N.B.-The answers to Sections A and B should be arranged and given up to the Examiners in two separate books, SECTION A. 1. Compare the number of degrees in any angle with the circular measure of the same angle. If the number of degrees in any angle be ten times the circular measure of another angle, compare the angles. 2. Prove that sin A+ cos2 A and (cosec A sin 4) (sec A - cos 4) (tan A+ cot 4) 1. 3. If A be a positive angle less than a right angle, prove that sin (90° + 4) = cos A. Shew that cos (6400° + 4) = sin (4330° + 4). 4. Find an expression for all the angles which have a given sine. Shew that all the angles whose sine and cosine are respectively equal to 9 11 3 cos 4, cos (A + B) cos (A − B) = cos Asin B, and sec 4+ sec (120° + 4) + sec (240° + 4) = 3 sec 3 4. SECTION B. 6. Having given L tan 11° 16' = 9.2993216, diff. for 1' 0006598, 7 find L cot 11° 16′ 10′′. 7. Shew that in any triangle the sides are proportional to the sines of 13 the opposite angles. One of the angles at the base of a triangle ABC is three times the other; prove that the perpendicular drawn from the vertex A to the base BC divides the base into segments which are in the ratio of c to o 26. S. Find the cosine of an angle of a triangle in terms of its sides. 9. Solve a triangle, baving given the three sides. The sides of a triangle are 14, 16, 18; find the least angle, having given log 2 3010300, L tan 24° 5' 40" 96505069, and L tan 24° 5' 50" 9.6505634. 5 10 10. A straight line AB subtends an angle of 30° at a point P; a man walk- 11 ing one mile from P to a point Q in PA observes the angle AQB to be 60°, and again walking ths of a mile from Q to a point R in Q observes the angle ARB to be 150°. Find the distance between A and B. TUESDAY, 5TH NOVEMBER; [10 A.M. TO 1 P.M.] INORGANIC CHEMISTRY. N.B.-The two Sections should be kept separate. Definite chemical changes should be represented by equations. SECTION I. 1. A mixture of one volume of nitrogen and three volumes of hydrogen 14 has the same composition as two volumes of ammonia gas. Why is the former considered to be a mechanical mixture and the latter a chemical compound? Explain fully what you mean by the statement that the formula H2O represents two volumes. 2. How many grammes of ammonium nitrate are required to form 12 2,000 c.c. of NŐ, and what volume of nitrogen can be got from 10 grammes of ammonium nitrite ? (N: 0 = 14:16.) 3. Give an account of the preparation and chief properties of common phosphoric acid and of the acids formed from it by the action of heat. Mention tests by which they are distinguished from each other. 4. Give some account of the methods of obtaining nitre from nitrogenous matters and from Chili saltpetre. 12 12 SECTION II. · 5. Why is commercial oil of vitriol not pure sulphuric acid? Explain 13 how it acts differently on bone-ash according to the quantity of acid which is added. What are the products of this reaction and for what purposes are they used? 6. By what general method may those acids be prepared which are 12 volatile but not very easily decomposed by heat? Mention two of these acids, and sketch an apparatus which may be used for preparing them. 7. Name the principal forms in which calcium carbonate occurs in nature, 13 and point out the sources from which lime is manufactured. Describe the process of manufacturing lime. How may the carbonate be produced from lime water and from calcium chloride, and what evidence is there for the existence of a bicarbonate of calcium ? 8. Mention three metals which are extracted from their ores by means 12 of carbon. To what previous treatment (if any) are their natural ores submitted and what changes do both the ores and the carbon undergo during the extraction ? WEDNESDAY, 6TH NOVEMBER. [2 P.M. TO 5 P.M.] PHYSICS. SECTION I. 1. Explain "Conservation of Energy" and prove that perpetual motion 10 is not possible. Is the earth's motion around the sun perpetual motion? 2. State the principle of Archimedes and show how it may be applied to 10 find the specific gravity of solids and liquids. 43 A piece of glass weighs 60 grams in vacuo, 42 grams in water, and grams in alcohol. Find the specific gravity of glass and alcohol. 3. Describe shortly the different kinds of vertical water wheels and 15 explain under what circumstances the different kinds are most advantageously applied. Through a canal flow every minute 30 cubic meters of water driving an overshot-water-wheel of 4 m. diameter. Find the H. P. produced, supposing that 20 per cent. of the energy are lost. 1 H. P. =75 kilogrammeters per second. 4. Describe a common air-pump and explain its action. 8 5. What is a magnet? How many kinds of magnets do you know? 12 Define "pole" and "axis" of a magnet. What is the effect of breaking a magnet to pieces? Why is a magnet of only one pole impossible? How do you distinguish between a magnet and a magnetic substance? SECTION II. 6. Explain the following experiment :-two rods, the one of iron and the 12 other of bismuth, are covered by a thin layer of wax. They are both heated at one end by the same flame. At the beginning the wax melts quicker on the rod of bismuth, whilst later on a larger part of the wax is molten on the iron. Explain fully. 7. Explain the influence of change of temperature on clocks, and show the effect of it is avoided in Graham's mercurial pendulum. 8 8. Define "hygrometry," and describe Daniell's hygrometer. What 15 improvements were made on the instrument by Regnault ? 9. Enumerate the different sources of heat and show how the heat due 10 to impact of bodies may be calculated. A lead bullet of 1 kilogram weight strikes a found to have increased after impact by 400°C. Specific heat of lead= '03. Use the C. G. S. Neglect the fraction in your answer. target, and its temperature is MONDAY, 4TH NOVEMBER. [2 P.M. TO 5 P.M.] 1. Describe the structure of a newly formed vegetable cell, and mention 15 the functions performed by its several parts. What alterations does the newly formed cell undergo, when it forms part of a permanent tissue? 2. Give a short account of Carbon Assimilation taking place in plants. 15 What conditions are favourable to this process? 3. Describe the general arrangement of epidermal tissue in temperate and 10 warm climates, and in land and water plants both floating and submersed, 4. Describe the general and microscopic structure of a foliage leaf, 10 and mention the functions performed by its various parts. 5. What is the arrangement of the parts of a flower? Give a brief 15 resume of the interaction of the two innermost whorls? Distinguish between conjugation and fertilisation, and self and cross fertilisation. 6. What is the nature of the food of plants? What are its sources ? 15 How are food materials absorbed and circulated in the plant ? 7. Describe the general structure of a seed of a phanerogam, and the 15 phenomena of its germination. What circumstances favour and retard the germination process? 8. Describe the plants placed before you. 10 WEDNESDAY, 6TH NOVEMBER. [10 A.M. TO 1 P.M.] AGRICULTURE. 1. To what crops is salt petre generally applied in India? Saltpetre 7 being a valuable manure, why is it not generally used by the cultivators ? 2. What is a Harrow? What purposes does it serve? Compare the 15 English harrow with the native implement, giving sketches in illustration. 3. Give the analyses of Castorcake and Bonemeal. 20 4. What is humus? What do you know of its origin and of its proper 15 ties ? 5. What does the term capillarity as applied to soils mean? Why is 15 a soil of good capillary power usually more valuable than a soil poor in this respect? 6. Calculate the cost per day of irrigating an acre of land by a mot. 20 N.B.-The two Sections should be kept separate. Definite chemical changes should be represented by equations. SECTION I. 1. Describe fully the process of manufacturing coal gas, giving a sketch of the plant, mentioning all the products resulting from the destructive distillation and the methods adopted for removing those that are not required for illuminating purposes. 2. What do you understand by diatomic monobasic, tetratomic dibasic and tetratomic tribasic acids? Mention one acid belonging to each class, describing its preparation and properties. 14 12 |