APPENDIX A. Senior Mathematics. Arithmetic and Algebra. 1846. 1. A person bought 125·125 yards of cloth at the rate of 7 yards for a gold mohur ; and afterwards sold 92-05 yards at the rate of 5 yards for a gold mohur, and the remainder at the rate of 9 yards for a gold mohur. Did he gain or lose? and how much? 12 2. What is the present value of Co.'s Rs. 1155-12 due 3 years hence, at 41 per cent. per annum, and at what rate will the same sum amount to Co.'s Rs. 1926-4, at compound interest in 4 years. ..... 18 3. Exhibit the square root of 29 in the form of a continued fraction:-and show that 4. Find the number of combinations of n things taken 3 and 3 together (without reference to the general formula). A B and C are all p years of age; and it appears that out of m persons of that age n of them arrive at the age of p + 3; what is the probability that 2 of them at least will be alive at the end of 3 years. 5. Investigate the relation between the co-efficients and the roots of the general equation and in the quadratic equation 20 25 Geometry. 6. Any two sides of a triangle are together greater than the third side. 7. In a circle, the angle in a semicircle is a right angle, but 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. 8. In equal circles, angles, whether at the centres or circumferences, have the same ratio which the circumferences on which they stand have to one another: so also have the sectors. Of what use is this proposition in showing that the fraction arc radius centre. is the measure of the angle subtended by the arc at the 9. The side of a regular hexagon inscribed in a circle, is equal to the radius. Show also from having an inscribed regular polygon given, how to inscribe another in a circle, having double the number of sides. 10. To draw a straight line perpendicular to a plane from a given point above it....... ............... Trigonometry, Plane and Spherical. 11. Prove the following: Sin a Cos (3 T = 3 a) 2 and show (not by substitution in any other formula, but independently) that 12. When two sides of a triangle, and the included angle are given, find the remaining side, and adapt the result to logarithmic computation. Explain the use of a subsidiary angle, and what method should be used in determining the above side, when the included angle is very small, and one of the sides nearly equal to the other 35 |