80.

Va, traître, laisse moi.

Les Juifs n'attendent rien d'un méchant tel que toi.
Misérable, le Dieu vengeur de l'innocence,

Tout prêt à te juger, tient déjà sa balance.
Bientôt son juste arrêt te s ra prononcé.

Tremble: son jour approche, et ton règne est passé.

(a) Donnez votre appréciation de ce passage.

(b) Comment Aman se trahit-il ? Comment Esther l'accusa-t-elle, et comment justifia-t-elle les Juifs ?

HISTORY--ENGLISH, GREEK AND ROMAN.

1. (a) Give a brief account of the political state of Europe at the time of the Revolution of 1688.

(b) What were the aims of Louis the Fourteenth and the means at his disposal? Explain fully.

2. Distinguish between legislative and executive functions. What is meant by the dispensing power?

3. Show briefly how England and Scotland came to be one nation, and give an account of the ecclesiastical settlement in the latter country.

4. Discuss (a) the foreign policy and (b) the financial policy of Robert Walpole.

5. Give a brief account of the great Methodist revival.

6. Sketch the conflict between the government and the press in the reign of George III.

7. Write a note on the influence of the sea power upon history. Illustrate by reference to the Greek war with Persia, the Punic war, the Napoleonic war, the Spanish-American war.

8. "As fast, then, as the nations grew up the Empire fell in pieces." Explain fully. What features of the old Roman system are reflected in the present European system of nations?

9. Write brief notes on Pericles, Themistocles, the Gracchi.

ALGEBRA.

1. Employ the method of re-arrangement and grouping of terms to find the factors of the expression

p2 (y + r) − q2 (r+p)+r2 (q+p)+pqr.

2. Given that a+b=5 (a−b), find the numerical value of the

(ii) 3x-y-z = 5; 3y − z − x = −7 ; 3z − x − y=5.

4. In a certain constituency, on election day, 1500 electors did not record their votes. There were three candidates, A, B, and C. B obtained together 75 per cent. of the votes cast; B and C together 60 per cent. If C had not stood, and if the votes cast for him had been divided between A and B in the ratio 9:16, respectively, B would have headed the poll by 200 votes. How many electors were there in the constituency, and how many votes did A, B and C each actually receive?

5. Define a quadratic equation, and show how to solve the equation ax+b+c=0.

a

Ві

show that

В B1

If a, ẞ are the roots of the equation x2+ax+b=0, and a1, B, the roots of the equation +c+d=0, and if a2d=be2.

7. A reservoir has a supply pipe, A, and an exhaust pipe, B. A can fill the reservoir in 8 minutes less time than B can empty it. If both pipes are open, the reservoir is filled in 6 minutes. In how many minutes will it be filled if A is open and B closed ?

8. (i) 'Divide a 1x by + a 2x b−−2b-3y by ax-b-y.
(ii) Extract the square root of

4x-12xy + 9y% + 16xz3⁄4—24yz1⁄4 +16z.

(iii) Obtain the square root of 87-121/42.

(iv) Find the value, when x=1/3, of the expression
2x-1 2x+1

1. Define a right angle; and prove that the angles which one straight line makes with another on one side of it are together equal to two right angles.

Prove in the manner of the above proposition that, if A, B, C, D, be four points in order on a straight line, the sum of AB, BD is equal to the sum of AC, CD.

2. Define parallel straight lines. Enunciate the two propositions which state the conditions under which two straight lines can be proved to be parallel; and state and prove the converse of these two propositions.

If DE, DF drawn from any point D in the base of BC of an isosceles triangle ABC to meet AB, AC in E, F be parallel to AC, AB, the perimeter of the parallelogram AEDF is constant.

3. Define a parallelogram. Enunciate the propositions in which Euclid states the conditions under which two triangles are proved to be equal in area only; and prove one of them.

Points A, B, C are taken, one in each of three parallel straight lines. If BC, CA, AB meet the lines through A, B, C, respectively, in a, b, c, prove that each of the triangles ABC, Abc, Bca, Cab, is equal to half the triangle abc.

4. Define a square, a gnomon; and prove that if a straight line be divided into any two parts, the squares on the whole line and on one of the parts are together equal to twice the rectangle contained by the whole and that part together with the square on the other part.

If BAC be an acute angle of the triangle ABC, and BD, CE be drawn perpendicular to CA, AB, respectively, then the rectangle contained by BA, AE is equal to the rectangle contained by CA, AD.

4. Define a rectangle. Divide a straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.

Prove that, when a straight line is divided as in this proposition, the square on the line made up of the given line and the smaller part is equal to five times the square on the larger part.

6. Define a circle. If two circles touch one another externally at any point, the straight line joining their centres shall pass through that point of contact.

Describe a circle passing through a given point and touching a given circle at a given point.

7. Define an angle in a segment of a circle. An angle in a semi-circle is a right angle; an angle in a segment which is greater than a semicircle is less than a right angle; and an angle in a segment which is less than a semi-circle is greater than a right angle.

The circle described on any two sides of a triangle as diameters intersect on the third side.

8. If from a point without a circle two straight lines be drawn, one of which cuts the circle and the other touches it, the rectangle contained by the whole line which cuts the circles and the part of it without the circle shall be equal to the square on the line which touches the circle.

PHYSICS.

1. (a) Describe in detail how the heat from a hot water furnace in the basement of a house reaches the occupants of a room in the second flat. If alcohol were used instead of water, what difference would result, and why?

(b) A kilogram of ice at 15° C. is heated to a temperature of 105° C. Narrate all the facts brought out by this experiment.

2. (a) Distinguish virtual from real images. What kind of mirror always makes the image smaller than the object? What kind makes it larger or smaller according to circumstances? Explain in each case.

(b) Enumerate the laws of refraction of light and explain what is meant by the index of refraction. A ray of light passing from air into water falls at a given angle on the water surface. Make a geometrical construction to determine the path of the refracted ray, the index being .

3. (a) What physical facts have led to the conclusion (1) that all matter is made up of small particles, and (2) that each particle in the universe attracts every other particle?

(b) State Archimedes' principle and explain its application (1) in the building of ships, and (2) in the construction of balloons.

4. (a) A charged sphere A is brought near to an insulated conductor B. Describe the electrical condition of B, (1) when A is placed near B; (2) when B is grounded; (3) when B is again insulated and removed, and (4) when B is insulated and A brought nearer than at first?

(b) Eight cells are connected in series. Find the current strength, having given that the E.M.F. of each cell is 1 volt, the internal resistance 2 ohms and the external resistance 4 ohms. Define the technical terms used in stating this problem.

5. (a) What is the effect of striking a bell with different degrees of force? What change is made in the vibrations produced? What property of sound remains the same?

(b) The report of a cannon is heard 12 seconds after the flash is seen. How far away is the cannon? Temperature 20° C.

6. (a) A bicycle rider moves up a grade in the face of a wind. Against what forces does he do work? In what way does he expend energy? From which of these expenditures can be get a return of energy? Give sufficient reasons for your conclusions.

(b) A mass of rock weighing 600 lbs. falls to the ground. Find the kinetic energy of the mass at the end of the third second of its fall. (g=32.)

7. (a) In the case of a shot fired at a target, state (1) why the velocity of the shot changes, (2) the nature and the direction of its motion, and (3) why the target is made hot on being struck?

(b) ABCD is a parallelogram such that the diagonal AC is perpendicular to the side BC. Three forces act at the point A and are represented in magnitude and direction by AB, CA and AD. Shew that these forces are in equilibrium.

PRACTICAL PHYSICS.

GROUP 1.

1. Define impenetrability and perform two experiments illustrating this properly.

2. State Newton's 3rd law of motion. Give three illustrations. If this law did not exist what could happen? Discuss action and reaction in the case of a horse pulling and moving a heavy load.