(a) ABC, ADC are two right angled triangles on the same hypothenuse AC. If AD, BC intersect in E, shew that the rectangle AE,ED is equal to the rectangle BE, EC.

VII.

(a)

Prove that the angle in a semicircle is a right angle.
Two equal circles touch one another externally at A, and a
straight line BAC is drawn terminated by the circles
in B and C. Shew that the centre of the circle which
passes through C and touches the circle AB in B, lies on
the circumference of the circle AB.

VIII. If from any point without a circle two straight lines be drawn, one of which cuts the circle but does not pass through the centre, and the other touches it; prove that the rectangle contained by the whole line which cuts the circle, and the part of it without the circle is equal to the square on the line which touches it.

(a) BA, AC are chords, in the same straight line, of two circles

which intersect in A. From B a tangent BD is drawn to the circle ADC, and from C a tangent CE to the circle BEA. With centres B and C, at the distances BD, CE respectively, circles are described intersecting in F. Join BF, FC, and shew that the angle BFC is a right angle.

THURSDAY, 23RD DEC., 2 TO 5 P.M.

INDIAN HISTORY.

A. L. VENKATARAMANA PUNT, M.A.; THE VERY REV. J. COLGAN.

PART I.

I. (a) What part did each of the following persons play in the wars of the English with Mysore ?

(b) Enumerate the reverses sustained by the English in their wars with Hyder and his son.

II. Write short notes on

(a) The expulsion of the Rohillas.
(b) Mr. Vansittart's Government.

(c) The rise and fall of Fort St. David.

(d) The conquest of the Northern Circars by the English.

(e) The Dutch settlements in India.

III. Say what you know of Sir T. Roe, Sevagi, Behram, Lord Macartney, and Yudhisteer.

IV. Name the Moslem dynasties that ruled over Delhi from the death of Shahabudin Ghori to the accession of Akbar. State briefly the circumstances which led to the fall of each.

V. Sketch the career of Mahmud of Ghazni,

VI. Who were the Aguikools, the Pandiyans, and the Kauravas !

PART II.

VII. State the principal measures of reform in the Judicial and Educational Departments introduced by Lord William Bentinck whilst Governor General of India.

VIII. What social improvements distinguished the administration of Lord Dalhousie? What Provinces were annexed during his tenure of Office as Governor General? Give the dates of their annexation.

IX. What were the immediate causes of the following events as recorded in Indian History.

·

X. Give one historical fact connected with each of the following: Vizier Ali, Chetoo, Kereem Khan, Trimbakji, Maha Bandoola, Goolab Sing, Meeanee, Ghazni, Mahidpore, Yandaboo, Sobraon, Chillianwallah.

XI. Give the name and date of the first and the last battle in the 2nd Burmese War, 1st Mahratta War in the present century, and 2nd Sikh War.

FRIDAY, 24TH DEC., 10 A. M. TO 1 P. M.
PHYSICS AND PHYSICAL GEOGRAPHY.

W. A PORTER, M. A.; GEORGE Duncan, Esq.

PART I.

I. State the property of air and the property of water illustrated by the experiment in your text book of letting down a corked bottle into deep water.

Would the experiment succeed if the bottle was filled with water before it was corked? Give your reason.

II: State in round numbers the depth at which the pressure on a square inch would be double that of the ordinary atmospheric pres sure in each of the following cases :

(3) In the same vessel when placed under the receiver

of an air pump in which the barometer stands

at 10 inches.

III. A cork is floating in a vessel of water and a glass tumbler is inverted over it and pushed down till it is wholly immersed. In what part of the tumbler will the cork be seen?

IV. When a body floats in water, what are the two forces that keep it in that position?

Shew how to determine which of two given fluids is heavier bulk for bulk, with no other apparatus than a rod weighted at one end which floats in both.

V. Water at the temperature of 0° on the centigrade scale is gradually heated to about 10° on the same scale; what changes of volume take place in the process?

To what general law is part of these changes an exception?

VI. Describe an experiment in which the application of cold water makes water that has ceased to boil begin boiling again.

What would be the effect of pouring boiling water on the flask immediately after the cold and why?

What fact is proved by this experiment?

VII. Give two instances in which heat is communicated to a body without increasing the temperature.

A lb. of water at 0° on the centigrade scale mixed with a lb. of boiling water gives 2 lbs. at nearly 50°; whereas a lb. a of ice at 0° mixed with a lb. of boiling water gives 2 lbs. of water at about 101°. State the inferences from this experiment, and determine from it the amount of heat required to melt a lb. of ice.

PART II.

6

VIII. Explain the terms 'Dew-point', Hard water', 'Silt', 'Crevasse','Crater', and Breakers'.

IX. State the physical fact or facts to be inferred from each of the following statements:

(a) Coral is made of lime.

(b) In A, a certain range of mountains, the snow line is 15,000 feet above the sea; while in B, another range, it is only 5,000 feet above sea level.

(c) A and B are two streams of equal width, but of unequal depth, running together to form a third stream C, which also is of the same width as A or B.

X. What proofs are there that the interior of the earth is intensely hot?

XI. State the different ways in which islands are formed.

XII. Briefly state the cause or causes of the phenomenon in each of the following cases :

(a) Glaciers which come out of the snow fields are not made of
snow, but of ice.

(b) An iceberg is seen advancing in the face of a stiff breeze,
(c) Large boats carrying many tons of merchandise, can at cer-
tain regular short intervals of time, pass up the Thames
(to some distance past London) without the aid of wind
or steam or manual labour.

(d) A strong current from the Atlantic Ocean continually flows through the Straits of Gibraltar into the Mediterranean

Sea, and many large rivers empty themselves into the
Mediterranean also; yet it does not overflow.

(e) The rain-fall on the west coast of this Presidency is far
heavier than that of the west coast of Ireland, though in

each case the rain-bearing clouds for the most part travel over an immense extent of sea.

(f) The Saraswati or Kaggar rises in the hills between the Satlej and the Jamna, and taking a south-westerly direction, disappears without losing itself in another river, a lake, or the sea.

FRIDAY, 24TH DEC., 2 TO 5 P.M.

GENERAL GEOGRAPHY.

C. C. FLANAGAN, M. A.; REV. E. H. DUBOIS.

PART I.

I. Name the following

(1) The peninsulas of Europe and America which stretch in a northerly direction.

(2) The rivers of Europe and America which flow into the Arctic Ocean.

(3) The boundaries of the great plain in the north-east of Europe. (4) The boundaries of the great central plain of N. America. II. Give the position of the following and state one interesting fact in connection with each :

Lofoden Isles, Fredrickshall, Lipari Isles, Ajaccio, Cherbourg,
Tierra del Fuego, Sveaborg, Faroe Isles.

III. Sketch a map of the Gulf of Mexico showing the States which form its northern boundary, Mexico and Yucatan; and marking on it two capes, two mouths of rivers, one gulf, and the towns Havana, Tampico and Vera Cruz.