2. What diseases are more especially considered to have a relation to 100 soil? Give shortly reasons in each case for your answer. Describe a safe method of earth burial of those dead of dangerous infective diseases, and an alternative method of disposal of such bodies SECOND HALF. Examiner J. N. MITRA, Esq., M.B., M.R.C.P., L.S.A, 3. What qualitative tests would you employ to detect the following 100 impurities in water : 4. You are asked to advise as to the sanitary arrangements in a pro. 100 posed new house in a town where water-carriage of sewage is compulsory. Give your views on the following points : (a) Position of waterclosets. (b) Connection of soil-pipes, rain-water pipes, bath and sink-wastes with the house drains. (c) Connection of house drains with the street-sewer. (d) Size of house drains and soil-pipes. 200 marks are reserved for the Oral Examination. First Examination in Engineering. 1905. MATHEMATICS. FIRST PAPER. COMPUTATIONS AND MENSURATION. Examiner-G. W. KÜCHLER, ESQ., M.A. The figures in the margin indicate full marks. 30 88 1. Find to an inch the diameter of a square whose side is 57 yards. 2. Find to the nearest pie the value of 27mds. 31srs. 9chks. at 30 Rs. 125 4a. 9p. a maund. 3. 850 gallons of water are poured into a tank 7 ft. 6 in. long by 5 ft. 3 in. broad; what is the depth of water in inches to two places of decimals? A pint of water weighs a pound and a quarter, and a cubic foot of water weighs 997 oz. 40 4. Define the terms logarithm, characteristic, mantissa; shew that 30 the logarithm of a product is equal to the sum of the logarithms of its factors. 5. Explain the method of proportional parts in finding logarithms 15 and antilogarithms; the time of oscillation of a pendulum in seconds is given by T=2T find approximately the time (with the help of logarithms) when 1=627, 25 and g=987. (a) the area of a triangle when a≈ 17·9 cm, b=13·4 cm, c=11'6 cm. 25 7. The angle of elevation of the summit of a mountain due N. is 50 15°33′, and on walking 6,000 yds. due West, it is found to be 12°57'. Find the height of the mountain. 8. State Simpson's rule for finding the area of an irregular figure. The ordinates of an irregular piece of land are 37, 4:25, 5·15, 7-8, 8.55, 6, 4.15 yards respectively; find the area in square yards. 9. (a) Shew that the area of segment of a circle 10 25 where c is the length of the bounding chord, and h the height. (b) The circumference of a circle is 129 inches, find its area. 10. The external diameter of a hollow steel shaft is 20 inches and its internal diameter is 11 inches; calculate the weight of the shaft if the length is 35 feet, the specific gravity of steel being taken as 7.8. 20 45 2. Prove the binomial theorem for a negative index. 3. Prove the expansion If find a in terms of y. 4. Prove De Moivre's theorem and find by means of it the cube roots of unity. 40 5. Find the sum of the sines of a series of angles in Arithmetical pro- 25 gression. 7. Find the angle contained by the pair of straight lines ax2+2hxy+2y2=0. 25 Find condition that key+ax+by+c=0 should represent a pair of 20 straight lines. 8. Define the terms pole and polar. Find the equation of the polar of the point (*1, y1) with respect to the circle x+y=a2, and shew that if the polar of a point A passes through B, the polar of B passes through A. 5 25 15 9. Find the locus of the middle points of parallel chords of the ellipse. 30 In the ellipse 2x2 + 5y2=7, find the diameter conjugate to y=20. 10 10. Shew that the equation to an hyperbolic referred to its asymptotes 30 takes the form zy= and find the coordinates of its foci. 15 MATHEMATICS. THIRD PAPER.? STATICS AND DYNAMICS. Examiner G. W. KÜCHLER, ESQ., M.A. The figures in the margin indicate full marks. 1. Explain clearly what is meant by saying that a particle moving in a straight line has an acceleration of a ft. per sec. per sec. 10 A heavy particle is thrown vertically upwards from a point h ft. above 30 the ground with a velocity of u ft. per second; find when it will reach the ground. 2. Enunciate and prove the parallelogram of velocities. 20 A man bicycles due west with a velocity of 10 miles an hour; if the 20 wind is north and has a velocity of 22 ft. per sec. find the velocity of wind relatively to the man in direction and amount. 3. Shew that the path of a projectile in vacuo is a parabola. 25 If its initial velocity is u and its angle of projection a, find the distance 15 from the point of projection after a time t. 15 4. Enunciate Newton's laws of motion. A train of 100 tons is moving up an inclined plane of 1 in 50 with a 25 uniform velocity of 30 miles an hour; if the friction is Too of the weight of the train find (1) the force exerted by the engine; (2) the retarding force of the breaks if they can bring the train to rest in 220 yards without turning off steam. 5. Find the resultant of two given parallel forces acting on a rigid body. 25 A uniform rod 3 ft. long and 5 lbs. in weight lies on a horizontal plane; 10 find the least force applied at a distance of 7 inches from one end which will raise that end from the plane. 6. Find the centre of mass of— (a) a uniform triangular lamina; 7. Shew that ary system of coplanar forces can be reduced to a single 25 force or a couple.. One end of A a beam AB, weight W, rests against a smooth vertical 20 wall, and a cord attached to the other end B passes over a smooth pulley C, vertically above A and sustains a weight P. Find the pressure on wall. 8. What are the conditions which a correct balance should comply 35 with? Shew how they are attained. 9. What other principle besides that of the conservation of momentum 25 has to be assumed in order to solve the problem of the impact of two elastic spheres? Write down the equations for direct impact. What are the conditions that the spheres should interchange velocities 20 in the latter case? 10. Define work and energy; find the energy lost in the case of direct 40 impact of two elastic spheres. Is it ever=0?.. (a) a cos x (b) e (c) log sin (a2+x2). 5 30 2. Assuming that ƒ (x + h) = f (∞) + Ah + Bh2 + ...find the value of the 20 coefficient of h n. Find the first three terms in the expansion of seca in ascending integral 20 powers of a. 3. Find the limiting values of— 4.5 4. Shew that, if f(x) has a maximum or minimum value when a=a, 15 (a)=0. Find the maximum cone of given slant height. 25 5. Find the equations of the tangent and normal to the curve 20 y= f(x). If the coordinates of a point on a parabola be given by (am2, 2am), shew 20 that the equations of the tangent and normal are given by 8. Find the area, (a) of the ellipse, (b) of the loops of the curve:40 y2( a − x ) ➡ x2(a+x). 9. Find formulae for the coordinates (≈, ÿ) of the centre of mass of a 15 plane lamina bounded by a given curve and the axis of . Find the position of the centre of mass of a right cone, whose density 25 varies as the distance from the base. |