A dodecagon, six of whose sides are equal to a, and six equal to b, is inscribed in a circle; prove that the radius of the circle

is √ a2 + b2 + √3ab; and that the area of the dodecagon is

8. Find exponential values for sin x and cos x. Given tan (+0) cos 2a = tan p, prove that

5

N. B. The figures in the margin indicate full marks.

1. Find the length of the perpendicular drawn from the point aß to the straight line Ax + By + C = 0.

2

2.

Find the polar equation to the straight line passing through the two points (r, 0,) ( 0).

3

Thence deduce the condition that three points may lie in a straight line, and interpret the result geometrically.

3. Obtain an expression for the area of a triangle in terms of the co-ordinates of its angular points.

5

Find the area of the triangle included by the straight lines

4. Explain what is meant by the terms pole and polar.

Find the co-ordinates of the pole of the line Ax + By + C = 0 with respect to the circle ( a)2 + (y — B) 2

2 = y2.

5. What is meant by the radical axis of two circles? Prove that the radical axes of three circles intersect in a point.

5

Find the co-ordinates of this point for the three circles whose equations are

(x − a)2 + (y

(x − a)2 + (y

6. Define a parabola, thence obtain its equation in the simplest form, and trace its figure from the equation.

7. Obtain the equations to the tangent and normal at any point of a parabola in the form

Common tangents are drawn to the circle x2+ y2 the parabola y2 4 ax. Find their equations.

= , and

8. Obtain the polar equation to an ellipse, a focus being the pole and an axis the initial line. Also find the equation to the tangent at any point.

Prove that tangents drawn from an external point subtend equal angles at either focus.

4

6

5

9. What is meant by conjugate diameters of an ellipse? 7 Find the co-ordinates of the extremities of one conjugate diameter in terms of the co-ordinates of the extremities of the other diameter.

ab

Shew that the area of the parallelogram formed by normals at (a2 b? ) the extremities of conjugate diameters of an ellipse is sin3 2, where is the eccentric angle of one of the extremities. 10. All chords of a conic section which subtend a right angle at a given point of the curve pass through the same point in the normal at the given point.

11. If the normals at two points of a parabola intersect on the curve shew that the line joining the two points intersects the axis at a fixed point.

6

B. I. Examination.

1881.

JURISPRUDENCE.

Examiner-MR. B. L. GUPTA, C. S.

1. What are the ultimate sanctions of all laws? From what authority do those sanctions emanate? Whence and how do laws based upon custom and judicial decisions derive their binding force? 2. Give the judicial sense of the terms “intention,” “negligence," "malice."

3. (a) "It is a general rule that courts of law will not move unless some duty or obligation is broken." What exceptions, if any, are there to this rule ? (b) Obligations may be neither ex contractu nor ex delicto. Illustrate by examples.

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4 A Hindu on his deathbed gives directions for the distribution of his personal property after his death. Are such directions valid ? What rules must be observed to make the execution of an unprivileged will valid ?

5. On what grounds may a will, though duly executed, be declared void by a court of law?

6. Explain (a) Residuary legatee (b) Onerous bequests (c) Election (d) Specific legacy (e) Ademption.

7. What are the prerogatives and legal attributes which attach to the Crown of England ?

8. What, according to Blackstone, was the origin (a) of the right of property; (b) of the right of inheritance; (c) of the right of dispos ing of one's property or a part of it, by testament?

9. When, how, and by what authority were the Supreme Court and the Sudder Dewany Adalat respectively constituted? State briefly their respective functions, and their relative position, as resulting from the legislation of 1781.

10. What control, if any, has the Governor-General, as such, over the different legislative bodies in the country?

LAND TENURES, &c.

Examiner-MR. B. L. GUPTA, C. S.

1. What provision is there in Reg. VIII of 1793 against the levy of abwabs and mathants? Is there any similar provision in Act VIII (B. C) of 1869? If so, state it.

2. How are the rights of intermediate tenure-holders, of mortgagees, and of other persons having an interest in a putnee taloog, affected

by its transfer, (a) by private sale, (b) by public sale in execution of a decree, (c) by public sale, at the instance of the zemindar, for arrears of jumma?

3. State the nature and extent of the interest which the owner or the occupier of land acquires over accretions formed by alluvion. What liabilities, if any, attach to such interest ?

4. Does a ryot cultivating his land under a lease for a fixed period acquire a right of occupancy? If so, may this operation of the law be defeated by any express stipulations to the contrary?

5. May one of several joint-mortgagors redeem (a) a portion of the property by paying his share of the debt, (b) the whole property by repaying the whole of the debt? In either case, should your answer be in the affirmative, what would be the respective rights and liabilities of the parties interested as against one another?

6. A obtains a decree for redemption of property pledged to B, but neglects to execute it until the decree is barred by limitation. Has A any remedy left?

7. Under what circumstances, if any, could a civil court annul a sale under Act XI of 1859 ?

8. What advantage, if any, is there in having a document registered, the registration of which is optional?

9. Under what circumstances may a registering officer lawfully refuse to register a document, and what remedy is open to the aggrieved party after such refusal ?

10. Explain" servient tenement," "dominant tenement," "enjoyment as of right," "affirmative easements," and "negative easements," and state fully in respect of what subjects, and how, rights to easements may be acquired, and how, after their acquisition, such rights may be lost?

11. When, if at all, may a foreign rule of limitation be pleaded to a suit in British India; and how far, if at all, are suits in British India, on contracts entered into in a foreign country, subject to the law of limitation obtaining in such country?

HINDU AND MAHOMEDAN LAW.

Examiner-MR. C. PIFFARD.

1. What are the principal points of difference between the Dayabhaga and the Mitákshara schools of law?

2. What questions were at issue in the Shiva Gunga case and how were they decided by the Privy Council?

3. A dies leaving a widow, a daughter, a daughter's son, a sister, a sister's son, and a brother's grandson. In what order will they

inherit to his estate? Supposing A's daughter's son to die leaving a son, after A's death, but before the death of A's widow, when will such son take the inheritance?

4. In a family governed by the Mitákshara law can a stepmother succeed to the estate or share in the estate once inherited by her stepson? Does the same rule prevail in families governed by the Dayabhaga?

5. A dies leaving a son B, a daughter C, a widow D, and a brother's grandson E. B dies unmarried and is succeeded by his mother D, who afterwards remarries and dies leaving a son F; C died in the lifetime of D. having previously in pursuance of authority given to her by her, duly adopted G. Upon D's death, E, F, and G claim the estate which had descended from A to B. Which of them is entitled to it ?

6. What are the principal provisions of the Hindu Wills Act? To what extent, if any, does a subsequent marriage affect the validity of a will by a Hindu, Mahomedan and Christian respectively? A, being sonless, makes a will, leaving all his immoveable property to his brother; a son is afterwards born to him; does the birth of such son affect the validity of A's will?

7. A dies leaving two son B and C, a son's son D, a daughter's son E, and a widow F the mother of B. How will his estate be divided?

8. Who are the only heirs not liable to be excluded by other heirs?

9 What is wukf? What conditions are indispensable for its validity?

10. What is the share of the husband of an only daughter when there are no sons? Of two or more daughters in the like case? Of a son's daughter when there is also an only daughter, and when there are also two or more daughters?

11. Enumerate the legal sharers and residuaries, and state in what respects their rights differ. Enumerate also the four classes of distant kindred and the persons included in each class?

12. What is shoofad or preemption? How, and by whom, and under what circumstances, can this right or privilege be claimed or exercised? What formality, if any, must be observed by the person claiming it. By what legal devices may a claim of preemption be evaded ?

CONTRACTS AND TORTS.

Examiner-MR. C. PIFFARD.

1. What is specific relief and how can it be enforced?

2. In what case is a court bound to refuse specific performance of a contract?