سوالات

بستار متعدّی رابطهٔ R = (a,b),(b,c),(c,d),(d,b) دارای چند عضو است؟

درخت T که دارای ۳ رأس درجهٔ ۵ است، حداقل دارای چند برگ است؟

طبق تعریف زیر، گراف G چند یال دارد؟ هر زیر مجموعه ۳ عضوی از مجموعه x = ۱, ۲, …, ۱۰ را یک رأس G درنظر بگیرید. دو رأس A و B مجاورند اگر و تنها اگر اشتراک A و B تک عضوی باشد ( A ∩ B = ۱ ).

گراف G از مرتبه ۱۵ با مینیمم درجه δ = ۳ ، دارای ۳ مؤلفه همبندی است. تعداد حداقل و حداکثر یال‌ها را با q_min و q_max نمایش می‌دهیم. در این صورت (q_min ، q_max) کدام است؟

گراف G با مجموعه رئوس V = ۲,۳,۴,...,۲۰ به‌صورت زیر تعریف می‌شود که دو رأس i و j مجاور هستند اگر و تنها اگر i و j نسبت به هم اول باشند. کدام مورد درباره G درست است؟

با استفاده از حروف کلمهٔ falafel چند کلمه به طول ۵ می‌توان ساخت؟

چهار عدد متمایز از دنباله‌ی -۴,-۳,-۲,-۱,۱,۲,۳,۴ را انتخاب می‌کنیم. احتمال اینکه حاصل‌ضرب اعداد انتخاب شده مثبت باشد، چقدر است؟

مجموعهٔ S با 1∈ S و ضابطهٔ استقرایی x∈ S ⇒ (x+۳∈ S , (x-۲)^۲+۲∈ S) تعریف شده است. مقدار S∩ ۱,۲,…,۲۰ کدام است؟

می‌خواهیم پنج زیرمجموعه‌ی A, B, C, D, E از مجموعه‌ی X = ۱,۲,۳ انتخاب کنیم به‌طوری که A ∪ B ∪ C = D ∩ E . به چند طریق می‌توان اعضای این زیرمجموعه‌ها را انتخاب کرد؟ (پنج زیرمجموعه لزوماً متمایز نیستند.)

چند گراف کامل دو بخشی وجود دارد که قابل تجزیه به ۳ درخت فراگیر باشد؟ (در تجزیه یک گراف به چند زیرگراف، هر یال گراف دقیقاً در یک زیرگراف ظاهر می‌شود.)

اعداد مجموعه 1,2,...,n را با دو رنگ سیاه و سفید رنگ کرده‌ایم به‌طوری که تفاضل هر دو عدد سیاه، سفید است و تفاضل هر دو عدد سفید، سیاه است. حداکثر n چقدر است؟

ضریب جملهٔ x^۴ در عبارت زیر کدام است؟ (x+√۲+۱)^۸ + (x+√۲-۱)^۸ + (x-√۲+۱)^۸ + (x-√۲-۱)^۸

a و b دو رقم متمایز هستند به‌طوری که برای هر n ∈ N ، مضربی طبیعی از n با ارقام a و b وجود دارد. a و b به‌ترتیب کدام است؟

تعداد سه‌تایی‌های مرتب (x,y,z) از اعداد صحیح که در نامساوی x + y + z ≤ ۶ صدق می‌کنند، کدام است؟

تعداد ۷ نهال چنار، ۴ نهال سپیدار و ۳ نهال سرو باید در یک ردیف با رعایت شرایط زیر کاشته شوند: نهال‌های ابتدا و انتهای ردیف چنار باشند. هیچ دو نهال سرو مجاور هم نباشند. هیچ دو نهال سپیدار مجاور هم…

به چند طریق می‌توان مجموعه ۱،۲،۳،…،۱۳۹۷ را به ۴ زیرمجموعهٔ ناتهی افراز کرد که در هیچ یک، دو عدد متوالی وجود نداشته باشد؟

I have to say, I'm not particularly ................ in my own understanding of the true nature of fear, even though I make my living drawing horror images. 1) mutual 2) confident 3) possible 4)…

We must stop seeing nuclear ................. as a dangerous problem and instead recognize it as a safe byproduct of carbon-free power.

My father has always been with his money. I didn't have to pay for college or even for the confused year I spent at Princeton taking graduate courses in sociology.

Even though a cease-fire, in place since Friday, has brought temporary from the bombardment, the threat the strikes will return leaves people displaced yet again.

What you'll hear, often, is that you should ……………… your passion; quit your job and live the life you want. 1) undermine 2) partake 3) pursue 4) jeopardize

We must stop seeing nuclear .................. as a dangerous problem and instead recognize it as a safe byproduct of carbon-free power.

They say that "the EI" did not meet the historic criteria for being registered, as it ……………… the view from the street of other historic buildings and because the structure generally downgraded the…

Read the following passage and decide which choice (1), (2), (3), or (4) best fits each blank. The first step in the process of becoming an Olympic sport is (8) a sport from the International Olympic…

Cloze passage (mark the blank for item 9): "The first step in the process of becoming an Olympic sport is (8) a sport from the International Olympic Committee (IOC). The IOC requires that the…

Read the following passage and decide which choice (1), (2), (3), or (4) best fits each space. Passage (excerpt): The first step in the process of becoming an Olympic sport is … a sport from the…

PASSAGE 1 (excerpt): Human-computer interaction (HCI) has been the focus of attention for researchers in the past decade, with considerable work being done in the various modalities for communicating…

Read the following passage and answer the question. PASSAGE 1: Human-computer interaction (HCI) has been the focus of attention for researchers in the past decade, with considerable work being done…

PASSAGE 1: Human-computer interaction (HCI) has been the focus of attention for researchers in the past decade, with considerable work being done in the various modalities for communicating with a…

PASSAGE 1 (excerpt): Paragraph 1: Human-computer interaction (HCI) has been the focus of attention for researchers in the past decade, with considerable work being done in the various modalities for…

PASSAGE 1 Human-computer interaction (HCI) has been the focus of attention for researchers in the past decade, with considerable work being done in the various modalities for communicating with a…

PASSAGE 2: That part of mathematics which is usually called Set Theory encompasses two distinct groups of definitions and results. Firstly, we have those concepts (including that of an infinite set)…

Read the relevant excerpt from PASSAGE 2 (paragraph 2) and answer the question. Paragraph 2: "The Greeks were the first to realize the close relationship between mathematics and logic. One of the…

Read the passage and answer the question. PASSAGE 2: That part of mathematics which is usually called Set Theory encompasses two distinct groups of definitions and results. Firstly, we have those…

Reading passage (PASSAGE 2): That part of mathematics which is usually called Set Theory encompasses two distinct groups of definitions and results. Firstly, we have those concepts (including those…

PASSAGE 2 (excerpt): That part of mathematics which is usually called Set Theory encompasses two distinct groups of definitions and results. ... These concepts were first introduced into mathematics…

Passage 3 (paragraph 1): In the sciences, mathematics is used to build a model of the observed reality. In physics, for example, scientists propose mathematical systems describing physical objects…

PASSAGE 3 (paragraph 1): In the sciences, mathematics is used to build a model of the observed reality. In physics, for example, scientists propose mathematical systems describing physical objects…

Passage (excerpt): “Unlike these natural sciences, in computer science we study artificial objects: computers, programs, programming languages. Despite this difference, the science is not…

Read the passage and answer the question. PASSAGE 3: In the sciences, mathematics is used to build a model of the observed reality. In physics, for example, scientists propose mathematical systems…