ایک دن جنم پا تا پی او ایک روزناس ہوتا ہي مای پ آواگون ای یه تیری استری اور بوت دنیا کا یہی اور دھن اور چالیس دن کا اسباب بھوجن کا موجود ہی ا سکو لے اور یہان ره جب تلک بابت تجهه پر مهربان ہو وے مین نے غصے میں چاہا کہ اس بت پر اور وہان لعنت کرون کے رہنے والون پر اور اس ریت رسم پر لعنت و هي مرد عجمی ا پنی زبان مین مانع ہو ا کہ خبر

دار هرگز دم مت مار*

II. Translate into idiomatic Hindustani :(a) Hear me, I pray you.

(b) I took him for another person.

(c) Would that my brother had come.

(d) He would have done it if he had dared.

(e) I scarcely had time to enter the house when he saw me. (f) I act according to my conscience.

(a) I do not recommend you to try to learn every thing. Far from it. But while you have one great object in view, you can attend to other things which have a bearing on your object. If you were now sent on a special errand to Bombay, while the great object before you would be to do your errand well and expeditiously, ought you not as you pass along, to use your eyes, and gaze upon the landscapes, the rivers, the hills, the waterfalls which lie in your path? Ought you not to have your ears open to pick up what information you can-story, fact, every thing of the kind-and thus return wiser? Would you not be fitting yourself, by every such acquisition, to be a more intelligent and useful man?

IV. Write in Hindustani a short essay on navigable river like the Ganges."

"The uses of a large

WEDNESDAY, 22ND DEC., 10 A.M. TO 1 P.M.

ARITHMETIC,

CAPT. W. H. COAKER, R.E.; CHARLES WATERS, M.A.

PART I.

I. A merchant purchases 231 gallons of spirit at Rs. 10-12-4 per gallon; 126 gallons at Rs. 12-11-7; and 70 gallons at Rs. 14-8-9; if he sell the mixture at Rs. 13 per gallon how much will he gain by the transaction?

II. Define a decimal; and show how its value is affected by affixing and prefixing cyphers.

III. Express the sum of 571428 of a viss, § of

and

3801 10136

317 of of a maund;

333 384

of a hundred weight as a decimal of one ton. (one viss

= 3 lbs. 2 oz.; one maund = 823 lbs.)

IV. If 210 coolies in 7 days of 10 hours each dig a channel 1 mile long, 6 feet broad, and 2 feet deep; in how many days of 7 hours each should 35 coolies dig a channel 660 feet long, 73 feet broad, and 24 feet deep? and how many cubic feet does each cooly dig in an hour?

V. The expenses of a family when rice is 12 seers for a rupee are 50 rupees per inonth: when rice is 14 seers for the rupee the expenses are 48 rupees a month (other expenses remaining unaltered). What will they be when rice is at 16 seers per rupee?

PART II.

VI. What are the prime factors in 45090045, and what is the smallest whole number by which it must be multiplied in order to become a perfect square ?

VII. The cost of carpeting a room is £7-4-0, and of papering the same room, with paper at 23d. per square foot, £ 10-12-6. The length of the room is 18 feet, and if the width had been 4 feet less the cost of the carpet would have been £1-16-0 less. Find the height of the room.

VIII. Find the sum for which the difference between the simple and compound interest at 5 per cent. per annum for three years is £ 12-4-0.

IX. What length of wire will go round the edges of a cube the surface of which contains 187 yards 0 feet 54 inches.

What is the least number of such cubes which will contain an exact number of cubes whose edges are 1 foot 3 inches ?

X. A merchant's average rate of profit for five years was 5 per cent. on his capital, and for the first four years his average profit was 4 per cent. What was his rate of profit the fifth year?

WEDNESDAY, 22ND DEC., 2 TO 5 P.M.

ALGEBRA.

REV. J. H. WALTON.

1. Remove from brackets (c−a−b) — { (b + c

and of {(a + √T — a2) ( b − √ 1 − b2) — (a — √ 1 − a2)

(b+ √1-63)} and simplify the result.

IV. What must be the form of m in order that am

20 a 5 + 11 a 3 + 24

V. Reduce to its lowest terms 24 a5 +11 a2 + 20°

VI. State and prove the rule for finding the Least Common Multiple of the two Algebraical Expressions P and Q.

Find the L. C. M. of 1 + a + a5 and 1 + a1 + a3.

Nax

√ a + √ x + √ a + x

a+b+c

VII. Simplify

b

-

c

a + b

VIII. Find what term is wanting to make the following expression a complete square: (a2 x4 + 64 b2) -- 4 (ax2 + 8 b) (a - b) x.

-

X. A person sets out to walk to a certain town. But when he has accomplished a quarter of his journey, he finds that if he continues at the same pace, he will have gone only ths of the whole distance when he ought to be at his destination. He therefore increases his speed by a mile an hour, and arrives just in time. Find his rates of walking.

THURSDAY, 23RD DEC., 10 A. M. TO 1 P.M.

GEOMETRY.

F. S. EVANS, M. A.; G. THOM, M. A.

PART I.

I. Give the enunciations only of the propositions to which the following are corollaries :

(a) Every equiangular triangle is also equilateral :

(6) All the angles made by any number of straight lines meeting at one point are together equal to four right angles :

(c) The difference of the squares on two unequal straight lines is equal to the rectangle contained by their sum and difference.

II. ABC is a triangle, and the side BC is produced to D. Prove that the exterior angle ACD is greater than the angle ABC.

III. Prove that triangles on the same base and between the same parallels are equal to one another.

(a) Two equal triangles have two sides of the one equal to two sides of the other. What conclusion do you draw with respect to their included angles ?

(b) Through the point A of any triangle ABC a straight line is drawn parallel to the side CB: and through C a straight line CD of length equal to AB is drawn, meeting the straight line through A parallel to CB in D, and cutting AB in E. Prove that CE is equal to EB, and AE to ED.

IV. ABC is an equilateral triangle, and from A, B, perpendiculars are drawn to CB, AB respectively, intersecting in E. Through E a straight line EF is drawn parallel to BA meeting BC in F, and through F a straight line FG is drawn perpendicular to AB meeting AB in G. If AG be bisected in K, prove that the straight line AB is trisected in K, G.

V. If a straight line be divided into any two parts, prove that the rectangles contained by the whole and each of the parts are together equal to the square on the whole line.

PART II.

VI. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, prove that the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.