ALGEBRA AND TRIGONOMETRY. Examiner-MR. A. M. Nash, M. A. 1. Solve the equations (1.) 4V 22 + x + 4 = 572 — 4x — 17. (2.) x + y 5xy, x® +ya 3528 ye. 2. What is the radix of the scale in which 524 is a square number? Transform the number 192.17571428 from the scale whose radix is ten to the scale whose radix is seven. 3. Prove that n(n-1) n”—n(n-1)" + n(n-1)(n-2) (n-3) + ... : = in. 3 10 72 3 + + 1 3 3 3 is 4 4 12 + 1 3" 1 5. Sum to n terms the series 5 11 + +.. 1.3.5 2.4.6 3.5.7 6. If n be any odd number greater than 3 and prime to 3, na + n'— no n is divisible by 2520. 7. If B, y be the two values of which satisfy the equation A cos (e to a) + B sin (e to a) = C, prove that tan 8 B ty B A tan a tan 7 A? + B^ - Co A + B tan a с 8. ABC is a triangle, AA', BB', CC are drawn perpendicular to the opposite sides : prove that the area of the triangle ABC: the area of the triangle A'B'C': :1:2 cos A cos B cos C. 9. The sum of the squares of the perpendiculars let fall from a point P upon the sides of a regular polygon of n sides is nra cosa + nd”, where r is the radius of the circumscribing circle and d the distance of P from the centre. 10. Show that -lcosna cos no t n cos (n − 2)e + nin-1) cos(n—4)0+ ... n What is the last term of this series? cos (a + B) – cos (a + 28) + 11. Sum to infinity the series + 1 cos (a + 3B) ANALYTICAL CONIC SECTIONS. Examiner-W. GRIFFITHS, M. A. 1. Find the polar equation to a straight line. Prove that the polar equation to the straight line passing through the points r,, and 7,20, is riper sin (0, – 0..) to ror sin (Or — 0) + ro, sin (0 - 0)=0. 2. Obtain the most general equation to the circle referred to rectangular axes. Find the condition that the line a cos a to y sin a h may be a tangent to the circle. Interpret the result geometrically. 3. State what relations are indicated in the case of conic sections by the terms pole and polar. Assuming the equation to the tangent at any point of a parabola, obtain the equation to the polar at the point h, k, and explain clearly every step in your argument. The locus of the poles of tangent lines, drawn to the circle 22 described on the major axis of the ellipse =l, with respect + ya + = + 1 to the ellipse is the curve 74 a2 4. Obtain the equation to the normal at any point of an ellipse whose equation is 3:2 =1 in terms of the eccentric angle of the point. Prove that four normals can be drawn through any point hk. 5. What are conjugate diameters ? Obtain in any manner the equation to an ellipse referred to two conjugate diameters as axes. Prove that the locus of intersection of straight lines drawn through the foci parallel to pairs of conjugate diameters is the 22 ellipse 62 6. Define the term asymptote. Prove that the triangle which any tangent of a hyperbola forms with the asymptotes is of constant area. CP is any semi-diameter of a hyperbola, of which C is the centre. A straight line QHK parallel to CP cuts the curve in Q and the asymptotes in H and K. Prove that QH. QK = CP3. 7. Prove that the condition that the equation a.x2 + 2hay t by2 + 2fy + 25x +c=0 may represent two straight lines is abc + 2fyh -- af? — bg® ch= 0. + a? =1. 8. If the equation of the second degree given in the preceding question represents straight lines, show that the angle between 2_ha ab the lines will be given by tan 0 = a + b Prove that the locus of points at which the tangents drawn to the parabola ya 4ax, include an angle a is y’ — 4 ax - tan 'a (ct — a). 9. Prove that the co-ordinates of the point of intersection of tangents at the points (a cos 0, a sin 0) (a cos o, a sin o) of the 0 + $ 2 circle w t ya = 42 are a =. a cos a sin to 2 and y = 0 A quadrilateral is drawn circumscribing a circle. Prove that the line joining the middle points of the diagonals passes through the centre. B. L. Examination, 1879. JURISPRUDENCE. Examiner-MR. P. O'KINEALY. 1. To what extent is the Common and Statute Law of England applicable to India ? 2. Contrast the powers of the former Supreme Court and the present High Court of Calcutta with regard to their jurisdiction as Courts of first instance. 3. Distinguish between the estate of a Hindu widow and an ordinary life-estate in the English Law. 4. Illustrate the maxim " Delegatus non potest delegare." In connection with this maxim, state what is Mr. Markby's opinion as to the powers of subordinate legislative bodies. Do you think his views are correct ? 5. Dr. Cowell says “ Joint tenants under the English law are in a very different position from members of a joint Hindu family under the Mitakshara law.” Explain this. 6. Could an adopted son be given in adoption ? Give your reasons. 7. What are the essentials of a valid custom ? 8. • Throughout Bengal a man who is the absolute owner of property may now dispose of it by will, as he pleases, whether it be ancestral or not." A Hindu governed by the Bengal school dies leaving surviving him three unmarried sons, A, B, and C. By his will he left his property to A for life, remainder to his first and other sons in tail, remainder to B for life, remainder to B's first and other sons in tail, remainder to C for life, remainder to C's first and other sons in tail, remainder to the right heirs of A. Would these limitations be valid ? Give your reasons. 9. An undivided Hindu family governed by the Mitakshara law consisted on the 1st of January 1854 of a father and one adult son. The father, on the 1st of January 1855, alienated a portion of the ancestral estate. A second son was born on 1st January 1857. The father died on 1st January 1864. On the 1st January 1870, the two sons brought a suit for possession of the family property on the ground that the father had alienated without their consent or without legal necessity. Suppose you were engaged for the defend. ant in the suit, what defence would you put forward ? Give your 10. Define a law. Enumerate the different “sources of law." Is it correct to say there are different sources of law ? reasons. LAW OF MORTGAGE, &c. Examiner-MR. P. O'KINEALY. 1. A has a tank on his premises in Calcutta of which he is the sole owner. B disputes this, alleges he has a right to fish there, and on several occasions, the last of which was on the 1st of January 1877, caught and took away fish from the tank. Supposing A wishes to bring a suit against B, basing his cause of action on what B did on the 1st of January 1877, within what time must he file his plaint 80 as not to be barred by limitation ? 2. “Limitation is negative prescription.” “Limitation is part of the Lex foci.” Is there any, and if any, what discrepancy between the two propositions ? Act XV, 1877, December.—"At the determination of the period hereby limited to any person for instituting a suit for possession of any property his right to such property shall be extinguished.” It is concluded from this that twelve years' possession adverse the rightful owner or owners enables a person who has entered wrongfully into possession to pass a good title to the land. What assumption, if any, is necessary to support this conclusion ? 3. What is the effect of non-user in regard to easements ? A has a right of way over certain lands belonging to B. He stops using it for thirty years, and then recommences the use of the way. Shortly after A recommences to use the way, B begins to build a house on the path. Has A any remedy against B ? Suppose B had built the house before A began to recommence the use of the way, would A have any remedy? Give your reasons. 4. A has a house built, the west wall of which abuts on the land of B. In this wall there are two windows, which have been in exist. ence more than 20 years. B, without A's permission, builds on his own land a wall up against A's house, which completely covers up A's west wall. What, if any, is A's remedy against B? Would it make any difference if just before B had built his wall A had opened out six new windows in his west wall ? Give your reasons. 5. Who is entitled to have a will registered ? When may the registering officer refuse to register a will presented by any person other than the testator ? 6. Sec. 32 of the Registration Act says, that a document may be presented by agent " duly authorized by power of attorney executed and authenticated in manner hereinafter mentioned.” What powers of attorney are recognizable for the purposes of this section ? How is such a power proved ? 7. Under the Rent Law can a landlord sue to enhance the rent of a ryot who has no right of occupancy ? Give your reasons. 8. State the position of a second mortgagee as regards both the mortgagor and the first mortgagee. Suppose the mortgagor pays off the first mortgagee, what is the effect as regards the second mortgagee Would the result be different if the first mortgagee had purchased the interest of the mortgagor? Give your reasons. 9. Explain and illustrate what is meant by the Doctrine of Lis pendens. 10. State and explain the provisions of the Limitation Act relating to trusts. |