Test de niveau Master – Évaluez vos compétences pour l’admission et la réussite

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1. Consider the following passage when answering the next question A strip of mauve light rimmed by green - that is how STEVE (Strong Thermal Emission Velocity Enhancement) appears, an optical phenomenon discovered by astronomers in 2018. It distinguishes itself clearly from auroras, which are typical of the more extreme latitudes, and now a study by NASA excludes the possibility that they have to do with airglow, a luminescent phenomenon of the atmosphere. So, what is it? Auroras are phenomena caused by the interaction between charged particles coming from the Sun and Earth’s magnetic field which is displayed near magnetic poles. On the other hand, airglows are caused by specific chemical phenomena and occur at all latitudes. “STEVE does not appear to line up with either of these two types of phenomena,” says Joshua Semeter, professor at Boston University. STEVE is visible at southern latitudes and can also be distinguished from auroras by its predominant mauve-pink coloration. One study argues that it has to do with extremely hot particles connected to some phenomenon which can be connected to Earth’s upper atmosphere, but the mystery is yet to be solved. 10. According to the passage, what differentiates STEVE from airglow?

Its specific coloring

Its visibility at primarily southern latitudes

The temperature of its particles

It cannot be deduced from the passage

2. Let X be a continuous random variable; its probability density function is shown below.

the expected value of X is equal to 1

the probability that X is greater than 1 is greater than 0.5

the probability that X is greater than 1 is less than 0.5

the expected value of X is greater than 1

3. In a symmetric distribution:

the mean is smaller than the median

the mean is greater than the median

the mean and median coincide

the variance is equal to one

4. Consider the following passage when answering the next question For Hegel, nature does not display freedom, but rather only randomness and necessity, and even if it is subject to external laws, this does not save it. Nature, in fact, is only the externalization of the idea being outside of itself and is dispersed in space and time. It is a kind of decline of the idea, even if Hegel justifies it as a necessary stage toward reaching the spirit’s self-consciousness. Hegel says no more: he sees that nature exists, but he does not explain why it exists. According to the passage, which of the following statements is consistent with Hegel’s thought?

Nature is the manifestation of the idea in time and space

Nature is the necessary elimination of the idea

The expression of the idea in nature impedes the spirit’s self-consciousness

No connection exists between the consciousness of the spirit and the expression of nature

5. Consider also the table below when answering the next question :

Description de l'image

In academic year 2021/2022, the number of students enrolled in the first year of Sociology was equal to 2,700. Assuming that the percentage decrease of enrolled students between the first and second year of enrollment is constant, how many students will enroll in the second year of Sociology at the University of Padua in academic year 2023/2024, knowing that there will be no new enrollments from other universities?

1,680

1,825

1,660

1,510

6. Let us suppose that the percentage of foreign students attending the universities of a certain country is 20%. Three students are selected at random. The probability that none of the three is foreign is:

(0.2) * (0.8) * (0.16)

2 * (0.2)^2 * (0.8)

(0.8)^3

3 * (0.8)^3

7. Knowing that: • production in Molise of the 4 products cited is equal to 100 tons • the production of apples in the 4 regions cited represents 40% of national production • the production in Lazio of the 4 products cited represents 40% of total fruit and vegetable production • the production of citrus fruits in Sicily represents 50% of national production • the region Molise reports the same production of olives as Lazio, the same production of apples as Tuscany, and 5% of national production of citrus fruits how much does the production of grapes in Molise amount to

10 tons

15 tons

20 tons

45 tons

8. Knowing that the number of permits: • to construct new buildings in 2020 will double compared with 2019 • to construct new residential buildings is for 1/3 of its total related to downtown Milan • to construct already standing buildings in the province of Milan represents 5% of permits at the national level what is it correct to affirm in this regard?

In 2020 the number of permits to construct new buildings will be greater than that to construct already standing buildings

In 2019 there are 40,000 permits to construct new residential buildings which are not for downtown Milan

In 2019 there are 2,100,000 permits to build at the national level

In 2019 the number of permits to construct new buildings in the province of Milan is 3.5% of that at the national level

9. A random number X assumes values 0 and 1 with equal probability. Which of the following statements is true?

The value of X is positive with a probability of 1

The expected value of X is 1 because 1 is the highest value X can assume

If X is a random sum of money, a risk-averse assessor assigns it a certain equivalent of less than 0.5

The random number Y = 1/X has a finite expected value

10. The random number Y = 1/X has a finite expected value

Only C

Only B