مثنوی اگر دنیا نباشد درد مندیم وگر باشد به مهرش پای بندیم بلائی زین جهان آشوب ترنیت که رنج خاطرست از هست و رنیست قطعه مطلب گر توانگری خواهی جز قناعت که دولتی ست هنی گر غنی زر بدامن افشاند تا نظر در ثواب او نکنی کز بزرگان شنیده ام بسیار صبر درویش به بیت که بذل غنی اگر بریان کند بهرام گوری نه چون پای ملخ باشد زموری WEDNESDAY, 15TH APRIL. [10 A.M. TO 1 P.M.] ARITHMETIC AND ALGEBRA. T. COOKE, M.A., M.I., LL.D.; DINANATH ATMARAM [The black figures to the right indicate full marks.] 1. Express as the fraction of £10 the difference between 3 5 3 2 8 and 8 X; and find the value of of a ton of sugar when 1 + 2 (1 + 2}) 15 155 7 3. A manufactory turns out 50 tons of iron goods weekly, 10 using up for that purpose 51 tons of iron at £6. 158. per ton, 100 tons of coal at 118. 6d. per ton, and £45 worth of other materials; rent, rates and taxes amount to £219 annually; wages and incidental expenses to £75 per week. At what price per cwt. must the iron be sold in order that the works may gain 8 per cent. per annum on a capital of £35,000 ? 4. A trapezoid, the parallel sides of which are as 3: 4, is to be out from a rectangular board 12 feet long, and 2 feet wide; find the lengths of the parallel sides, that the trapezoid may be one-third of the board. 9 5. Find the square root and cube root of the number whose reciprocal is 003977. 8 6. Given log 230103 and log 32 = 1·50515; find log 9 3/625, log 0000025 and the value of the expression 128 x 25+ 80 001 × 500 × 2 7. Solve the equations 11 S 2x = 3Y 8. Find the value of each of the following expressions : 10. Solve the equations (a.) (3x-1)2 + (4x-2)2 = (5x-3)2 3)2 11. A man has a number of Rupees which he tries to arrange in the form of a square. On the first attempt he has 130 over. He then increases the side of the square by 3 Rupees and he has only 31 over. How many Rupees had he? 8 12. Two pieces of cloth are bought for Rs. 44-8-0. One 10 is three yards longer than the other, and each cost as many half Rupees the yard as it is yards in length. What are their lengths ? WEDNESDAY, 15TH APRIL. [2 P.M. TO 5 P.M.] EUCLID AND TRIGONOMETRY. T. COOKE, M. A., M.I., LL.D. [The black figures to the right indicate full marks.] 1. Distinguish clearly between a geometrical point and line and a physical point and line, and define ratio and similar rectilineal figures. 2. If from the ends of a side of a triangle there be drawn two straight lines to a point within the triangle; these shall be less than the other two sides of the triangle, but shall contain a greater angle. If two points be taken in the base of a triangle at equal distances from, and on opposite sides of, the middle point of the base, show that the two lines joining these points with the vertex of the triangle, shall always be less than the sides of the triangle but greater than twice the line joining the middle of the base with the vertex. 3. The angles in the same segment of a circle are equal to one another. 5 6 6 7 Let two circles cut each other in the points A and B. From A draw the two lines ACD and AEF on the same side of AB and cutting both circles, make the two triangles CEB and DBF and show that the triangles are equiangular. 8 4. To describe an isosceles triangle having each of the 8 angles at the base double of the third angle. Give the analysis of the above Problem. 6 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 7 Show that the triangles CEB and DBF in the deduction to Question No. 3, are to one another in the duplicate ratio of the radii of the circles in which they are inscribed. 7 6. Define the term cosine and give a general expression for all angles which have the same cosine. 4 7. Find the sine of (A+B) and show that 4 2 (Cos A+Cos B)2= Sin2(A+B)+4 Cos A Cos B Cos2 A+B 5 2 5 8. At the top of a pillar 100 feet high, the elevation of the summit of a tower is observed to be 30° and at the foot of the pillar it is 60°, find the height of the tower. 9. Find the cosine of 18°. Let ABCDE be a regular pentagon, join BE and from A draw AG perpendicular to CD cutting BE in F, bisect FG in H and let O be the centre of the pentagon, then show by trigonometry only that OH is one-fourth of any radius of the pentagon. 10. Find an expression for the area of a regular pentagon in terms of one of its sides. THURSDAY, 16TH APRIL. [10 A.M. TO 1 P.M.] LOGIC. THE REV. D. MACPHERSON, M.A.; JAMES M. CAMPBELL, C.S. [The black figures to the right indicate full marks.] 6 1. Define Logic. What do you consider the province of Logic as a Science, and as an Art ? 2. "He who has been bitten by a serpent fears a rope." How far is the conclusion here drawn logical? Can 6 you expand the proverb into a syllogism? 3. Explain the terms analysis and synthesis, illustrating 8 their use by shewing, shortly, the difference between teaching Logic analytically and teaching it synthetically. 4. What is a syllogism, an enthymeme, and a sorites. Give an example of each of these forms of argument, using either words or letters of the Alphabet. 5 Define and divide Fallacies, explaining what is meant by a petitio principii, an ignoratio elenchi, and an argumentum ad hominem. 9 9 |