Questões - ITA 2005 | Gabarito e resoluções

(ITA - 2005) O menor inteiro positivo n para o qual a diferena fica menor que 0,01

(ITA - 2005) Um composto slido adicionado a um bquer contendo uma soluo aquosa de fenolftalena. A soluo adquire uma colorao rsea e ocorre a liberao de um gs que recolhido. Numa etapa posterior, esse gs submetido combusto completa, formando H2O e CO2. Com base nestas informaes, CORRETO afirmar que o composto

(ITA - 2005 - 1 FASE )So de 100 Hz e 125 Hz, respectivamente, as frequncias de duas harmnicas adjacentes de uma onda estacionria no trecho horizontal de um cabo esticado, de comprimento l = 2 m e densidade linear de massa igual a 10 g/m (veja figura). Considerando a acelerao da gravidade g = 10 m/s2, a massa do bloco suspenso deve ser de

(ITA - 2005 - 1 FASE )Considere o vo existente entre cada tecla de um computador e a base do seu teclado. Em cada vo existem duas placas metlicas, uma delas presa na base do teclado e outra, na tecla. Em conjunto, elas funcionam como um capacitor de placas planas paralelas imersas no ar. Quando se aciona a tecla, diminui a distncia entre as placas e a capacitncia aumenta. Um circuito eltrico detecta a variao da capacitncia, indicativa do movimento da tecla. Considere ento um dado teclado, cujas placas metlicas tm 40 mm2 de rea e 0,7 mm de distncia inicial entre si. Considere ainda que a permissividade do ar seja 0 = 9 . 10-12 F/m. Se o circuito eletrnico capaz de detectar uma variao da capacitncia a partir de 0,2 pF, ento, qualquer tecla deve ser deslocada de pelo menos

(ITA - 2005 - 1 FASE ) A 15C e 1 atm, borbulham-se quantidades iguais de cloridreto de hidrognio, HC(g), nos solventes relacionados abaixo: I - Etilamina II - Dietilamina III - n-Hexano IV - gua pura Assinale a alternativa que contm a ordem decrescente CORRETA de condutividade eltrica das solues formadas.

(ITA - 2005 - 1 FASE ) Seja e uma funo dada por Considere as afirmaes: I )f injetiva e sobrejetiva. II)f injetiva, mas no sobrejetiva. III), para todo x D, x 0. IV), para todo x D. Ento, so verdadeiras

(ITA - 2005 - 1 FASE )As questes de 11 a 17 referem-se aos seguintes pargrafos: 1 The smaller boys were known by the generic title of littluns. The decrease in size, from Ralph down, was gradual; and though there was a dubious region inhabited by Simon and Robert and Maurice, nevertheless no one had any 5 difficulty in recognizing biguns at one end and littluns at the other. The undoubted liltluns, those aged about six, led a quite distinct, and at the same time intense, life of their own. They ate most of the day, picking fruit where they could reach it and not particular about ripeness and quality. They were 0 used now to stomach-aches and a sort of chronic diarrhoea. They suffered untold terrors in the dark and huddled together for comfort. Apart from food and sleep, they found time for play, aimless and trivial, among the white sand by the bright water. They cried for their mothers much less often than 15 might have been expected; they were very brown, and filthily dirty. They obeyed the summons of the conch, partly because Ralph blew it, and he was big enough to be a link with the adult world of authority; and partly because they enjoyed the entertainment of the assemblies. But otherwise they seldom 20 bothered with the biguns and their passionately emotional and corporate life was their own. They had built castles in the sand at the bar of the little river. These castles were about one foot high and were decorated with shells, withered flowers, and interesting 25 stones. Round the castles was a complex of marks, tracks, walls, railway lines, that were of significance only if inspected with the eye at beach-level. The littluns played here, if not happily at least with absorbed attention; and often as many as three of them would play the same game together. 30 Em ... and though there was a dubious region inhabited by Simon and Robert and Maurice,... (linha 2), uma outra forma de escrever o trecho and though there was...

(ITA - 2005 - 1 FASE ) Assinale a opo que contm a afirmao ERRADA relativa curva de resfriamento apresentada a seguir.

(ITA - 2005 - 1 FASE ) O circuito da figura a seguir, conhecido como ponte deWheatstone, est sendo utilizado para determinar a temperatura doleo de um reservatrio, no qual est inserido um resistor de fio detungstnio RT. O resistor varivel R ajustado automaticamente demodo a manter a ponte sempre em equilbrio, passando de 4,00 para 2,00 . Sabendo que a resistncia varia linearmente com a temperaturae que o coeficiente linear de temperatura para o tungstnio vale = 4,00 103 C1, a variao da temperatura do leo deve ser de:

(ITA - 2005 - 1 FASE ) O nmero complexo 2 + i raiz do polinmio f(x) = x4 + x3 + px2 + x + q, com p, q IR. Ento, a alternativa que mais se aproxima da soma das razes reais de f

(ITA - 2005 - 1 FASE )As questes de 11 a 17 referem-se aos seguintes pargrafos: 1 The smaller boys were known by the generic title of littluns. The decrease in size, from Ralph down, was gradual; and though there was a dubious region inhabited by Simon and Robert and Maurice, nevertheless no one had any 5 difficulty in recognizing biguns at one end and littluns at the other. The undoubted liltluns, those aged about six, led a quite distinct, and at the same time intense, life of their own. They ate most of the day, picking fruit where they could reach it and not particular about ripeness and quality. They were 0 used now to stomach-aches and a sort of chronic diarrhoea. They suffered untold terrors in the dark and huddled together for comfort. Apart from food and sleep, they found time for play, aimless and trivial, among the white sand by the bright water. They cried for their mothers much less often than 15 might have been expected; they were very brown, and filthily dirty. They obeyed the summons of the conch, partly because Ralph blew it, and he was big enough to be a link with the adult world of authority; and partly because they enjoyed the entertainment of the assemblies. But otherwise they seldom 20 bothered with the biguns and their passionately emotional and corporate life was their own. They had built castles in the sand at the bar of the little river. These castles were about one foot high and were decorated with shells, withered flowers, and interesting 25 stones. Round the castles was a complex of marks, tracks, walls, railway lines, that were of significance only if inspected with the eye at beach-level. The littluns played here, if not happily at least with absorbed attention; and often as many as three of them would play the same game together. 30 O significado do termo untold em They suffered untold terrors in the dark... (linha 6)

(ITA - 2005 - 1 FASE ) Quando uma barra metlica se desloca num campo magntico, sabe-se que seus eltrons se movem para uma das extremidades, provocando entre elas uma polarizao eltrica. Desse modo, criado um campo eltrico constante no interior do metal, gerando uma diferena de potencial entre as extremidades da barra. Considere uma barra metlica descarregada, de 2,0 m de comprimento, que se desloca com velocidade constante de mdulo v = 216 km/h num plano horizontal (veja figura), prximo superfcie da Terra. Sendo criada uma diferena de potencial (ddp) de 3,0x10-3V entre as extremidades da barra, o valor do componente vertical do campo de induo magntica terrestre nesse local de:

(ITA - 2005) Considere a equao em x onde a e b so nmeros reais positivos, tais que.A soma das solues da equao

(ITA - 2005 - 1 FASE ) A 25C, uma mistura de metano e propano ocupa um volume (V), sob uma presso total de 0,080 atm. Quando realizada a combusto completa desta mistura e apenas dixido de carbono coletado, verifica-se que a presso desse gs de 0,12 atm, quando este ocupa o mesmo volume (V) e est sob a mesma temperatura da mistura original. Admitindo que os gases tm comportamento ideal, assinale a opo que contm o valor CORRETO da concentrao, em frao em mols, do gs metano na mistura original.

(ITA - 2005 - 1 FASE )As questes de 11 a 17 referem-se aos seguintes pargrafos: 1 The smaller boys were known by the generic title of littluns. The decrease in size, from Ralph down, was gradual; and though there was a dubious region inhabited by Simon and Robert and Maurice, nevertheless no one had any 5 difficulty in recognizing biguns at one end and littluns at the other. The undoubted liltluns, those aged about six, led a quite distinct, and at the same time intense, life of their own. They ate most of the day, picking fruit where they could reach it and not particular about ripeness and quality. They were 0 used now to stomach-aches and a sort of chronic diarrhoea. They suffered untold terrors in the dark and huddled together for comfort. Apart from food and sleep, they found time for play, aimless and trivial, among the white sand by the bright water. They cried for their mothers much less often than 15 might have been expected; they were very brown, and filthily dirty. They obeyed the summons of the conch, partly because Ralph blew it, and he was big enough to be a link with the adult world of authority; and partly because they enjoyed the entertainment of the assemblies. But otherwise they seldom 20 bothered with the biguns and their passionately emotional and corporate life was their own. They had built castles in the sand at the bar of the little river. These castles were about one foot high and were decorated with shells, withered flowers, and interesting 25 stones. Round the castles was a complex of marks, tracks, walls, railway lines, that were of significance only if inspected with the eye at beach-level. The littluns played here, if not happily at least with absorbed attention; and often as many as three of them would play the same game together. 30 Assinale a opo que expressa uma ideia no contida no texto.