, he noted with disgust that he was spending more time sipping his red diary and Chicken Soup, alternately, to convince himself that he could crack this chapter if he really applied himself instead of actually applying himself to cracking the chapter. He was deeply and self-consciously conscious of still being unable – despite the tons of high voltage self-motivation he was bringing to bear on his recalcitrant psyche – to bring himself to believe, at an emotional–psychological–visceral level what he intellectually grasped, and unable to translate, so to speak, cognitive fact into lived knowledge of the kind that could generate the desired outcomes in terms of empowerment and capacity-building such that he could see himself as a glorious academic gladiator competing joyfully with other academic gladiators for a respectable podium finish. But inexplicably, he was unable to practise what he preached to himself. Instead, all he wanted was out. But there was no out. He was in, very in, as his male parent never tired of reminding him, and the only option he had was to haul his ass to the toilet seat, set his bottom down calmly, and not get up till he got his shit together.
Getting one’s shit together, as Roll No. 27 knew already, was easier said. It was 3.45a.m. already. He’d been on the same page since 2.17a.m., having woken up at 2.05a.m., brushed his teeth and done his neck rotation exercises before settling down at his desk, as he’d planned, to crack the semi-conductors first, being the easiest of the chapters.
But though he was still physically seated at the table, much time had passed since his concentration stood up and left. He was already thinking of getting an earlier start tomorrow, which he could if he went to bed earlier. If he could time his daily mandatory quota of sleep to coincide with the hours when distraction was at its peak – say, from 7p.m. to 1a.m. – he could still get his minimum requirement of six hours’ sleep and be up at 1 and well-positioned to max out on the quietest time of the twenty-four-hour cycle.
The big question was, would that even make a difference? Put differently, would even that make a difference? There was a crick in the second vertebra from down up that he tried to get rid of by doing a seated twist but it wouldn’t go away. You never are 100 per cent mentally available for your studies, are you now, his negativity asked him. Never, he agreed. Even now, this early in the morning, and it really was early by any yardstick, his best time for study, full quiet, no distractions (save the occasional barking of a street dog, but that couldn’t be helped, and besides it didn’t really count as a distraction as the sound of the barking did not carry any meaning that could draw his mind away from the subject at hand [semi-conductors], or rather the barking did not carry any meaning at all – except perhaps for other dogs, or some human who was within biting/chasing range of the barking dog), and no regrets (about having wasted a part of the day) troubling him when he was trying to focus, and yet he hadn’t been able to concentrate or make any progress with the bits and pieces of concentration he did manage to muster for some eighty or ninety seconds max at a stretch before hitting a pothole of distraction. On the positive side, he still had time to get some study miles behind him before he actually started trailing his timetable, yet again.
If he were to put a determinedly positive spin on it, as of this moment, 3:45:58, he still did enjoy a comfortable head start on the day. Undeniably he did. For he could, technically speaking, waste his time or let his mind wander for the next two hours and still not have regrets about having wasted a part of the day because the day did not start until 5.45, which was the time he had set for himself for starting on his daily studies in his official timetable. But a couple of days back he had hit upon the idea of setting up a parallel, unofficial timetable that began a few hours earlier than his official time table so as to keep the pressure off himself. So that even if his mind kept buzzing off, and he managed to get done only, say, forty-five minutes of actual studying considered in terms of his mind being involved directly (and solely) in processing the concepts and data of his syllabus textbook open in front of him and not the quantum of time he happened to be bodily bonded to his desk-chair (which was not an easy task either), he would still have a surplus of forty-five minutes – one entire half of a full-time football match – to begin his study day with, which should come in handy in combating the pathological negativity and hangdog mode he had a tendency to slip into if he slipped up on his concentration by even ten seconds in the crucial first hour of his first official study session of the day.
But this head start, instead of being a source of security and imbuing him with an attitude of relaxed and confident positivity toward his studies, only seemed to encourage his mind to goof off even more – the typical hare mentality of the hare–tortoise parable. In the hour he had been studying, or rather, sitting, just beyond the rim of the off-white spotlight produced by his table lamp, his chin supported by hands conjoined at the base of the palms, the prickly mood of his sleep-interrupted eyes compounded by the excessive brightness of the page burning under a 40W bulb 13 inches away, his mind abandoned the silicon-doped boron (or was it vice versa?) and dwelled instead on the socio-biological injustice of his eyes being pressed into the hard labour of transporting meaning-resistant text from the page to an uncomprehending brain during a period of time mandated by God and Nature for rest and recovery, thereby challenging directly the study timetable that another faction of the same mind had thought up and sought to institutionalize.
The rebellious faction of Roll No. 27’s mind seemed to receive much support from Roll No. 27’s eyes, or at least one of them, given their asymmetrical musculature.1 Roll No 27’s eyes’ rays of visual attention, which, according to their JD, were required to converge on lines of text, were now doing their own thing – another way of saying this would be to say that they seemed to have developed a mind of their own, which was a fallacy for they were all acting on the orders of the various competing factions of the same mind, i.e. Roll No. 27’s. And these rays of visual attention of Roll No. 27’s eyes began to diverge, at first a little, and then some more, and then some more, until they ended up taking a wide collective U-turn of sorts, away from the page, and turned inward – into Roll No. 27’s own mind, into his past, his present and the future that was already visible to those who could see his past and his present, and at the same time, they also continued to transmit, via the conventional neural circuit, packets of lexical and conceptual data to Roll No. 27’s brain which, also resentful at being yanked into night duty during its me-time, stalled over the potentially lucrative pieces of knowledge2 packed into the pages of the physics refresher positioned at the centre of the above-mentioned spotlight which had turned the immediate physical environment of Roll No. 27 (beyond the page) into a zone of sombre, post-apocalyptic grey where glowed dully, like abandoned luxury cars, the shiny bonnets of several fat textbooks that lay in peaceful slumber on the floor, heavy reminders of the syllabic miles to be covered for which he had given up his sleep.
But let alone miles, Roll No. 27 had trouble covering millimetres. He simply could not study. Something had to be wrong with the engine of his psychic apparatus. The gears necessary for him to be able to focus would not click into place, and on the odd occasions that they did, would not remain in their slots. Changing tack, he moved away from semi-conductors to the section on the capacitance of a parallel plate capacitor but it only made him ponder his own impending academic and existential incapacitation – caused, it seemed to him, by his mind’s enormous resistance to the abstractions of physics, its poor conductivity of numerical logic, and the extreme marks-dependence of his personal happiness and public self-esteem.
2
What is the probability that an ordinary year has 53 Sundays? (1 mark)
Delhi boy Harish Goel emerged the national topper with a jaw-dropping score of 100 out of 100 in chemistry, physics, biology and mathematics in the Central Board of Secondary Education Class XII examination, the results of the Delhi region of which were announced here on Wednesday. The only ‘disappointment’ being English Core, in which he got 97.
Another Delhi boy, V. Chandrasekhar, emerged the commerce topper, and the all-India humanities toppers were Shakti Sethi and Veena Majumdar, also from Delhi.
‘I am elated right now,’ said Goel, on his way to a television studio to give his first interview of the day. ‘I did not take tuitions, but I studied hard for twelve to thirteen hours every day throughout the Board exams,’ he said, even as his mother added, ‘whatever Harish wanted, Harish usually got’.
‘He was a very focused child, I’ve never had to scold him to study or concentrate like other parents. He knew what he wanted and he went after it,’ she said, adding that he was their only child and ‘wanted to be good at everything he did’.
Goel was especially grateful to his school, Vaikunt Valley, Paschim Vihar, and had a special method that helped him get ‘awesome’ scores. ‘I studied throughout the year, and by the time the exams came around, I was in my third revision,’ said Goel, adding that he intended to study physics at St. Jobs’s, in Delhi.
3
A given rectangular area is to be fenced off in a field whose length lies along a straight river. If no fencing is needed along the river, show that the least length of fencing will be required when length of the field is twice its breadth. (6 marks)
What was the name of the river? What colour was it? Blue, like in the maps in his atlas? Green, like in the holiday pic the boy who thought himself Salman Khan showed him? Shit-brown, like the one they drove along on a road trip to Kashmir? How cool was the water? How swift? How deep? Roll No. 27 calculated that he needed to study, outside of school, at least eight hours on school days and sixteen hours on school holidays (not excluding Sundays, bank holidays, Diwali and his birthday). He had arrived at the figures of eight and sixteen when, following his flop show in the quarterlies, at the suggestion of his male parent, he’d decided to benchmark his study routines with best-in-class practices. His class, 11-B, was already the best of the four sections (A, B, C and D). Matching his study routines with the best of his own class ought to ensure he followed the best practices of his entire batch which ought to ensure he got as close to Harish Goel as humanly possible.
So he conducted an informal quantitative survey of his class’s upper percentile’s study practices. The questions were, of course, couched in casual terms, embedded in segments of data he proffered about his own routines (not that his respondents were interested in knowing them) so as to pre-empt any suspicion about his motives. He quickly discovered that his classmates belonged to two categories.
The first category consisted of specimens who refused to admit they ever studied, who would tell him, on the morning of the exam, that they hadn’t even ‘touched’ the subject in the past month because they had expended the entirety of their time reserves on cricket-playing and TV-watching and these specimens typically scored in the high nineties and were expected to top the school if not the district and the state.
The second category consisted of entities, admittedly less superhuman but no less extraordinary who casually let it drop they could study only fifteen hours (instead of their usual quota of sixteen) on Sunday because they had cousins visiting over the weekend who wouldn’t leave them alone to study and they told him, on the morning of the exam, that they were feeling 10.5 per cent sleepy because they had been up from 9 p.m. to 6 a.m. preparing (managing only an hour of sleep from 6.05 a.m. to 7.05 a.m.) and these organisms finished in a narrow band from the high eighties to the low nineties and, though they were destined to gain admission to any college of their or their progenitors’ choice, they nevertheless berated themselves every time over what they deemed an abysmal performance (a performance Roll No. 27 would have been thrilled to a million little pieces with) because they were yet again several percentage points below the Category 1 specimens despite having worked several times longer and harder than them.
In this class, Roll No. 27 was of course a bottom-feeder, though he had never been one until his male parent had shifted him to this elite school for his Class 11 and Class 12. But whatever school he was in, the subjects were the same, as his male parent had pointed out to him several times and the brain capacities were also, presumably (unless he had suddenly turned an idiot), the same. So, if he worked as hard as the toppers, there was no reason why he could not do better than finish second last – on the positive side, there still was one student behind him (Roll No. 33).
Given the same right inputs he ought to obtain the same right outputs. The equation in his head was as follows:
P + (Q x H) = M
While P was a constant and stood for a given subject (physics, maths, chemistry, whatever), Q, H and M were quantitative variables and represented IQ, hours of study, and marks obtained, respectively. The higher the IQ of the student and the higher the number of hours of study, the greater the marks he or she scored.
Evidently, Roll No. 27 did not believe his Q to be below that of his competitors. So all he needed to do was match his H with those of his academic betters.3 Of course he could not benchmark his H on those of the first category even though their self-proclaimed H (or lack thereof) seemed to work rather well for them. So it had to be the second category. But though hour-wise targets gave him at a practical level the motivation to affix himself to a single point in space for long periods of time by virtue of having his posterior in non-stop contact with the seat of the metallic folding chair that was now paired with a metallic folding study table, Roll No. 27’s fundamental problem remained as intractable as ever.
4
Q: How did you study? Did you follow a schedule?
A: I used to get up at 6 in the morning. 7–12 in the morning was the peak concentration time for me. I think it’s very important to set your biological clock to the time of the exam, usually 10–1 in the morning, so that you are mentally alert while giving the exam.
From a certain perspective, it would be a gross simplification to say that Roll No. 27 could not study, for saying so would imply that this was simply a personal, and perhaps idiosyncratic dysfunction, which was simply not true – not the whole truth in any case. Sure, it was true that he was a student (an occupation he had had no hand in choosing, and having been enrolled in school by his parents soon as he reached a certain age, he had continued in the semi-incarceration [physical and mental] built into schooling as an institution without there being any mutually meaningful consultations on the matter between him and his parents, either on the nature of, or the necessity for, or the rationale behind, the kind of schooling he would be subjected to, and organize his life around, for an entire decade, and whose impact on his psyche and/or suitability for his temperament would not become a matter of discussion until after he had been processed, stamped and ejected from the said system), but that was more a description of the social status accorded to him by default than an identity he had actively sought for himself – at least as of then. The fact of the matter was that it had become irrelevant whether or not he thought of himself (primarily) as a student. And yet, despite this irrelevance (which he could glimpse in stray moments of perspicacity), he had, via the emotional carrot-and-stick policy of his parents, his peers, and the cumulative social expectations of the network of blood-and-non-blood relations and well-wishers at large, internalized the achievement-orientation that had come to characterize high school studentship in most of the higher-end English-medium private schools that the middle-class and well-to-do sent their children to. But the tragedy (or comedy, as the case may be, depending on your temperament as an observer) in the case of Roll No. 27 was that while he had uncritically bought into the hyper-competitive, ‘I achieve, therefore I am’ mind-set, his own emotional and psychic wiring were ill-suited for such an orientation, having evolved, presumably, for a different, more benign, cooperative rather than competitive, living environment. It was this fundamental disjunction that produced the existential paralysis resulting in a crisis of mid-life-ist dimensions in this sixteen-year-old soul, now in Class 11, in the final segment of the penultimate year of school education, while less than a week away lay, like the proverbial crouching tiger, his annual examination – an examination which would determine, on the basis of his performance in it, whether or not his school would promote him to Class 12, which was a class he needed to get to in order to appear for the Boards that would follow exactly a year from now, and he knew, and his parents knew, that his performance in the Boards would determine the trajectory of the rest of his material life and if he wanted that trajectory to point upward and not downward, he needed to do well in the Boards, and to be able to do well in the Boards, he must first qualify for it, and to be able to qualify for it, he needed to do well in the Class 11 annual exams, and to be able to do well in the Class 11 annual exams, he needed to be able to do something he simply could not do: study.
As he sat there at his desk, Roll No. 27 tried to once again think his way out of his predicament. But before he could even begin to do so, another part of him reminded him that this very attempt to think about his current situation was itself another way of avoiding what was his only priority and task right now: finish the chapter on semi-conductors, so he could move on to optics. So once again he tried, in vain, to persuade the words on the page to unload their meanings onto his brain. His mind (to his mind) seemed unable to pause long enough on a given locus of attention for him to be able to feed it some (or any) bolus of necessary fact or theory or knowledge that might be usefully retrieved during the examination. On the contrary, his delinquent mind seemed to combine the whimsy of a monkey injected with narcotics with the motility of a freshly ejaculated sperm as it continued to taunt him, and squirmed out of his feeble attempts to capture it and hold it still, and even as he willed his thoughts to infiltrate the meaning of the paragraph he was now re-reading for the eighty-third time, they continued to skitter around like dust particles, his thoughts, dancing the Brownian dance. He was a student who had to study, and the oppressive imperative, it seemed to him, had transformed him instantly into a student who could not study.
But this transformation, if true, was neither instantaneous nor complete. If there was indeed a structural issue here, he thought, how then could he manage to focus for nine hours at a stretch if he was reading a novel by D.H. Lawrence or a treatise by William James – reading materials his scholastic peers either did not care for, or would not, he suspected, be able to summon the necessary mental focus for. As for discussing them with his hyperactive sibling, he likely stood a better chance trying to tickle himself.
But he was not going to be assessed on his understanding of Sons and Lovers or The Varieties of Religious Experience, not yet. Even among his mandated subjects of study, he still could access, occasionally, and through the steely capillary tubes of his own thirst for knowledge, the odd water table of joyful learning (as he did when he’d spent an entire day in the school library lost in a book on how Bohr came up with the Bohr model of the atom, and on another occasion, at the National Book Fair, he’d spent four hours standing, reading a paperback on the Theory of Everything until he was shamed out of the stall by one of the stall assistants) amid the desert of facts and knowledge packaged into 20-mark questions and Match the Followings and True-or-Falses. But those water tables were few, and though enjoyable, were all either theoretical (with little bearing on formula derivations, ability to use notations, ability to solve numericals) or out of syllabus or irrelevant from the examination point of view. It wasn’t lost on Roll No. 27 that while the examination had a point of view, he, as a student-examinee, wasn’t allowed one.
5
A speaks truth in 60 per cent of the cases, while B in 90 per cent of the cases. In what per cent cases are they likely to contradict each other in stating the same fact? In the cases of contradiction, do you think the statement of B will carry more weight as he speaks truth in more number of cases than A? (7 marks)
The paradox being that while it was true Roll No. 27 could not study, it was even more true that he was very sincere about his studies. He always had been, whether he could study or not, did well or not. He always strove to give his best, to work the hardest, to be disciplined, to revise regularly, to follow a strict and regular schedule of daily revision, to not watch too much TV, to go to bed on time, to submit his assignments on time, to not think bad thoughts, to not spend too much time reading storybooks or out-of-syllabus books, to pray to God every day, to bathe every morning, to have his meals at the same time every day, to do dynamic meditation for twenty minutes every morning to improve his concentration, to eat vegetables irrespective of whether he liked them or not because his female parent never tired of reiterating that she would rather spend on vegetables than on doctors or medicines, to consume almonds soaked in milk every morning despite a deep-seated aversion for almonds surpassed only by a deeper-seated aversion for milk that should have but did not, to his tragic disappointment, qualify as lactose intolerance, to do yoga every day, especially sirshasana and viparitakarani as they both improved the memory by increasing blood supply to the brain, apart from also having the more immediate bonus effect of clearing his blocked nose by increasing blood supply to the nose (which they could do because the nose happened to be on the way, so to speak, for all the blood travelling to the brain, and the increased blood circulation in the nasal area, in combination with conscious, slow-motion breathing, consisting of a premeditated duration pattern for inhalation and exhalation in the ratio of 1:2, caused a sustained application of optimal pressure on the semi-viscous particulate waste matter obstructing the free flow of air traffic in his nasal pathways, effecting said waste matter’s eviction).
Though Roll No 27 was not always successful in abiding by all (or any of) these injunctions, he strove to speak the truth at all times, to never cheat, to never consciously mislead anyone in anything, and to be conscientious in everything he did – in short, he was a model student in every way. Or rather, in every way except one: results.
The word ‘results’ evoked in him a volcanic eruption of hatred and disgust that was out of all proportion and totally out of character given his extremely timid and retiring disposition. Even his younger sibling and assorted cohorts taunted him about his paltry aggregates just to amuse themselves with the rare flashes of passion that animated his otherwise stolid visage. When his simple pendulum experiments in the physics lab did not give him the results they were supposed to as per the laws of simple harmonic motion or when his magnesium behaved like sodium or when his mouse died before he could pin down its circulatory system, to him it signified a secret pact between physics, chemistry and biology to humiliate him. Autonomous physical phenomena, when they made contact with his consciousness, assumed the form of personal insults flung at him by an inscrutably wilful world, and undermined the objective reality of the world inside his head, where results were no more than an interesting diversion, only of mundane importance, and ultimately nothing more than a manifestation of maya.
But ‘results’, tragically for Roll No. 27, was a word wielded routinely, and aggressively, by nearly everyone he knew, and in particular by his male parent, in a multitude of tonal variations yielding an array of interpretive possibilities signifying any of a number of emotional and/or rhetorical effects, from irony to sarcasm to anger, resignation, frustration, helplessness, despair, doubt, etc., and Roll No. 27 could never really escape even for a few minutes of his waking life a paralysing consciousness of the fact that he (Roll No. 27) was actually a perfect student except for the results, and indeed, everybody who came in contact with him automatically assumed that he was a perfect student until they came to know of his results, for seen through the unsparing filter of results, Roll No. 27 was not just an underperformer but, in the words of a cruel classmate he happened to overhear (and perhaps was meant to overhear), Roll No. 00.
Roll No. 27’s aggregate total in the half-yearly exam held a few months ago had been the second-lowest in a class of thirty-six students, higher only than that of Roll No. 33. But Roll No. 33 at least had the excuse of being a repeater, having missed four months of the previous academic year due to successive attacks from typhoid and jaundice (it must be added, however, that there also floated rumours suggesting far more glamorous reasons for Roll No. 33’s prolonged disappearance, including, according to one version, a failed love affair with an older woman that Roll No. 33 sometimes alluded to in a vague and mysterious way but would not categorically confirm or deny).
But Roll No. 27 did not even have the consolation of a failed love affair, and far from being a repeater – and God forbid such a fate ever befalling him – he had never, in his entire academic career (his amorous career, being non-existent, was immune to success/failure judgements), thought of himself as a failure. And not only had he never thought of himself as a failure, he resented anyone slotting him – even in their own minds – as a dumb student (the red lines in his report card denying him even the dignity of a rank, however low) despite him having failed, repeatedly and consistently, in four of his six subjects (he never came close to the pass mark of 40 in physics, chemistry, maths and biology, while managing to scrape through in the early-to-mid-40s in his purportedly favourite subjects of English and Tamil – and these two, unfortunately for him, were subjects that nobody seemed to care whether he did well in or not since he was a science student and the only thing that mattered was his performance in PCMB) in the last twelve testing events as a higher secondary school student, of which eight were class tests (they involved only a fraction of the syllabus and were easier to prepare for and do well in) and four were the quarterly/half-yearly/annual examinations (these involved, as their names suggest, the quarter or half or the whole of the syllabus of the subject, and a very serious view was taken of your performance, with a poor one typically provoking a summoning of parents for a meeting with the class teacher, the concerned [failed-] subject teacher[s], and/or the vice principal/principal, and if the poor performance recurred in the academic year-closing annual examination – the last, the most decisive, the Big Daddy of all the examinations, and second in importance only to the all-important BOARDS – you could be officially pronounced a ‘fail’ and not promoted to the next grade and be forced to endure the extreme shame and disgrace of having to repeat a grade, spend a year competing with, and suffering the taunts of, kids one year your junior, being finger-pointed at and whispered about as that ‘fail case’, and be relegated to the ‘untouchable’ class in the eyes of the wider world, or at least that part of the world whose opinion of him mattered to him, and stand accused of befouling the legacy of his dead older sibling, and this was the worst kind of humiliation/nightmare that Roll No. 27 could imagine, and lived in mortal terror of living through, as a student), his failing streak essentially going back to the first class test of Class 11. It was this annual examination that Roll No. 27 was currently not able to study for at 3.58 a.m.
6
Assume that a meditation and yoga course reduce the risk of heart attack by 30% and the intake of certain prescribed drugs reduces its chances by 25%. At a time, a patient can choose any one of the two options with equal probabilities. It is given that after going through one of the two options, the patient selected at random suffers a heart attack. Find the probability that the patient followed a course of meditation and yoga. Interpret the result and state which of the above stated methods is more beneficial for the patient. (10 marks)
When, in the half-yearly exam in Class 11, for the first time ever since entering the portals of academia a dozen or so years ago as a moderately cute three-year-old enrolled in LKG with little or no expectations from him by way of academic performance (at least none that he had internalized back then or could remember having internalized at that age), he failed in a subject in single digits, his parents had shed tears of fear, hysteria and helplessness at this sudden inability of their technically eldest son and primary carrier of family prestige and beacon of hope for their future and their best bet at fixing the fiasco of their dead first-born – the third-born, displaying wisdom beyond his years, had never threatened to come anywhere close to academic excellence, taking, by some mysterious genetic instinct, extreme care to languish at the heart of the normal probability distribution bell curve right from LKG onward – letting them down not just academically but also socially and filially by failing in his duty as a student and son, and their tizzy-trauma of near-cardiac proportions at his successive failure, which peaked (or should we say, troughed) with his single digit result in mathematics (4/100), changed, perhaps forever, the way Roll No. 27 was thought of by his parents. For until then, neither Roll No. 27 nor his parents had ever believed him to be anything but a good student. True, he had never been brilliant, had never stood first in class (the lone instance had been in Class 6 when AK, the usual first-ranker, had fallen sick and missed two subjects in the quarterly exam and so it didn’t really count though Roll No. 27 did get a First Rank badge for it that he wore for two months – feeling all through like a pretender and having to endure jealous sarcastic barbs from AK who had come to think of the First Rank badge as his personal property – before it was reclaimed by the aforementioned first rank monopolist and Roll No. 27, instead of the disappointment everyone expected him to feel, felt only relief, and was secretly glad to be somewhat freed of the burden of teacherly expectations [over and above the burden of parental expectations] and the performance anxiety that went with sporting the First Rank badge, which, furthermore, had the effect of putting him in the spotlight in the classroom, with the teachers expecting him to take the lead in answering pedagogically useful but otherwise dumb questions posed by them in the classroom and also in a number of other ways set an example for other students so that if, for instance, he turned up for class without having finished an assignment his fault was not merely that of not having finished an assignment but also of letting down the class as a whole, which looked up to him, etc.), but he had nevertheless always been among the top five or six in a given class right through school. But things began to change for Roll No. 27, slowly at first, and then rapidly.
The first time it happened, Roll No. 27 had sobbed uncontrollably for twenty-five minutes (give or take a few seconds). He had just turned fourteen. He was in Class 9, and in superb form academically, despite being in a new school where he had entered the fray as an unseeded player, as it were – nobody knew him, nobody shared their notes with him, and he had to rely on his own intelligence, hard work, and engage in persistent nagging of his teachers to get his doubts cleared and problems resolved.
He tasted some spectacular early success to the extent that he upset the by then established class hierarchy to rank second at the end of the quarterlies, having scored an unprecedented centum in maths and physics in two consecutive class tests. Now, finally, the cream of Class 9 not only began to take note of him, they even began to acknowledge him as one of their own, lending him their Tin Tin and Asterix and Hardy Boys, including him in their hand-cricket matches and book-cricket tournaments, and even approaching him on one occasion to settle an argument regarding the reproductive system of fern, for it was by then widely acknowledged that he ‘owned’ biology, just as JH, the class and school topper, owned maths and physics, and CA, his male parent’s then boss’s only son, owned chemistry, and they were each of them regarded as the final arbiters on any difference of opinion in these subjects, (unless, of course, someone wished to ask the teacher directly). Roll No. 27 even received handsome positive reinforcement for his academic achievements from his female parent who kept her promise to get him a new bicycle if he scored 100/100 in maths (a subject that had traditionally been his Achilles heel).
But barely a couple of months post his majestic triumph in the quarterlies, one October evening, a Tuesday, Roll No. 27 was at his study table in his room at home, preparing diligently for a class test in biology (one of his favourite subjects), when he found himself unable to concentrate. When it happened, he probably did not even know what was going on, and probably did not use concepts like ‘concentration’ to understand what was happening, or not happening. All he knew was that he could not sit at his desk for more than fifteen seconds at a time. Something unknown and nameless welled up inside him, a force that found no mention in his science textbook. It unleashed a churning within that felt both delicious as well as terrifying. Like being on a cliff edge high above the waves with the wind on your face and the waves so far away they seem like children playing softly in the sand. His knees would get all wobbly and dizzy from the height and the looking down and a hand reached out to him, making him lean forward and take a step and another, and then let himself drop, like gravity’s baby, into the seductive whispering far below, and that’s when he had stood up, his chair scraping the floor as he did so. He was sweating, and felt the way you feel when you’ve already stopped rotating on your axis but the room you were in was yet to.
He thought this was a way of being tired. But he hadn’t even played that evening. He had come home, changed, snacked, chatted about school with his female parent, read Agatha Christie for a bit, and then, at six sharp, had put away his Agatha Christie for his biology class notes.
But bizarrely, he had found it impossible to sit at his desk. Could be a magnetic pole was embedded in his chair, of the kind that would repel the magnetic pole embedded in his backside. He got up, looked out of the window of his room, at the curtained windows of the semi-detached houses across the street, at a sad little Bajaj scooter with its tongue out and head cocked as it waited outside a neighbour’s gate, at pigeons chasing each other across and out of his frame of vision. He came back to his desk. He got up again, turned on the TV in the other room, turned it off. He went back to his desk. Got up again, walked to the telephone, dialled a number at random. It began ringing. A woman’s voice said hello. He put the receiver back, returned to his desk. Got up again, slipped on his sandals, went out. He walked to the park. A teenaged, servant-type girl pushing a baby in a perambulator, two teenaged, non-servant-type girls playing badminton with zero rallies, neither able to reach or return the other’s wayward serve, a group of under-ten kids arguing around a heavily bandaged cricket bat. He flung a stone at a tree, missed. He began walking home. On the way, he aimed a stone at a lamp post, missed again. His female parent had not locked the door. He let himself in, after three gulps of semi-cold water from the refrigerator, sat down at his desk again. He listened to his fingers drumming on the study table, his ring-finger, middle-finger, forefinger, in a rapid downward sequence on the hardness of wood, again and again and again, beating a simple rhythm that meant nothing to him, or maybe everything.
He got up, went to the refrigerator, and returned to his chair with Milk Bikis biscuits, determined to stay put, to stick to his timetable, which stipulated that he had to be doing biology for ninety minutes, followed by maths for ninety minutes, before winding down with English homework for fifteen minutes. But again, instead of the meanings of the black marks on the page he was supposedly reading, his mind kept filling up – of its own accord – with thoughts and images he knew not from where, thoughts and images he had not sanctioned, and did not know he had not sanctioned until they were already there, like guests landing up at a hotel closed for renovation and insisting on staying the night. One such intrusive image was that of the dark brown bud-like birthmark on the lower-left quadrant of the chin of the face of the plump girl who sat diagonally one row behind him to his left on the aisle-side of the girls’ side of the class. He had never thought of himself as the kind of boy who talked to girls and had never thought of them as anything but fierce, tough, and somewhat boring and monomaniacal fellow competitors for academic prestige. But now the face of this girl, who was not even the prettiest in the class, floated in his mind’s eye insistently, to the extent of making it difficult for him to intellectually register the letters and words he was reading-chanting-memorizing. According to his timetable, he was supposed to finish female gametophytes in forty-five minutes, but when forty-five minutes had passed, he had made no headway, which puzzled him all the more because he had nothing against female gametophytes, did not find them boring or difficult to understand, and was actually curious to know all that was humanly possible to know about them.
He finally decided, in confusion, that his mind, perhaps, was not in a ‘mood’ for biology and, abandoning his timetable, switched to chemistry one hour ahead of schedule. But it only got worse. He tried to focus his mind on the conversion process of Benzoyl Chloride to Benzaldehyde but the girl’s face kept disrupting the process (the attempted focusing of his mind, not the chemical conversion).
As the evening faded into night and dinner time came by and still no progress had occurred on either his biology or chemistry lessons, Roll No. 27 basically, as they say, lost it. Terrified that this might be the onset of a permanent condition, some as yet unknown form of learning disability or impairment, he broke down, and was found sobbing violently at his desk by his female parent, who reacted with even greater terror. It was an indication of how terrified Roll No. 27’s female parent was by her offspring’s sobs that she had assumed, to his complete bafflement, that Roll No. 27’s tears were tears of contrition because he had done something terrible and shameful, and even as she interrogated him through the refracting lens of her own terrified tears, unable to register her offspring’s murmured response that he had no clue what it might be that was bothering him and no words to articulate the vague pre-formed mush of thoughts that stampeded through his brain like a panicky horde fleeing a psychotic bull, her mind was already rehearsing the scene that she knew would be enacted were she to share this important development of potentially far-reaching significance with his male parent.
Roll No. 27, it goes without saying, begged his female parent not to discuss the incident (of his unexplained inability to concentrate/study accompanied by extreme restlessness and followed by unexplained tears) with the male parent, but the female parent, despite having reassured her offspring that she would desist from doing so, did exactly that after Roll No. 27 had fallen asleep, as she found it impossible to keep her peace when she was serving food to the male parent, who, she felt, did not deserve the proverbial bliss of ignorance regarding a matter that had made such a wide tear in the fabric of serenity she had patiently been trying to weave around her life and live inside of, and so she, more out of resentment at the male parent’s ignorance than anything else, poured out everything regarding the aforementioned incident to her offspring’s male parent, taking care to request him in the same breath not to say anything about it to their mutual offspring. But the male parent, having come home late (it was a quarter past 11) after a hard day of office politics and backbiting and taking shit from everyone, was already a seething repository of accumulated bile that only needed an appropriate trigger for forceful expulsion.
Fortunately, however, the female parent prevailed upon the male parent not to wake their progeny for the purpose of having a discussion concerning the latter’s academic crisis. But the male parent raged on, the general import of his raging being as follows: what does it mean he’s unable to concentrate? Two slaps and concentration will automatically resume normal service. Here I am, breaking my back to send this rascal to school, and he is having trouble doing his studies? Tell the idiot I would be happy to save on his school fee if he cannot concentrate. Tell the idiot he can graze cattle if he cannot concentrate. Tell him he can become an assistant ice-cream vendor if he cannot concentrate. Concentration, my ball of mud! (And so on in that vein.)
The male parent, whose lifetime secret ambition was to become the global CMD of a global conglomerate, left for work every morning at a quarter to seven, though only after waking up at half past six, getting ready in about fifteen minutes, his breakfast packed for work by his progeny’s female parent, did not, in the following months, ever broach the subject of the failing concentration of his progeny with his progeny and the issue seemed to fade away as Roll No. 27 subsequently found a stop-gap (and ultimately, as it turned out, not at all satisfactory) solution for it: he found that he could concentrate reasonably well and his mind gave him no trouble if he sat down to study when it was already too late.
Roll No. 27’s concentration disintegrated like a biscuit dipped in hot tea if, on a regular weekday – like that Tuesday October evening – he tried to sit down at or about the self-appointed and traditional study time of 6 p.m. But on the morning of the day of an important exam, if he woke up at 4 a.m. and began to study – with no hope of (or time for) studying/mugging all the lessons covered by the exam, no hope of (or time for) acquiring a doubt-free understanding of all the requisite theoretical concepts, and no hope at all of clearing the exam with a score he wouldn’t die of shame of – he found that not only did he absorb knowledge and data like sawdust absorbing moisture, he even began to find the topics he hated, such as trigonometry, instantly interesting. So sound was his concentration for those few hours, the next thing he knew, it was already 8 a.m. and his female parent was harrying him to hurry if he didn’t want to miss the school bus.
But what was even more strange, every time he did this – i.e., avoid his studies until it was suicidally late to be commencing them – he was surprised by how well he did in the exams, as his test scores invariably trumped his forebodings of gloom and exceeded the most optimistic of his pessimistic expectations. And yet for all his success – he did manage to remain consistently in the top five of his class right through classes 9 and 10 – Roll No. 27 was never again at peace with himself as a student ever since the incident of his first ‘concentration crisis’ when he had sobbed for twenty-five minutes (give or take a few seconds). Though he may have appeared, to the casual observer, as an academically upwardly mobile student with a future ‘bright’ in every sense of the word ‘bright’, inside his head he was in continuous turmoil of the kind that was likened, by the dead first-born in a diary entry, to ‘being locked inside the negative space of a black hole along with all the light in the universe and all the thoughts in the universe with no chance of getting out of the negative space of the black hole’ and this unremitting inner turmoil wore him down and gave his default facial expression a suggestion of despondency, which did not go unnoticed by his classmates. His teachers, if they noticed, did not let on, or could not be bothered. His sibling, who despised him for cravenly seeking their male parent’s approval by trying to emulate the academic overachievements of their dead first-born, gave him a berth as wide as the Mediterranean, preferring to spray his attention on cricket and crime thrillers.
7
A cylindrical metallic wire is stretched to increase its length by 5 per cent. Calculate the percentage change in its resistance. (2 marks)
Roll No. 27’s anxiety over his concentration crisis was also rendered more toxic by the injuries to his self-confidence and self-esteem wrought by the very real possibility that he might never again figure in the same league as the elite academic athletes such as JH and CA, whose hallowed company and academic intimacy he had briefly enjoyed when he had scored successive centums in mathematics and physics in the early months of Class 9 and topped the quarterlies. His crisis, in other words, had produced the following contradiction: while Roll No. 27 believed that he belonged to the exclusive club to which JH and CA belonged, and probably enjoyed similar scholastic and cranial potential, his new-found inability prevented him from performing at the level they did, which meant that he ceased to enjoy their respect, and was evicted from their exclusive club of scholastic overachievers – an eviction he resented as an affront to his dignity and to his identity as their equal in intelligence, and he would not rest until he was back in that same elite club again and universally recognized as an achiever on a par with JH and CA. But he could do that only if he studied as they did: when it was too early to slog, not when it was too late. But that, he could no longer do, and this social dimension of his inability began to trouble him even more than the inability itself.
And as if to add another special layer of agony to his pre-existing multi-layered agony, his female parent began to stigmatize his inability to study as ‘laziness’ and ‘last-minute preparation’ and issued him a warning to the effect that if he did not mend his study patterns, she would inform his male parent about his ‘laziness’ and ‘last-minute preparation’, both of which signified to her (she had no doubt they would signify similarly to his male parent as well) Roll No. 27’s lack of respect for his parents’ hard-earned money invested in his schooling, as well as being a comment on his (lack of) character as revealed by his refusing to be more serious about his studies, for unlike the parents of other, richer students, his male parent did not yet have the financial resources to pay donation or capitation fee to get him the education he might need in a world of ever-rising college cut-offs that had no place for academic also-rans, and in this world that had no place for academic also-rans, even 99 per cent was no guarantee of a secure future, for many colleges had cut-offs of 99.99 per cent, and that (99.99 per cent) had to be his target if he was serious about his future, and he could not come anywhere close to meeting that target if he spent all his time reading storybooks or out-of-syllabus books and did exam study only last minute.
Though he hated her for threatening him over it, Roll No. 27 was, of course, intelligent enough to realize that his female parent was correct in her assessment. But, unfortunately, that realization did nothing to remedy his inability to study, which remained, and therefore so did his last-minute approach, which had anyway become his default mode of study. And while he cleared the class 10 Boards comfortably with this method, and even secured a percentage high enough to get him the stream of his (male parent’s) choice, and high enough for his male parent to be able to transfer him to The Most Prestigious School – a school that admitted only the academic crème de la crème of the country – this success only ended up obscuring the fact that his approach of study was a short-cut to scholastic perdition, and it was this perdition that befell Roll No. 27 in class 11, as his mind refused to have anything at all do with anything at all in the broken oval of illumination conjured by his study lamp in the pre-dawn darkness, preferring instead to embark on unscheduled flights of adventure that Roll No. 27 would surely have enjoyed if he hadn’t been too invested in getting it to follow his schedule.
One such flight, for instance, involved the persistence in his mind’s eye of the expression on his desk mate Roll No. 33’s face as he did his Salman Khan act which involved rapidly stabbing the wooden desk with the sharp end of a steel knife or compass needle through the gaps between the splayed fingers of his left hand, the stabbings going back and forth back and forth with rising velocity just like the angry, lovelorn, pre-muscular Salman did in that film, the blade a blur of glinting metal as it flew from the gap between thumb and forefinger to the gap between forefinger and middle-finger and middle-finger and ring-finger and then back via four stabs to the gap between thumb and forefinger while at the same time gradually reducing the stabbing space between fingers till the knife was forced to draw blood and puncture and scrape pieces of finger skin or even go right into the flesh or ram into the bone in its rapidfire up-down pistoning like the needle of a sewing machine and the point of it (pun intended) so far as Roll No. 33 could tell was to not just get the rhythm right and the speed right so you don’t stab yourself by mistake but the other way round, as in the point was to keep getting better at it and as you get better to keep stabbing faster and faster with the fingers getting closer and closer till it becomes impossible not to stab them and that’s the mega-point precisely as you then revel in the blood and the pain, and keep going for even more blood and pain if you felt like it, till all the other pain that was like the background hum of being – the psychic pain – is thoroughly vanquished by this simple hard little cute little physical pain with physical stuff like blood and this compassionate little kind-hearted pain was a pain that was generous enough to absorb your entire being inside and hug it to its heart, even if for only a few seconds, and liberate the self from the pain of the self by allowing it the fleeting dignity and fragile freedom of itself choosing its own pain from the suffering menu.
8
A group of men collectively have 9 steel, 7 plastic, and 4 cotton balls. If two balls were to be chosen at random, find the probability that they are both balls of steel. (3 marks).
One day toward the end of the academic year when he was in class 10, after the morning assembly, during which JH had been publicly commended by the principal for winning yet another first prize in yet another inter-school competition and making the school proud, Roll No. 27 had walked up to JH with the intention of congratulating him. JH was, as celebrities tend to do, holding forth to a group of sycophants and admirers, and when Roll No. 27 thought he had found a conversational opening, he started to address some congratulatory words to JH. But JH raised his hand in Roll No. 27’s direction, to silence him, and resumed his soliloquy. Roll No. 27, who had reflexively fallen silent at JH’s raised hand, felt compelled to wait for a chance to say what he had come to say before going his way. But JH continued to speak, not bothering to make eye contact or look in Roll No. 27’s direction even once even though Roll No. 27 stood almost directly across from him. Roll No 27 waited a full minute, trapped in his pauciloquy, listening to JH go on and on about a quiz competition where he had pointed out an embarrassing error on the part of the quizmaster and the quizmaster had hated him for it but had had no option but to acquiesce when one of the teachers in the audience came out with evidence to prove that JH had indeed been right, and how in the next round, which was the buzzer round, though the quizmaster tried his best to get back at him by ignoring him, he could not do so because the other contestants whom he wilfully favoured anyway did not have the correct answers and the quizmaster was forced to come to him when the question got repeatedly passed and he had ended up winning that round too, and eventually the competition as well, and by a handsome margin too, and the quizmaster had had to suffer the mortification of having to present the trophy to the very individual who had showed up the gaping holes in his quizmastery and whose guts he hated for having done so. Roll No. 27, who was getting late for his class, finally muttered ‘congratulations’ into the little aural hole at the centre of the circle formed by JH and his admirers and sycophants and slunk away, and as he did do, he could not help but notice that JH did not even seem to notice his departure and continued speaking without so much as a nod or a half-wave in his direction.
Roll No. 27 must have replayed this incident in his mind hundreds of times, wondering if he could have handled it differently, but every time he felt its shame as sharply as the first. He had only wanted to compliment JH, nothing more, but he had been made to feel as if JH would be doing him a favour by allowing him (Roll No. 27) to compliment him (JH) in front of other people, the insinuation being that Roll No. 27 had fallen so low in the academic status ladder (while JH had simultaneously risen so high) that it would actually be too much to expect JH to acknowledge the likes of Roll No. 27 – such, indeed, was the meaning of the snub. And Roll No. 27 could neither forgive JH for it, nor forgive himself for having gotten into a situation where he had to endure such a public humiliation.
If Roll No. 27’s story had been fiction,4 he would have buckled down, worked twice as hard as JH, beaten the crap out of him in the final exams and paid him back for his insult, with interest. But JH’s putdown had the opposite impact on Roll No. 27: it crushed whatever self-confidence and self-esteem he still had left.
He was now less able than ever to do his daily studies, more susceptible than ever to daydreaming and to what his female parent called ‘storybooks’. He, however, still paid attention in class, more out of habit, took notes, also out of habit, and these, combined with the furious mugging he did on the morning of the exams, kept him afloat – but only until Class 11.
9
According to Newton’s Law of Gravitation, the apple and the earth experience equal and opposite forces due to gravitation. But it is the apple that falls toward the earth and not vice versa. Why? (2 marks).
Class 11 was, till date, the worst year of Roll No. 27’s sixteen-year-old life, both academic and non-academic. In brief, theoretically speaking, his crisis could be summed up thus: His intuitive, and in all likelihood, subconscious, conception of education as the pursuit of knowledge was completely at odds with a systemic apparatus that conceived of education as the methodical acquisition of requisite skills, both informal (such as the ability to endure boredom for extended periods of time, the ability to dissociate emotion from the achievement of progress or lack thereof vis-à-vis the tasks on hand, the ability to defer gratification in the short-term or immediate-term for greater rewards in the long-term, etc.) as well as formal (solving mathematical equations, writing leave letters, memorizing and/or analysing data, etc.), and the efficacy of whose acquisition would be evaluated and graded through standardized processes known as examinations, and certified in the form of mark sheets and pass certificates. Roll No. 27’s mind, when pressed into slavery-mode in the service of the above-described system, rebelled, as any mind enamoured of the ways of freedom would. In other words, he was the apple that was destined to fall, though it was the earth that deserved to.
10
Define entropy. (2 marks)
On the first day of his class 11 annual examination (the subject was physics), around quarter to 7, Roll No. 27 was found by his female parent, who had come to give him his morning cup of milk, huddled beneath his desk, whimpering incoherently in a semi-conscious state. The female parent let out a cry that brought the male parent rushing to the room, and together they retrieved their offspring from under his study table, on which the night lamp was still on and fighting a losing battle with daylight.
The parents took turns trying to feed Roll No. 27, first some water, and then some milk, both of which leaked down his mouth and vest more than flowed down his gullet. They tried to calm him down, and assured him he need not appear for the exam if he did not feel like it. The male parent called work to convey that he would be coming in late, and called again to say he was taking half-day off, and called again to say he was taking the whole day off. The female parent was about to call her brother, Roll No. 27’s uncle, to ask for advice on what to do when the male parent snatched the phone away from her, asking her not to make a public spectacle of it. He then called up his best friend, a former colleague, who, after hearing him out, told him not to worry, that it was only a kind of panic attack induced by the prospect of having to appear for the exam and that he (his son) should, as an otherwise healthy boy, and given his genetic OS, be back to normal soon.
But even by mid-morning, there was no change in the state of Roll No. 27. He imbibed no solid foods nor any liquids other than what had been fed to him earlier in the day (of which more than half had not gone in). And he continued to whimper and utter words his parents could not catch no matter how hard they tried to do so, applying their ears to his mouth. The words, to them, sounded like ‘Mgyi Kn Byo It’ or like ‘Mgyu Zngnt Wyo’. It was either gibberish or some new language that they did not understand.
Toward noon, a decision was made to take him to a hospital, where they were given an appointment with a consultant psychiatrist. The consultant psychiatrist did a routine physical check-up of Roll No. 27, who was still not in a position to utter any words that might be intelligible to their available recipients. The consultant psychiatrist posed questions to the parents and listened to their answers with either growing impatience or growing indifference. He wrote out a prescription and asked them to come and see them with their offspring after three days.
11
Two PAN numbers, WEOXZ0987T and MSGBT9823D, take birth as human beings on planet earth. The probability that WEOXZ0987T will die a happy soul is 0.16. The probability that MSGBT9823D will die a happy soul is 0.12. The probability that both will die happy souls is 0.04. Find the probability that:
A: Both WEOXZ0987T and MSGBT9823D live and die in utter misery.
B. Only MSGBT9823D dies a happy soul. (5 marks)