CRIMINAL LAW. Examiner-MR. B. L. GUPTA, C. S. 1. What provisions, if any, are there in the I. P. Code specially affecting persons who own, occupy, or have an interest, in land ? 2. Define “mischief.” May a person commit mischief on his own property? Give reasons and illustrations. 3. Define “ wrongful gain,” “wrongful loss," " dishonesty' and * good faith." 4. Uuder what limitations, if any, are minors criminally respon. sible for their acts, and what application is there of the doctrine of burden of proof to this subject ? 5. To what extent, if at all, and under what limitations, if any, is a wrongful act, if done under compulsion, free from criminality ? 6. What offence or offences, if any, has Z committed in each of the following cases ? Give reasons for yonr answers. (a) Intending to annoy A, Z throws dirt and brickbats into A's house. (b) Z challenges À to a duel and in fair fight and without taking any undue advantage kills A. (c) Z sets his dog at A. The dog springs on A and bites him severely. '(d) Z padlocks the door of a room in the lawful possession of A, not believing in good faith that he has a right to do 80, and thereby prevents A from entering the room. (e) Z finding his toddy (tári) stolen every night by some person or persons unknown, puts poison into it. A drinks it by stealth and dies in consequence. (f) Z, in payment for goods purchased by him, gives a cheque on a bank, where he has no funds, and without intending at the time to put funds there. The cheque is presented and dishonoured. (g) A owes money to several persons who apply to Z, the village chowkidar, for the recovery of their just dues. Z, without intending any gain to himself, seizes some of A's cattle, against his will, and without his consent, sells them, distributes the proceeds among the creditors, and makes over the balance to A. 7. Distinguish between summons and warrant cases, and note the principal points of difference in the procedure prescribed for the trial of the two classes of cases, 8. May a magistrate holding preliminary enquiry into a case triable by the court of sessions examine witnesses for the defence ? Is he bound to do so, if the accused so desires ? 9. Under what circumstances, if ever, may the evidence of wit. nesses examined before the committing magistrate, be referred to by the sessions judge, and his judgment grounded thereon ? 10. What are the respective positions of assessors and jurors ? What course or courses are open to the judge, if he differs (a) from the opinion of the former, (b) from the verdict of the latter ? B. 6. E. aud L. C. E. Gxamination. 1880. ARITHMETIC AND ALGEBRA. Examiner-DR. H. W. M'Cann. 1. What is a “prime number" ? Resolve into prime factors the numbers 129600, 254016, 5775 : and hence determine the L. C. M. and G. C. M. of these numbers. 2. Explain what is meant by a “vulgar fraction” and show from your explanation that of is equal to 15. 11 of of 67 + 71 + 1944 + 8 221 Simplify 3 + + 47 - 1 of 1 680 3. Give and explain the rule for dividing one decimal number by another, and exemplify it by dividing •015265 by 2.5, -25 and by 25 successively. Divide 0163 by 0002, and .0002 by .0163. 4. A bath is supplied with water from two pipes, one of which can fill it in 12 minutes, the other in 15 minutes : there is also a discharging pipe, which would empty it, when filled, in 10 minutes. The first pipe is open alone for 4 minutes, and then the first and second open together for one minute: if now the third pipe be opened as well, how long will it take to fill the bath? 5. A with a capital of Rs. 60,000 began business on the 1st day of January, and wishing to extend his trade, he took in B as a part. ner, with a capital of Rs. 50,000 on the 15th March following: and on the 27th May they admitted C as a third partner, who brought Rs. 70,000 into the concern. On taking stock at the end of the year they find the profits of the firm to be Rs. 24,850 : how must this sum be divided amongst the partners ? 6. If 72 men can make an embankment 324 yards long, 12 yards wide, and 8 feet high. in 9 days, working 12 hours a day: how many men must be employed to make an embankment 1458 yards long, 40 feet wide, and 3 yards high, in 36 days, working 9 hours a day? (Solve this without using the “Rule of Three.") at (62 — 2) + 64 (c— a) + cf (a’ — ) 7. Prove a? (6 — c) + b2 (c-a) + co (a b) = (a + b)(b + c) (c + a) *(1-ya) (1 – 22) + y (1 — 2) (1 — 22) + z (1 — **) (1 — y") — 4 xy: 2 + y + z — xyz = 1- xy - yz — 2:1. 8. Explain the principle of the solution of quadratic equations, and show that, in the equation ax + bx + c = 0, the sum of the roots is , and the product of the roots is Resolve into the product of two linear factors the quadratic expressions 7 32 — 3* — 160, and mnwa + (n2 – mo) * — mn. 9. Solve the equations i i (i.) I a (b - x) * bic— x) ac- ax: (ii.) 2 + y (20 + 1) = 4. ya + x (y + 1) = 2. (iii.) az + cy + bz = cx + by + az = 6 x + ay + cz = a* + b3 + c3 — 3 abc 10. Insert n Harmonic Means between a and b. Prove that if aa, 69, ca be in Arithmetic Progression, then b + c, C + a, a + b, will be in Harmonical Progression. 11. Find the sum of the coefficients of the terms in the expansion of (1 + x) by the Binomial Theorem, where n is any positive integer. Show also that the sum of the coefficients of the odd terms is 2 4n +1 Find the coefficient of x in the expansion of Find the logarithm of 800/50 to the base 275. GEOMETRY AND CONIC SECTIONS. Examiner-Dr. H. W. M'Cann. 1. If a straight line be divided into two equal, and also into two anequal parts, the squares on the two unequal parts are together double of the square on half the line and the square on the line between the points of section. lilustrate this from Algebra. 2. If any chord of a circle be produced until the part produced is equal to the radius, and its extremity be joined with the centre of the circle, and produced to the circumference, of the two aros intercepted between these two lines, the one is 3 times the other. 3. Describe a circle which shall touch the base of a triangle and the two sides produced. Show that if the centre of the circle so described, and the centre of the circle inscribed in the triangle be joined to either extremity of the base, the joining lines are at right angles. 4. Give Euclid's definition of proportion, and illustrate it by proving that triangles of the same altitude are to one another as their bases. 5. A point moves so that its distances from two fixed points are in a constant ratio to one another. Prove that its locus is a circle. 6. When is a straight line at righv angles to a plane,' and when are two planes perpendicular to one another ? If two straight lines are parallel, and one of them is at right angles to a plane, the other is also at right angles to the same plane. 7. Show that, in a parabola, tangents at the ends of a focal chord intersect at right angles in the directrix Show also that, if from the ends of a focal chord perpendiculars be let fall upon the directrix, the intercepted portion of the directrix subtends a right angle at the focus. 8. The rectangles contained by the segments of any two intersecting chords of a parabola are to one another as the parameters of the diameters which bisect the chords. Hence show that if a circle intersect a parabola, the common chords are equally inclined to the axis of the parabola. 9. If perpendiculars be let fall from the two foci upon any tangent to an ellipse, prove that the feet of these perpendiculars lie, on the auxiliary circle, and the rectangle contained by the perpendiculars is equal to the square on the semi-axis minor. 10. Prove that in an ellipse the sum of the squares on two conju. gate semi-diameters is constant. If along the normal at any point of an ellipse a portion be measured equal to the conjugate semi-diameter, the locus of its extremity is a circle. 11. Define an asymptote of an hyperbola, and prove that the curve continually approaches its asymptote but never meets it. If a directrix of the hyperbola cut an asymptote in E, prove CE = CA, where C is the centre, and A a vertex. 12. If a chord Qq of an hyperbola be produced to meet the asymptotes in R, r, prove Q R = qr. Hence show that if the tangent at P meet one asymptote in T, and TQ, drawn parallel to the other asymptote, meet the curve in Q, and PQ be produced to meet the asymptotes in R,R', then RR' is trisected at the points P, Q. TRIGONOMETRY AND MENSURATION. Examiner-DR. H. W. M'Cann. 1. Explain what is meant by the “circular measure" of an angle, and prove that it is a correct measure. If D, G, 0, be respectively the number of degrecs, grades, and units of circular measure in any angle, find the relation between D, G, 0. 2. Trage the variations in sign and magnitude of the secant of an angle as the angle increases from 0° to 360°. Show how the trigonometrical ratios of all angles whatever, posi. tive or negative, may be made to depend upon those of some positive angle less than 45o. 3. Write down the general expressions for all angles which have (i) the same sine, (ii) the same cosine, (iii) the same tangent, as a given angle a. Solve the equations, obtaining the value of 0 in the most complete form, (a) Cot: 0 + 4 cos 0 = 6 (6) Sin 0 + cos 0 = 1 4. Obtain the formula cos (A + B) = cos A cos B — sin A sin B. Assuming its truth when A, B, A + B, are each less than a right angle, prove it when A and B each lie between 90° and 180°, and (A + B) lies between 180° and 270°. Express sin 2A, cos 2A, in terms of tan A, and express tan A in terms of cos 2A. 5. Given a, b, c, the three sides of a triangle, investigate a formula for determining cos log 8.9415 = .9514104, log 4:439 = 6472851, log 4 0805 = .6107027, log 8:583 = .9336391 L cos 11°52' = 9.9906180, L cos 11°53' = 9.9905914. 6. Show how to solve a triangle having given two sides and the angle opposite one of them, and explain completely the resulting ambiguity. If a = 36, b = 44, A=32°42', find B and C, having given log 3 = .4771213, log 11 = 1.0413927 L sin 41°20' = 9:8198325. |