Questões - ITA 2003 | Gabarito e resoluções

(ITA - 2003 - 1a fase) I want to be six again A man asked his wife what shed like for her birthday. Id love to be six again, she replied. On the morning of her birthday, he got her up bright and early and off they went to a local theme park. What a day! He put her on every ride in the park: the Death Slide, the Screaming Loop, the Wall of Fear everything there was! Wow! Five hours later she staggered out of the theme park, her head reeling and her stomach upside down. Right to a McDonalds they went, where her husband ordered a Big Mac for her along with extra fries and a refreshing chocolate shake. Then it was off to a movie the latest Star Wars epic, and hot dogs, popcorn, Pepsi Cola and MMs. What a fabulous adventure! Finally she wobbled home with her husband and collapsed into bed. He leaned over and lovingly asked, Well, dear, what was it like being six again? One eye opened. You idiot, I meant my dress size. The moral of this story is: if a woman speaks and a man is there to hear her, he will get it wrong anyway. O texto revela uma mulher:

(ITA - 2003 - 1a fase) I want to be six again A man asked his wife what shed like for her birthday. Id love to be six again, she replied. On the morning of her birthday, he got her up bright and early and off they went to a local theme park. What a day! He put her on every ride in the park: the Death Slide, the Screaming Loop, the Wall of Fear everything there was! Wow! Five hours later she staggered out of the theme park, her head reeling and her stomach upside down. Right to a McDonalds they went, where her husband ordered a Big Mac for her along with extra fries and a refreshing chocolate shake. Then it was off to a movie the latest Star Wars epic, and hot dogs, popcorn, Pepsi Cola and MMs. What a fabulous adventure! Finally she wobbled home with her husband and collapsed into bed. He leaned over and lovingly asked, Well, dear, what was it like being six again? One eye opened. You idiot, I meant my dress size. The moral of this story is: if a woman speaks and a man is there to hear her, he will get it wrong anyway. A frase: My father once told me that there were two kinds of people: those who do the work and those who take the credit. He told me to try to be in the first group; there was much less competition there, atribuda a Indira Gandhi. A inteno do pai de Indira, em relao filha, era provavelmente

(ITA - 2003 - 1a fase) What is life? To the physicist the two distinguishing features of living systems are complexity and organization. Even a simple single-celled organism, primitive as it is, displays an intricacy and fidelity unmatched by any product of human ingenuity. Consider, for example, a lowly bacterium. Close inspection reveals a complex network of function and form. The bacterium may interact with its environment in a variety of ways, propelling itself, attacking enemies, moving towards or away from external stimuli, exchanging material in a controlled fashion. Its internal workings resemble a vast city in organization. Much of the control rests with the cell nucleus, wherein is also contained the genetic code, the chemical blue print that enables the bacterium to replicate. The chemical structures that control and direct all this activity may involve molecules with as many as a million atoms strung together in a complicated yet highly specific way. (...) It is important to appreciate that a biological organism is made from perfectly ordinary atoms. (...) An atom of carbon, hydrogen, oxygen, or phosphorus inside a living cell is no different from a similar atom outside, and there is a steady stream of such atoms passing into and out of all biological organisms. Clearly, then, life cannot be reduced to a property of an organisms constituent parts. Life is not a cumulative phenomenon like, for example, weight. For though we may not doubt that a cat or a geranium is living, we would search in vain for any sign that an individual catatom or geranium-atom is living. Sometimes this appears paradoxical. How can a collection of inanimate atoms be animate? Some people have argued that it is impossible to build life out of non-life, so there must be an additional, non-material, ingredient within all living things a life-force or spiritual essence which owes its origin, ultimately, to God. This is the ancient doctrine of vitalism. An argument frequently used in support of vitalism concerns behaviour. A characteristic feature of living things is that they appear to behave in a purposive way, as though towards a specific end. PAUL DAVIES. God and the New Physics. N.Y. Simon Schuster, Inc.,1984. Assinale a opo cuja afirmao contenha a informao correta:

(ITA - 2003 -1a fase) What is life? To the physicist the two distinguishing features oflivingsystems are complexity and organization. Even a simplesingle-celledorganism, primitive as it is, displays an intricacy and fidelity unmatched by any product of human ingenuity. Consider, for example, alowlybacterium.Closeinspection reveals a complex network of function and form. The bacterium may interact with its environment in a variety of ways, propelling itself, attacking enemies, moving towards or away from externalstimuli, exchanging material in a controlled fashion. Its internal workings resemble a vast city in organization. Much of the control rests with the cell nucleus, wherein is also contained the genetic code, the chemical blue print that enables the bacterium to replicate. The chemical structures that control and direct all this activity may involve molecules with as many as a million atoms strung together in a complicated yet highly specific way. (...) It is important to appreciate that a biological organism is made from perfectly ordinary atoms. (...) An atom of carbon, hydrogen, oxygen, or phosphorus inside a living cell is no different from a similar atom outside, and there is a steady stream of such atoms passing into and out of all biological organisms. Clearly, then, life cannot be reduced to a property of an organisms constituent parts. Life is not a cumulative phenomenon like, for example, weight. For though we may not doubt that a cat or a geranium is living, we would search in vain for any sign that an individual catatom or geranium-atom is living. Sometimes this appears paradoxical. How can a collection of inanimate atoms be animate? Some people have argued that it is impossible to build life out of non-life, so there must be an additional, non-material, ingredient within all living things a life-force or spiritual essence which owes its origin, ultimately, to God. This is the ancient doctrine of vitalism. An argument frequently used in support of vitalism concerns behaviour. A characteristic feature of living things is that they appear to behave in a purposive way, as though towards a specific end. PAUL DAVIES. God and the New Physics. N.Y. Simon Schuster, Inc.,1984. Qual das palavras abaixo constitui um falso cognato?

(ITA - 2003 - 1a fase) What is life? To the physicist the two distinguishing features of living systems are complexity and organization. Even a simple single-celled organism, primitive as it is, displays an intricacy and fidelity unmatched by any product of human ingenuity. Consider, for example, a lowly bacterium. Close inspection reveals a complex network of function and form. The bacterium may interact with its environment in a variety of ways, propelling itself, attacking enemies, moving towards or away from external stimuli, exchanging material in a controlled fashion. Its internal workings resemble a vast city in organization. Much of the control rests with the cell nucleus, wherein is also contained the genetic code, the chemical blue print that enables the bacterium to replicate. The chemical structures that control and direct all this activity may involve molecules with as many as a million atoms strung together in a complicated yet highly specific way. (...) It is important to appreciate that a biological organism is made from perfectly ordinary atoms. (...) An atom of carbon, hydrogen, oxygen, or phosphorus inside a living cell is no different from a similar atom outside, and there is a steady stream of such atoms passing into and out of all biological organisms. Clearly, then, life cannot be reduced to a property of an organisms constituent parts. Life is not a cumulative phenomenon like, for example, weight. For though we may not doubt that a cat or a geranium is living, we would search in vain for any sign that an individual cat-atom or geranium-atom is living. Sometimes this appears paradoxical. How can a collection of inanimate atoms be animate? Some people have argued that it is impossible to build life out of non-life, so there must be an additional, non-material, ingredient within all living things a life-force or spiritual essence which owes its origin, ultimately, to God. This is the ancient doctrine of vitalism. An argument frequently used in support of vitalism concerns behaviour. A characteristic feature of living things is that they appear to behave in a purposive way, as though towards a specific end. PAUL DAVIES. God and the New Physics. N.Y. Simon Schuster, Inc.,1984. A expresso rests with, em destaque no texto, quer dizer:

(ITA - 2003 - 1 fase) What is life? To the physicist the two distinguishing features of1living systems are complexity and organization. Even a simple2single-celled organism, primitive as it is, displays an intricacy and fidelity unmatched by any product of human ingenuity. Consider, for example, a3lowly bacterium.4Close inspection reveals a complex network of function and form. The bacterium may interact with its environment in a variety of ways, propelling itself, attacking enemies, moving towards or away from external5stimuli, exchanging material in a controlled fashion. Its internal workings resemble a vast city in organization. Much of the control rests with the cell nucleus, wherein is also contained the genetic code, the chemical blue print that enables the bacterium to replicate. The chemical structures that control and direct all this activity may involve molecules with as many as a million atoms strung together in a complicated6yet highly specific way. (...) It is important to appreciate that a biological organism is made from perfectly ordinary atoms. (...) An atom of carbon, hydrogen, oxygen, or phosphorus inside a living cell is no different from a similar atom outside, and there is a steady stream of such atoms passing into and out of all biological organisms. Clearly, then, life cannot be reduced to a property of an organisms constituent parts. Life is not a cumulative phenomenon like, for example, weight. For though we may not doubt that a cat or a geranium is living, we would search in vain for any sign that an individual catatom or geranium-atom is living. Sometimes this appears paradoxical. How can a collection of inanimate atoms be animate? Some people have argued that it is impossible to build life out of non-life, so there must be an additional, non-material, ingredient within all living things a life-force or spiritual essence which owes its origin, ultimately, to God. This is the ancient doctrine of vitalism. An argument frequently used in support of vitalism concerns behaviour. A characteristic feature of living things is that they appear to behave in a purposive way, as though towards a specific end. PAUL DAVIES.God and the New Physics. N.Y. Simon Schuster, Inc.,1984. De acordo com o texto:

(ITA - 2003 - 1a fase) Seja z C. Das seguintes afirmaes independentes: I. Se , ento II. Se z 0 e, ento . III. Se , ento um argumento de w. (so) verdadeira(s):

(ITA - 2003) O valor de y2 - xz para o qual os nmeros ,x, y, z e sen 75, nesta ordem, formam uma progresso aritmtica, :

(ITA - 2003 - 1a fase) Considere a funo: A soma de todos os valores de x para os quais a equao tem raiz dupla :

(ITA - 2003 - 1a fase) Considere uma funo f : no-constante e tal que f(x + y) = f(x) f(y), x,y . Das afirmaes: I. f(x) 0, x . II. f(nx) = [f(x)]n, x , n *. III. f par. (so) verdadeira(s):

(ITA - 2003 - 1a fase) Considere o polinmio P(x) = 2x + a2x2 + ... + anxn, cujos coeficientes 2, a2, ..., an formam, nesta ordem, uma progresso geomtrica de razo q 0. Sabendo que -1/2 uma raiz de P e que P(2) = 5460, tem-se que o valor de (n2-q3)/q4 igual a:

(ITA - 2003 - 1a fase) Dividindo-se o polinmio P(x) = x5 + ax4 + bx2 + cx + 1 por (x - 1), obtm-se resto igual a 2. Dividindo-se P(x) por (x + 1), obtm-se resto igual a 3. Sabendo que P(x) divisvel por (x - 2), tem-se que o valor de (ab)/c igual a:

(ITA - 2003 - 1a fase) Das afirmaes abaixo sobre a equao e suas solues no plano complexo: I. A equao possui pelo menos um par de razes reais. II. A equao possui duas razes de mdulo 1, uma raiz de mdulo menor que 1 e uma raiz de mdulo maior que 1. III. Se e r uma raiz qualquer desta equao, ento . (so) verdadeira(s) :

(ITA - 2003 - 1a fase) Seja tal que a equao possua uma raiz dupla e inteira x1 e uma raiz x2, distinta de x1. Ento, (k + x1)x2 igual a:

(ITA - 2003 - 1a fase) Considere o conjunto S = {(a, b) N x N: a + b = 18}. A soma de todos os nmeros da forma, (18!)/(a!b!), (a,b) S, :