TIL - I 5. DENEME SINAVI İsim Soyisim E-Posta Telefon Q. 1 Two figures are congruent if they have the same shape and size. Only one of these statements is correct, which one?Deselect Answer Two rhombi (rhombuses) with the same area are congruent Two parallelograms with the same perimeter are congruent Two equiangular triangles are congruent Two isosceles triangles with the same measure of the vertex angles and the same perimeter are congruent Two isosceles triangles with the same area are congruent Q. 2 In the interval [0,2π] the equation sin²x=1/4Deselect Answer has an infinite number of solutions has no solutions has only two distinct solutions has four distinct solutions has only one solution Q. 3 Given the two circlesx²+y²+2x-2y+1=0 , x²+y²+6x-2y+9=0we can say thatDeselect Answer they do not intersect and the first is internal to the second they do not intersect and the second is internal to the first they intersect at four distinct points they intersect at two distinct points they are tangent (one point of intersection) Q. 4 In the figure, the continuous curve is the graph of the function y=f(x).The dashed curve is the graph of the function y=g(x), whereDeselect Answer g(x)=2-f(x) g(x)=-2f(x) g(x)=-f(x) g(x)=-f(x+2) g(x)=-2-f(x) Q. 5 The prime factorization of the number (3⁵+3²)²2² isDeselect Answer 2⁴3²7² 2³3³7² 2⁴3²7 2⁶3⁴7² 2⁴3⁴7 Q. 6 Which of the following equations is the equation of the line that passes through the point (-1,-3) and is perpendicular to the line y=x ?Deselect Answer 2x+2y+8=0 x+y-4=0 x-3y-10=0 x-5y-2=0 2x+y=0 Q. 7 Arriving in the USA, an Italian tourist changes 10.000 euros (EUR) into dollars (USD); the exchange rate is 1 EUR = 1,4 USD. During the vacation, he spends 12.800 USD. Back in Italy, he changes the remaining USD back to EUR; the exchange rate is now 10 USD = 7,5 EUR. How much money has the tourist left?Deselect Answer 1.800 EUR 900 EUR 1.200 EUR 950 EUR 850 EUR Q. 8 The least common multiple of the monomials 8x³y⁶ , 6x²y⁶z², x⁴y³ isDeselect Answer 24x⁴yz² x³y³ 24x²y³z x²z² 24x⁴y³ Q. 9 Deselect Answer the set of the solutions of A) is included in the set of the solutions of B) the two equations have the same set of solutions the equations A) and B) have two solutions in common the equations A) and B) do not have any common solution the set of the solutions of B) is included in the set of the solutions of A) Q. 10 Deselect Answer A B C D E Q. 11 A woman has two children, Anna and Martino. The sum of the ages of the woman and Anna is 60 years more than Martino’s age. The sum of the ages of the woman and Martino is 70 years more than Anna’s age. How old is the woman?Deselect Answer 54 years old 65 years old 45 years old 68 years old 70 years old Q. 12 In the three-dimensional space, consider two spheres of radius 1 and centred, respectively, at the points P₁ and P₂ . If the distance between P₁ and P₂ is 3, then the intersection of the two spheres is:Deselect Answer an ellipse with different axes a point a circle the empty set a hyperbola Q. 13 Claudia does not know the correct quantity of sugar she has to add to the cake she is preparing. First she weigths 200 grams; she reads again the recipe and increases the quantity by 50%. She feels that it is too much and then decreases the quantity by 50%. How much sugar will Claudia put in her cake?Deselect Answer 300 grams 150 grams 200 grams 175 grams 100 grams Q. 14 Deselect Answer A B C D E Q. 15 The equation (2x⁴+5x²)³=0 hasDeselect Answer three real distinct solutions twelve real distinct solutions one (and only one) solution: x=0 no real solutions two real distinct solutions Q. 16 In the figure, it is shown the graph of the function:Deselect Answer y=cosx-2 y=2cosx y=2sinx-2 y=cosx-1 y=2cosx-2 Q. 17 SupernovaeWhen supernovae explode they jettison matter into space at some 9,000 to 25,000 miles (15,000 to 40,000 kilometers) per second. These blasts produce much of the material in the universe -- including some elements, like iron, which make up our planet and even ourselves. Heavy elements are only produced in supernovae, so all of us carry the remnants of these distant explosions within our own bodies.Supernovae add enriching elements to space clouds of dust and gas, further interstellar diversity, and produce a shock wave that compresses clouds of gas to aid new star formation.But only a select few stars become supernovae. Many stars cool in later life to end their days as white dwarfs and, later, black dwarfs.But massive stars, many times larger than our own sun, may create a supernova when their core's fusion process runs out of fuel. Star fusion provides a constant outward pressure, which exists in balance with the star's own mass-driven, inward gravitational pull. When fusion slows, outbound pressure drops and the star's core begins to condense under gravity -- becoming ever denser and hotter.To outward appearances, such stars begin growing, swelling into bodies known as red super giants. But at their cores shrinking continues, making a supernova imminent.When a star's core contracts to a critical point a series of nuclear reactions is unleashed. This fusion staves off core collapse for a time -- but only until the core is composed largely of iron, which can no longer sustain star fusion.In a microsecond, the core may reach temperatures of billions of degrees Celsius. Iron atoms become crushed so closely together that the repulsive forces of their nuclei create a recoil of the squeezed core -- a bounce that causes the star to explode as a supernova and give birth to an enormous, superheated, shock wave.Supernovae also occur in binary star systems. Smaller stars, up to eight times the mass of our own sun, typically evolve into white dwarfs. A star condensed to this size, about that of Earth, is very dense and thus has strong enough gravitational pull to gather material from the system's second star if it is close enough.If a white dwarf takes on enough mass it reaches a level called the Chandrasekhar limit. At this point the pressure at its center will become so great that runaway fusion occurs and the star detonates in a thermonuclear supernova.A supernova can light the sky up for weeks, and the massive transfer of matter and energy leaves behind a very different star.Typically only a tiny core of neutrons, a spinning neutron star, is left to evidence a supernova. Neutron stars give off radio waves in a steady stream or, as pulsars, in intermittent bursts.If a star was so massive (at least ten times the size of our sun) that it leaves behind a large core, a new phenomenon will occur. Because such a burned-out core has no energy source to fuse, and thus produces no outward pressure, it may become engulfed by its own gravity and turn into a cosmic sinkhole for energy and matter -- a black hole. Supernovae from massive starsDeselect Answer will provide new energy and matter can eventually give rise to black holes have very small cores produce a large amount of pressure leave only a small amount of neutrons Q. 18 Supernovae occur whenDeselect Answer large stars have an excess of fuel star fusion creates a rise in pressure the core of a star condenses and heats up the core of a star begins to cool down and expand stars as big as our sun run out of fuel Q. 19 White dwarfsDeselect Answer cannot attract material from another star occur when a star reaches the Chandrasekhar limit can become supernovae when their pressure increases can become red super giants can evolve from stars smaller than our sun Q. 20 During the process in which a star is transformed into a supernovaDeselect Answer the core gradually heats up until it reaches an extremely high temperature a black dwarf usually occurs a black hole usually occurs an extremely hot wave is produced as a result of the explosion iron atoms expand rapidly Q. 21 SupernovaeDeselect Answer compress new stars absorb matter from space clouds produce the iron in our blood are found every 25,000 miles in space often become white dwarfs Q. 22 If it is true that:- all engineers are logical thinkers- Anthony is an engineer- logical thinkers like scooterswhich of the following statements is certainly NOT true?Deselect Answer Whoever is a logical thinker is an engineer Anthony has the prerequisites to be a good logician It cannot be denied that Anthony likes scooters Anthony is a logical thinker and likes scooters All engineers like scooters Q. 23 How can you insert the + (plus) or the - (minus) sign in the following sequence of numbers :14 16 13 12 11 in order to have -6 as a result?(Example: if I insert + - in the sequence 5 6 7 the result is 5 + 6 - 7 = +4 , if I insert - + the result is 5 - 6 + 7 = +6)Deselect Answer + - - + - + + + + - - - - - + + - + - + Q. 24 Discussing their personal finances, four friends (Alan, Brian, Conan e Donald) state that:- Alan has less money than Conan- Brian has less money than Conan- Conan has more money than Donald- Brian has more money than AlanThen, which of the following statements is NOT NECESSARILY correct?Deselect Answer Brian is not the poorest Donald has less money than Conan the alphabetical order of the names is not the same as the (increasing order) of the money owned Alan is the poorest among the friends the richest among the friends is Conan Q. 25 Anna, Bruno, Carlo and Daniela are considering whether to go to Cortina next weekend.We know that:- if Carlo goes, Daniela will also go- if Anna doesn't go, Daniela won't go either- if Anna goes, Bruno will also goWhich of the following statements can be deduced?Deselect Answer If Bruno doesn't go, Carlo won't go either They'll all go Anna and Bruno will go Nobody will go If Anna goes, Carlo will also go Q. 26 The product of 40 integer numbers is positive. From this information we can deduce that it is necessarily true that:Deselect Answer the number of positive factors is either zero or an even number 2 factors are positive and 38 factors are negative all factors are positive 20 factors are positive and 20 factors are negative at least two factors are negative Q. 27 A ball is thrown vertically from the ground upwards with initial velocity . After a while the ball hits the ground again. If the initial speed doubles (), how does the time of flight change ?Deselect Answer impossible to answer because the value of the maximum height reached is not known quadruples Double down increases 8 times remains unchanged Q. 28 The surface of a conducting sphere is uniformly charged with a charge q. The electrostatic field at a point P outside the sphere Deselect Answer is inversely proportional to the square of the distance of point P from the surface of the sphere is inversely proportional to the distance of the point P from the surface of the sphere is inversely proportional to the square of the distance of point P from the center of the sphere is always null is inversely proportional to the distance of point P from the center of the sphere Q. 29 A cart of mass M = 25 kg is moved along a frictionless horizontal plane with an acceleration parallel to the plane of 8 m/s 2 . What is the value of the force that is applied to the trolley, knowing that it forms an angle of 60° with the plane?Deselect Answer F = 200N F = 4000N F = 400N F = 40N F = 2000N Q. 30 Consider the circuit shown in the figure, whereR₁=10Ω ,V=30V, and the current is / = 2A. How much is the resistance worth R₂? Deselect Answer R₂=7.5Ω R₂=10Ω R₂=15Ω R₂=1Ω R₂=5Ω Q. 31 A hermetically sealed container with rigid walls contains an ideal gas at temperature T 1 = 300 K and pressure p 1 = 1 Pa. What pressure does the gas reach if the container is cooled down to a temperature of T 2 = 270 K?Deselect Answer 11.1 Pa 1.11Pa 0.9Pa The pressure does not change 0.09Pa Q. 32 A ball is thrown up. Which of the following statements is false?Deselect Answer The kinetic energy of the ball decreases as it rises. The ball's potential energy increases as it rises. As the ball rises, gravity opposes the motion. As the ball rises, gravity does positive work on it. The ball's kinetic energy is a function of its speed. Q. 33 A body, initially at the origin of a Cartesian reference system, moves 5 meters in the second quadrant of the (x,y) plane along a line whose direction makes an angle equal to θ with the y axis. Then the body moves 4 meters parallel to the y-axis. Knowing that at this point the final distance d of the body from the x-axis is equal to 6.5 m, what is the angle θ?Deselect Answer 60⁰ 45⁰ 30⁰ 0⁰ the data is not sufficient to formulate an answer Q .34 A warrior rotates the "bolas" (a rope with a stone attached to one end) on his head with an angular velocity of 2 rad/s. At one point he lets go to strike the opponent. If the bola string is 0.5 m long, how fast are the bolas thrown?Deselect Answer 1 m/s 0.25m/s 4m/s 2m/s It is not possible to calculate it because it is necessary to know the mass of the thrown object. Q. 35 A mass bucket M is lowered from above using a rope subjected to a modulus tension T. The acceleration of the bucket has modulus and points downwards. Which of the following relations is correct?Deselect Answer T=-M(g-a) Mg+T+Ma=0 T=M(g-a) T=M(g+a) Q. 36 What is the mean radius of the Earth ?Deselect Answer 6.38 x10³ km 6.38 x10¹⁰ km 6.38 x10⁶ km 6.38 x10⁵ km 6.38 x10⁹ km Q. 37 What kind of representation is used in the figure? Deselect Answer Blueprint Front elevation Accidental perspective Isometric orthogonal axonometry Central perspective Q. 38 The smaller the denominator of the representation scale, the more the area represented isDeselect Answer properly represented more extensive and the map less detailed less extensive and more detailed map more extensive and more detailed map less extensive and the map less detailed Q. 39 Which is the command to make a new directory in the terminal?Deselect Answer del rm ren mkdir cd Q. 40 Given the figure, which will be the value of a at the end of the programDeselect Answer 120 30 12 20 15 Q. 41 Convert 47 (in base 10) to the corresponding base-2 numberDeselect Answer 101111 101110 111 101010 47 Q. 42 Given the two orthogonal projections of the object (top view and front view), identify the third corresponding view (side view)Deselect Answer 4 1 3 2 5 1 out of 1
