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احوال سے

اتنے مین مقر بان درگاه اس بزرک کے میرے

آگاه ہوے اعزاز و اکرام سے مجھے لے آئے اور ایک مقا بلند میرے واسطے مقرر لیکن عجز و انکسار سے مئین نہایت نبيه ببٹها اور يهم شعر پڑا۔

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کیا

بند هاد نل ون اي صاحب مرے

امر ہو تو بیٹهون بند ون مین ترے کہا اسنے ايسي بانون کي يہ جاگہ نہین *

*

بیہ

گر مری آنکھون پہ تو بيٹهے یہی ناز تها ؤن مين ترا ای نازنین

(c)

کھینتا ہی

دو مصور نے آپس میں کہا کہ

ام دو نون تصویر کهینین دیکهین کون اچھې

ایک نے انگور کې خو ش كي شب دهم کهیني اور دروازے پر لٹکا دی چڑیان اسپر چونچ مارنے لگین دیکهنے والے بہت خوش ہوئے ایک دن لوگ دوسرے مصور کے گھر گئے پو چھا کہ تمنے کهان تصویر کھیني ی اسنے کہا کہ اس پردے کے بیعے پہلے مصور نے برد پر ہاتهه ركها بسموها کم پرده نہین دیوار مین در دے

تب دوسرے مدور نے کہا تمہارے

کا نقش کهیعا اي

کام

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(d)

بدأ م

سے چڑ یون نے فریب کھا یا اور میری نقا شي تم نے الكهون آگے ضعا ک کی داستان کرون اسكي اب سلطنت کا بیان سپهدار مر تا ض تازي شم کا عمران خسرو ذوا لكرام کہ تها تازیان مین وه فرمان روا رعیت نوازی میں مشغول تھا هزاران بز واشتر و گاو میش رکھا تھا سپهدار فرخنده کیش

WEDNESDAY, 18TH DEC., 10 A.M. To 12-30 P..
ARITHMETIC.

.
CAPTAIN W. H. COAKER, R.E.

I. Find by Practice the value of

.tons 17 Cwts

.
2 qrs
.
24 lbs
.
at Rs
.
125-6-8 per ton

9 (.ه)

(b. 29,764 articles at Rupees 1-11-95 each. II. The materials of an old building were sold for Rupees 1,500 upon condition that they should be removed within 30 days under a penalty of Rupees 10 per day for every day beyond 30 days. The purchaser employed 40 men at 3} annas per day to do the work, and after selling the materials for Rupees 2,365, he cleared Rupees 190 by bis bargain. Find the number of days the men were at work. III. (a) Divide 0576 by 180, and by 2018, (6.) Find the value of 2:8 of 2:25

4.4-2.83 +

of 82. 1:36

1:3 + 2.629

2

}

IV. A and B enter into partnership ; A supplies the whole of the capital, amounting to Rupees 45,000 upon condition that the profits are to be equally divided, and that B pays A interest on half the capital at 10 per cent. per annum, but receives Rupees 120 per mensem for carrying on the concern. Find their total yearly profits when B's share is equal to one half of A's share.

V. Find the difference between the true discount on Rupees 259-2, due two years hence, and the interest on the same sum for two years, allowing in both cases simple interest 4 per cent. per annum.

VI. A room, 21 feet long by 13 feet wide is surrounded by walls 1 feet thick, and 14 feet high. There are two doors each 41 feet by 6 feet, and one window 3 feet by 41 feet. Find (1) the cost of building the walls at the rate of Rupees 5-1-0 per cubic yard, and (2) the number of bricks each measuring 9 inches x 4 inches x 21 inches, required for the work.

VII. If 38 men working 6 hours a day can do a piece of work in 12 days, find in what time 57 men working 8 hours a day can do a piece of work twice as great, supposing 2 men of the first set to do as much work in 1 hour, as 3 men of the second set can do in 11 hours.

VIII. Extract the square root of .002, and of 764:9, each to four places of decimals.

IX. A person’s net income from 5 per cent. Government paper is Rupees 1,225 after paying income tax at the rate of 2 per cent. Find the number of shares of Rupees 1,000 each owned by him.

WEDNESDAY, 18TH DEC., 2 to 3-30 P.M.

ALGEBRA.

S. SRINIVASA RAGHAVA AIYANGAR, B.A.

+

008 + 3.0 3 + 5x + 15 20 4 + 3 + 3003 + 30 2 I. Simplify

Q3 + 2x2 + 5x + 10 it 4 + 2x3 + 3x2 + 4x 4 II. Show that (x3 – 3x) 4 8 (2c6 6x4 + 9. 2 2) is an exact square and resolve the whole expression into factors. III. Show that (i) if a + b + c = 0 then a (b – c): + b (c –a): +

cla b)3 = 0,

97

b + ac

+

+

= 7.

(ii) if a + b + c= 1, ab + bc + ca = }, abc
1
1

1
then

(27 a + bc

ct ab
IV. Solve the following equations.
(1)

4 (x + 5) 3 (x + 6)
x + 6

*C + 5
(2) x + y +z = ax + by + cz = 0,

y
+
+

1.
b
a-C

b V. A mail coach runs between two places A and B and back again. A traveller who starts walking from A 5 hours before the mail coach is overtaken by it half-way between A and B. He then doubles his rate of walking and meets the mail coach on its returu journey 3 miles from B. The traveller then goes to B at the same rate and returns, and by the time he comes again midway between A and B, the mail coach reaches A. Find the distance between A and B and the rate at which the mail coach runs.

a

THURSDAY, 19th DEC., 10 to 12 A.M.

GEOMETRY.

CHARLES WATERS, M.A.: W. LEEMING, M.A.

PART I.

1. At a given point in a given straight line, make a rectilineal angle equal to a given rectilineal angle.

An obtuse angle ABC is divided by BD so that the angle CBD is double the angle ABD. CD is drawn parallel to AB, and CE at right angles to CD meets DB produced in E. Shew that DE is twice BC.

II. Prove that in any right angled triangle the square which is described upon the side subtending the right angle is equal to the squares described upon the sides which contain the right angle.

Prove that, in the above figure, the area of a six-sided figure formed by a side of each square and the three straight lines which join the adjacent corners of the squares is equal to four times the area of the original triangle together with twice the square on the hypothenuse.

III. Two equal circles intersect one another so that the centre of eack circle is on the circumference of the other. From a point on the circumference of one of these, straight lines are drawn through the 'centres A, B, meeting the circumference of the other circle in P and Q. If AQ, and PB be joined, shew that one of the angles APB, AQB, is four times the other.

PART II. IV. If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.

V. Produce a given straight line so that the rectangle contained by the whole line thus produced and the part produced may be equal to a given square.

VI. If from a point without a circle there be drawn two-straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square on the line which meets it, the line which meets shall touch the circle.

VII. ACB, DCB are two circles, intersecting in B and C. P is a point in BC produced. PA is a tangent to ACB, PDE a chord of DBC. AD and AE cut the circle ACB in F and G. Shew that FG is parallel to DE.

THURSDAY, 19th Dec., 2 to 5 P.M.

INDIAN HISTORY.
C. C. FLANAGAN, M.A.: E. B. POWELL, LL.B. :

GEO. MILNE RAE, M.A.

PART. I

I. (a.)-State what you know regarding the ancient kingdoms

of Pandya and Chola. (6.)-Name the kingdom of which Calicut originally formed

an important part. (c.)—When did Calicut become an independent principality ?

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