LOGIC
1
Considering the statement: "The recruits of the Pontifical Swiss Guard must necessarily be Swiss citizens from birth, Catholic, male, between the ages of 19 and 30, and must have undergone a period of training in the Swiss army", Which of the following statements is certainly FALSE regarding last June's enlistments?
2
Three sets A, B, and C each contain 4 elements; if A∩B∩C contains 1 element, 1 element belongs only to C, and the number of elements belonging only to A is 1 more than the number of elements belonging only to B, in how many ways can the three sets be represented using Venn diagrams?
3
Which of the proposed terms correctly completes the following proportion? hygrometer: humidity = X: wind
4
Alice opens the wardrobe and counts the boxes of her shoes. If she divides the number of boxes by 2, the remainder is 1. If she divides it by 3, there is no remainder. If she divides it by 5, the remainder is 4. Knowing that the number of boxes is greater than 4 and less than 45, how many possible solutions are there?
5
Nicolò has marbles of different diameters but all made of the same material. He fills three identical cube-shaped boxes (S1 with 125, S2 with 27, S3 with 64 marbles). Which of the three boxes will have the greatest weight?
6
Enea places three circles on a plane so that each of them is tangent to the other two, and their centers form the vertices of a right triangle. Knowing that the radii are integers, which triple can represent the radii?
7
Teacher Alice reminded her students that a function is differentiable only if it is continuous, and that if a function is continuous, then it is integrable. Which deduction is correct?
8
Enea bought 10 birds (partridges €12, pigeons €9, quails €6). He bought at least two of each. Total expense €81. How many partridges did he buy?
9
A pastry shop reduced packs from 12 to 10 pieces, keeping the price at €9. By what percentage has the price of a single pastry increased?
10
Four natural numbers a, b, c, d are such that a < b < c < d. To which number should Enea add 1 so that the product of the three unchanged numbers with the modified one is as small as possible?
GENERAL KNOWLEDGE
11
In which year were the racial laws promulgated in Italy?
12
In 1919, Gabriele D'Annunzio led the "March on Fiume". In which country is the city of Fiume located today?
13
Which term can be associated with both definitions: "document issued with commercial references" and "act of witchcraft"?
14
In four of the following terms, the suffix "-teca" has the same meaning. Identify the odd one out.
15
Who is the author of the play Mistero Buffo?
16
On which day is the Day of Legality celebrated, an occasion to commemorate the massacres of Capaci and Via D'Amelio?
17
Which car manufacturer was the first to introduce the assembly line?
18
Which English term refers to the narrative technique that consists of the free representation of a person's thoughts exactly as they appear in the mind?
19
What is meant by the term "legislature"?
20
In which of these sentences is the verb in the passive form?
21
Which of the following statements is/are true? (A1: Hydrogen isotopes names; A2: Atom mass range; A3: Electron/Neutron count)
22
Which of the following is a work by Niccolò Machiavelli?
BIOLOGY
23
In a DNA molecule consisting of 6000 nucleotides, of which 20% are guanine, what will be the number of adenine nucleotides?
24
Which of the following images represents prophase I of meiosis? (Note: Images not displayed)
25
Which of the following events is not present in the division of a prokaryotic cell?
26
A diploid cell in the G2 phase of the cell cycle has:
27
The graph shows the photosynthetic activity of a plant as a function of photon flux. Which statement is correct?
28
Which of the listed processes does not lead to ATP synthesis?
29
Glycolipids are important components of cell membranes. Which organelles are involved in their formation?
30
Recessive mutations in X chromosome cause color blindness. Francesca is not color-blind, but her father is. Francesca and Paolo (not color-blind) expect twins (M & F). Probability of color-blind children?
31
The epidermis is made up of:
32
The vertebral column has:
33
One of the following statements about gastric glands is incorrect:
34
In the circulatory system:
35
Bone marrow:
36
It is correct to say that:
37
The endocrine pancreas produces:
38
Cystic fibrosis is autosomal recessive. Two healthy parents have one sick child and two healthy children. Probability the next child will have the disease?
39
In the PCR cycle, the use of high temperature (95°C) has the purpose of:
40
Which of the following are not cloning vectors?
CHEMISTRY
41
A cylinder initially contains 100 mol of hydrogen gas at 4e5 Pa. After use, pressure is 1e5 Pa. Moles consumed?
42
Li (A=4, Z=1) decays by emitting a proton. What is the decay product?
43
Which pair has trigonal planar structure and central atoms with same number of valence electrons?
44
Which of the following is a decomposition reaction of ammonium nitrate?
45
Reaction 1 (slow) and 2 (fast) with KBrO3. How many moles of BrO3- consumed when all S2O3(2-) reacted?
46
An osmotic membrane separates solutions A and B (same salt). A is hypertonic. At equilibrium:
47
CuCl solubility 4.4e-4 mol/L. Add 0.1 mol CaCl2 to 1L sat. solution. What happens to [Cu+]?
48
Diagram of potential energy A+B <=> C+D. Correct statement?
49
Superoxide ion decomposition: 2 O2- + 2H+ -> O2 + H2O2. Oxidation numbers of oxygen?
50
Which statement regarding a buffer solution is correct?
51
Which pair are structural isomers?
52
Electron configurations. Which statement is always true regarding Hund's rule?
MATH/PHY
53
Solutions of 3e^x - 5e^-x - 2 > 0?
54
Value of sum: log(1/2) + log(2/3) + ... + log(9/10)?
55
For which real k does x^2 + y^2 - 4x + 2y + k = 0 represent a real, non-degenerate circle?
56
If x in [0, pi], solution of cos(x)/2 + 2sin(x) + 1/2 > 0?
57
Escape velocity v for mass m. What is escape velocity for mass 1.44m?
58
Inside conducting sphere (radius r, charged +), charge q placed at r/2. How does it move?
59
Conducting rod, current i, magnetic field B. Max force when?
60