Prova de 2010: Universidade Estadual do Ceará (UECE) — questões com gabarito

O coeficiente de x⁹ no desenvolvimento de

Os números complexos z = x + yi e w = y + xi satisfazem às igualdades |z| = |w| = 16. Se = 0, em que = x – yi e = y – xi, então o valor da soma |x| + |y| é

Uma circunferência, cujo centro está localizado no semi-eixo positivo dos x, é tangente à reta x + y = 1 e ao eixo dos y. A equação desta circunferência é

Duas circunferências em um plano, ambas com a medida do raio igual a 3 m, tangenciam-se externamente. Uma reta r, contendo os centros destas circunferências, as intercepta em três pontos P, Q e O, sendo O o ponto de tangência. Duas outras retas, no mesmo plano e perpendiculares à reta r, contendo os centros das circunferências as interceptam, respectivamente, nos pontos R, S e U, V. Com estas hipóteses a medida, em m² , da área do hexágono convexo com vértices nos pontos P, R, U, Q, V e S é

Se x é um arco localizado no segundo quadrante e cosx = - , então o valor de cosx + senx + tgx + cotgx + secx + cosecx é

Se x, y, z e w são as raízes da equação x⁴ + 2x² + 1 = 0, então

log₂|x| + log₂|y|+ log₂|z|+ log₂|w| é igual a

Se os números reais x e y satisfazem simultaneamente as igualdades 2 ^x+4 = 0,5^y e log₂(x+2y) = 2, a diferença y – x é igual a

Se a população de uma cidade aumenta a uma taxa de 2% a cada mês, o porcentual do aumento acumulado imediatamente após um período de quatro meses, com aproximação de duas casas decimais, é

As funções do primeiro grau f(x) = mx + n, e g(x) = px + q, são funções de R em R tais que o gráfico de f passa pela origem do sistema de coordenadas e intercepta o gráfico de g no ponto de abscissa igual a 3. Se o gráfico de g intercepta os eixos x e y, respectivamente, nos pontos (7, 0) e (0, 5) então o valor de m + n + p + q é um número localizado entre

The extract “A community without a written literature expresses itself with less precision, with less richness of nuance, and with less clarity than a community whose principal instrument of communication, the word, has been cultivated and perfected by means of literary texts. … A person who does not read, or reads little, or reads only trash, is a person with an impediment: he can speak much but he will say little, because his vocabulary is deficient in the means for self-expression.” contains verbs in the following tenses (irrespective of the sequence)

In terms of voice, the verbs in these three sentences “Literary works are born, as shapeless ghosts, in the intimacy of a writer's consciousness, projected into it by the combined strength of the unconscious, and the writer's sensitivity to the world around him, and the writer's emotions…”, “literature has been relegated--like some hidden vice--to the margins of social and personal life, and transformed into something like a sectarian cult…” and “Nothing better protects a human being against the stupidity of prejudice, racism, religious or political sectarianism, and exclusivist nationalism than this truth that invariably appears in great literature: that men and women of all nations and places are essentially equal.” are respectively in the

In the sentences “as readers of Cervantes, Shakespeare, Dante, and Tolstoy, we understand each other across space and time as members of the same species…” and “in the works of these writers, we learn what we share as human beings, what remains common in all of us under the broad range of differences that separate us.” one finds respectively

The sentences “No other discipline or branch of the arts can substitute for literature in crafting the language that people need to communicate.”, “Without it (literature), the critical mind, which is the real engine of historical change and the best protector of liberty, would suffer an irreparable loss.” and “…this world without literature, this nightmare that I am delineating, would have as its principal traits conformism and the universal submission of humankind to power.” contain, respectively, relative clauses of the following types

The sentences 

“I will offer a few arguments in favor of the view of literature as one of the most primary and necessary undertakings of the mind, an irreplaceable activity for the formation of citizens in a modern and democratic society, a society of free individuals.”

and

"Literature has been, and will continue o be, as long as it exists, one of the common denominators of human experience through which human beings may recognize themselves and converse with each other, no matter how different their professions, their life plans, their geographical and cultural locations, their personal circumstances.”

should be classified respectively as

According to the text, one of the things the Swedish Academy should not do is to

The period that could be considered as “The Great Style”

A prize-deserving serious literature should not only further people’s knowledge and their condition, but also try to

The policy of pragmatic consideration

An Academy’s principle that has frequently been misunderstood is the one concerning

As to criticism toward the Academy, the author of the text says that they tend not to take into account