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(a) Give the modern form of po clor.
(b) Give the infinitive of páinig.
(c) What is the proper extended form of damaò? (d) Parse dá bfuil a n-Éirinn.
Translate into English:
'Sé deip mo bean 'sé deir mo člann
Dá mbeidċeá mapb buò beag an sgeul.
expressing the result as a decimal.
Find, as a vulgar fraction in its lowest terms, the product of 567 and 2936507.
2. A clock is set right at noon on Monday, and is 2 minutes fast at noon on Tuesday. What is the proper time when it strikes 7 on Friday evening?
3. A square field contains 7 acres. Find the length of its diagonal to the nearest inch.
4. A grocer buys 3 cwt. of sugar at 24d. per lb., and 7 cwt. at 3d. per lb. He sells 182 lbs. at 34d. per lb. At what price per lb. must he sell the remainder to gain 37 his outlay?
per cent. on
5. A cistern has two pipes, one of which would fill it in 3 hours and the other in 4 hours. They are opened together, and in consequence of a leak in the bottom of the cistern they take 2 hours to fill it. When the cistern is full, the pipes are closed. In what time will the contents leak away, assuming the rate of leakage to be uniform?
8. Find x and y in their simplest forms from the equations
9. A man bought a number of sheep for £118.
He lost 9 of them, and then sold half of the remaining ones for £75, getting half as much again as he paid for them. How many sheep did he buy?
10. Two consecutive integers are taken, and fractions are formed by placing each over the other. Prove that the difference of these fractions is equal to the sum of the reciprocals of the integers.
PROFESSOR BROMWICH; PROFESSOR GIBNEY.
1. Two angles of a triangle are equal, prove that two of its sides are also equal.
2. Prove that the diagonals of a parallelogram are unequal unless it is a rectangle.
3. Two isosceles triangles stand on the same base and on the same side of it, prove that the line joining their vertices is perpendicular to their common base.
4. Show how to construct a square that shall be equal to a given rectilineal figure.
5. Prove a proposition of Euclid which shows that the square on the sum of two lines together with the square on their difference is equal to twice the sum of the squares on the two lines.
Demonstrate clearly that the proposition that you select. does prove this theorem.
6. A, B, C, D are four points on a circle whose centre is O, and the angle AOB is equal to the angle COD: prove that the arc AB is equal to the arc CD.
7. APB is any chord of a circle: prove that the rectangle AP. PB together with the square on the line joining P to the centre of the circle is equal to the square on the radius of the circle.
10. There is a square garden bed, and if each side of the bed be increased by 2 feet, the area of the bed will be increased by six square yards. Find the length of the side of the bed.
1. Enunciate the law of the triangle of forces, and show that it follows from the parallelogram of forces.
2. A uniform rod, weighing 3 lbs., has a weight of 2 lbs. hung on it at one end, and a weight of 1 lb. at the other. At what point can the whole be balanced?
3. Two equal parallel forces act in opposite directions. Show that they have the same total moment about every point in their plane.
4. A body is projected vertically upward with velocity of 80 feet per second. Find where it is after 2 seconds, and after 3 seconds, from the instant of projection.
5. A 2 lb. weight lies on a smooth table. What force must be exerted on it in order to get up a velocity of 4 feet per second in 3 seconds ?
6. What are the conditions that a body should float in equilibrium? If the specific gravity of ice is 9, and that of sea-water 1.03, find what proportion of the mass of an iceberg is above the surface.
7. Explain the action of a compression pump, such as is used for inflating a bicycle tyre.
8. The volume of a given mass of gas is reduced by 20 per cent. at constant temperature. What is the percentage increase of pressure produced?
9. A rectangular tank contains a liquid of specific gravity 8 to a depth of 2 feet. Find, in pounds, the pressure on a side of the tank, 3 feet long, taking the weight of a cubic foot of water as 621 lbs.
10. Explain how you would proceed to find the specific gravity of some solid substance which floats in water.
FIRST UNIVERSITY EXAMINATION.
PROFESSOR MAC MASTER.
1. Translate into English :
Aurora interea miseris mortalibus almam
2. (a) Set down the accusative singular of-glis, lis, tussis, vomis, and the genitive plural of-as, mus, nux, volucris.
(b) Give the superlatives in use of—egenus, frugi, nequam, nuper, salubriter.
(c) Distinguish in meaning between the following pairs of words-conqueri, conquirere; fugere, fugare; servire, servare; simulare, dissimulare; hac, huc; quandoque, quandoquidem; recte, rectâ.
* Tarchon, the Etruscan ally of Aeneas,