(x+1)3(x-1)3 1)2 = 2; (b) Solve graphically the simultaneous equations 4x+y=6 and 2y-x = 3; and explain how you get the result. 11. What is the value of silver per tola, when a fall of 2 annas in the price of a tola enables a man to buy for Rs. 30 eight tolas more than he bought before for the same amount? FRIDAY, 16TH NOVEMBER. [10-30 A.M. TO 1-30 P.M.] GEOMETRY. N.B.-The answers to the two Sections should be given in separate books. All figures should be drawn accurately. The use of intelligible abbreviations is recommended. SECTION I. 1. Shew by an exact diagram, giving a short explanation, how to construct the triangle, having given the two sides to be 7 cm. and 5 cm. and the included angle 65°; and measure the length of the third side in centimetres. = 2. If two angles of a triangle are equal, the sides opposite to these angles are equal.. The bisector of the interior angle at C in the triangle ABC meets AB in D; DF is drawn parallel to BC which meets the bisector of the exterior angle at C in Fand AC in E. Shew that DE = EF. 3. Triangles on the same base and of the same altitude are equal in area. Through A,B,C the angular points of the triangle ABC parallel straight lines are drawn to meet the sides BC,CA,4B (produced if necessary) in P,Q,R respectively. Prove that the area of the triangle PQR is double that of the triangle ABC. 4. The locus of a point which is equidistant from two fixed points is the perpendicular bisector of the straight line joining the two fixed points. SECTION II. 5. In any triangle the sum of the squares on two sides is equal to twice the square on half the base, together with twice the square on the median which bisects the base. In a triangle, three times the sum of the squares on the three sides is equal to four times the sum of the squares on the three medians. 6. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The perpendiculars AD, BE, CF on the sides of the triangle ABC meet in 0; AG is a diameter of the circumscribed circle of the triangle ABC. Prove that BGCO is a parallelogram. 7. The opposite angles of any quadrilateral inscribed in a circle are supplementary. Two circles intersect in the points A and B; from any point on the circumference of the one, two straight lines CAD and CBE are drawn to the circumference of the other; O is the centre of the circle CAB; the straight line COF meets the line DE in F. Shew that the angle DFC is a right angle. 8. Inscribe a regular octagon in a circle whose radius is 2 inches. Explain your construction and prove that the octagon is regular. WEDNESDAY, 14TH NOVEMBER. N B..-The two sections are to be answered in separate books. SECTION I. 1. Write a summary of the important events of the reign of Henry II and give a detailed account of the Constitutions of Clarendon. 2. Give the causes that led to the English Revolution of 1688 and describe how it was brought about in England, Scotland and Ireland. 3. Write what you know of: (1) The Catholic Emancipation Bill. (3) The suppression of the Monasteries. (4) The terms "Whig" and "Tory." 4. Write short notes on: John Wyclif; Robert the Bruce; General Wolfe; and Bolingbroke. 5. (a) Give the positions of the following and state what they are noted for : Agincourt; La Hogue; Naseby; Amiens; Yorktown; Amboyna; Buxar; (b) Name the countries through which the following rivers flow, mentioning the important towns on their banks : The Nile; the Rhine; the Indus; the Mississippi; and the Yangtse-kiang. SECTION II. 6. When, between whom and with what results were the battles of Panipat fought ? What is the importance of each of these battles in the history of India? 7. Write a short account of the Bahmani kingdom and its offshoots mention the circumstances under which they were conquered and annexed by the Moguls. 8. Sketch briefly the careers of the following: ; (1) Mountstuart Elphinstone, (2) Mahadaji Scindia, (3) Ahalyabai, (4) Labourdonnais. 9. Write short notes on :-Pitt's India Bill, the Peace of Lahore, the grant of the Diwani of Bengal, the Queen's Proclamation of 1858. 10. (a) What are the uses of the atmosphere ? (b) Account for the land and sea breezes; the spring and neap tides. THURSDAY, 15TH NOVEMBER. [2-30 P.M. TO 5-30 P.M.] LEMENTARY SCIENCE. N.B. Arrange your answer books in two separate sections, marking on each your number, name, and the section to which the answers apply. SECTION I. 1. What reasons can you give for saying that air is a mixture of Oxygen and Nitrogen and not a chemical compound? How can Oxygen be separated and obtained from the air? How is Oxygen usually prepared in the laboratory? 2. Give the names of five most important compounds that may be obtained by the combinations of two or more of the following elements : Hydrogen, Oxygen, Sulphur, Nitrogen, Chlorine. If 6 grains of Carbon and 22 grains of Oxygen are heated to redness in a hermetically closed tube, what substance and what amount of it is produced? 3. State all that happens when sulphur burns. What is oil of vitriol? What are sulphates? Describe the appearance of the sulphates of iron and copper. 4. What do you mean by "ammonium " and " ammonia"? Explain the cause of the blue flames which are frequently seen playing at the top of a charcoal fire. 5. Enunciate the parallelogram of forces. A picture hangs symmetrically by means of a string 4 feet long passing over a nail and attached to two rings fixed to the picture; the nail being foot 6 inches from the horizontal line joining the rings, and the picture weighing 12 lbs., what is the tension of the string? SECTION II. 6. Two weights rest in equilibrium on two opposite inclined planes having a common height and are connected by a chord passing over a pulley at their vertex; prove that the pressures on the planes are proportional to the length of their bases. 7. State what you know about the sun's appearance, distance from the earth, and magnitude. Show by a diagram how to account for the phases of the moon. 8. Explain the following terms :— Ecliptic, right ascension, universal gravitation, aphelion, perigee, equation of time. Draw neat sketches to illustrate clearly the following three phenomena, taking care to name all the essential parts of your drawings : (a) Total eclipse of the sun. (b) Annular eclipse of the sun. 9 Why does noon at Bombay occur about an hour later than at Calcuts? What relation roughly does the Indian Standard Time bear to Bombay and Calcutta times? How would you determine the latitude of Bombay? 10. Mention some reasons why we believe that our earth is rotating of .68 axis. Draw the figure given in your text-book to illustrate the fact that the two motions of the earth are not in the same plane. What fact in nature rendis from this non-coincidence? JEHANGIR E. DAVAR, Officier d'Académie, Univ. Gallic,' LOUIS PELTIER, B.A., B.Sc., Officer d'Académie, Univ. Shams-ul-Ulma JIVANJI JAMSHEDJI MODI, B.A. JAMSHEDJI MERVANJI ANTIA, M.A. ... ... ... KAVASJI JAMSHEDJI SANJANA, M.A. C. B. N. CAMA, M.A., LL.B., I.C.S. ... ... In French. In Avesta and Pahlavi. In Persian. In Mathematics. B. K. THAKORE, B.A. PESTONJI A. WADIA, M.A. The Rev. CHARLES FLINK, S.J. 1. Paraphrase :— MONDAY, 5TH November. [10-30 A.M. TO 1-30 P.M.] ENGLISH (Text-books.) SECTION I. SCOTT: Lay of Last Minstrel. The harp's wild notes, though hush'd the song, Now seems it far, and now a'near, Now meets and now eludes the ear; |