VI. In the following passage substitute appropriate synonyms for those words which you think are improperly used :

For three months there has been continual fine weather without an only shower and the grass is totally withered. As an effect there will be a durable famine, for although the cultivators have not been quiet, but have worked hard, there will not be almost as copious crops as last year. This failure will be the reason of much suffering to those who are not endued with property, and some tell that they will not be able to suffer their calamities, and that they think of willingly giving up their lands before they are compelled to do so. Their reasons in favor of this course are very heavy.

VII. Distinguish between the meanings of the passages in each of the following pairs :

(a) Will he not come home to-morrow? answer Yes.
Will he not come home to-morrow? answer No.

(b) I am glad to see you.

I am glad to have seen you.

(c) He said to his servant, you will come with me.'
He said to his servant, 'you shall come with me.'

(d) He asked if he might go to Madras.
He asked if he could go to Madras.

(e) If it rain you cannot go home.

If it rains you cannot go home.

VIII. (a) Explain how it has come to pass that there is now no difference in form between the gerundial and the common infinitive.

(b) Show the syntactical relation in which the two parts of each of the following compound words stand to one

another:

Even-tide; man-killer; snow-white; earth-shaking; dooms-day; oak-tree; earth-born; ill-looking.

IX. Spell the following words as you would pronounce them :-Rendezvous- kiln- corps-cupboard-diamond-medicine- heirphlegm-succumb-sieve-respite-rhythm.

dependent of the size of the angle, but dependent on the unit of angular measurement.

is

What will be the value of k when the unit of angular measurement

of a right angle? and express 78° 45′ in circular measure with the same unit.

II.

Trace the change in the sign and magnitude of the expression sin + sin 20, as @ changes from 0 to 2π.

III. Find an expression for all the angles which have a given tangent. If tan (2x-3B) cot (3 α 28)

and tan (2x+36)

=

Shew that both ¤ and ẞ are multiples of 18°.

IV. Find the sine of an angle of 18°.

Find the numerical value of sin2 24

sin2 6°.

V. The limit of

sine
0.

Find the limit of

when is indefinitely diminished is unity. sin 2x + 2 sin2 x 2 sin x COS X cos 2 x

when x = 0.

VI.

Expand log. (1 + x) in a series of ascending powers of x as

VII. Express the sine and cosine of half an angle in terms of the

sides.

Show that if in a triangle 1 cos 4, I

cos B, and 1 - cos C

are in H. P., sin A, sin B, and sin Care also in H. P. VIII, Find A and B in the following triangle C = 60°, «= 1'6, 665 having given:

log 3
= 4771213
log 78450980

L tan 46° 20′ = 10.0202203

L tan 46° 21' = 10.0204732

IX. The top of a pole, placed against a wall at an angle a with the horizon, just touches the top of the wall, and when its foot is moved a yards further from the wall, and its angle of inclination to the horizon is ß, it touches the top of a window; show that the perpendicular distance from the top of the window to the top of the wall is α + β a cot

2

X. When is a plane perpendicular to a plane? Define a prism, á cone, and a tetrahedron.

XI. If two straight lines which meet one another, be parallel to two other straight lines which meet one another, but are not in the same plane with the first two, the plane passing through these is parallel to the plane passing through the others.

XII. Three planes meet in a point, and through the common section of each pair, a plane is drawn perpendicular to the third, prove that the planes thus drawn generally pass through the same line,

TUESDAY, 21ST DEC., 2 TO 5 P.M.
LOGIC.

P. RANGANADA MUDALIYAR, M.A.; W. E. ORMSBY, L.L.D.

PART I.

I. Examine the definitions,-"Logic is the art and science of reasoning,"—" Logic is the science of the laws of thought as thought."

II. (a) Define the terms relative, privative, abstract, and connotative.

(b) Are abstract names connotative or non-connotative ?
(c) Describe the logical characters of the following terms.
The unthinkable, Virtue, Cruelties, Democracy, Ten thousand
horse, Apathy, A George, George IV., The Georges.

III. Determine the quantity and the quality of the following propositions and state their contradictories.

(1) Self-confidence is not inconsistent with great

weakness.

(2) Not every advice is a safe one.

(3) Hardly any virtue is quite safe from passing

into a vice.

(4) Not always knightly spurs are worn

The brightest by the better born.

IV. (a) State what difficulty is encountered in converting the proposition O by simple conversion or conversion by limitation.

(b) Convert the following by the method of conversion by contraposition.

(1) All just acts are expedient acts.

(2) Some useful things are disagreeable.

(3) No planets are self-luminous.

V. Give the rules of definition, and find which of the rules are violated by the following:

(a) Oxygen is a gas.

(b) Gold is the most valuable of the metals.

(c)

(d)

Force is that which produces motion.

An equilateral triangle is a triangle with three equal anglés.

(e) Pain is the absence of pleasure.

(f) All matter is either solid or liquid.

(g)

Uninteresting sensations are such as in themselves do not engage our attention.

(h) Parallel straight lines are straight lines which being preduced ever so far both ways do not meet.

VI. What four facts are implicated in the disjunctive proposition, "You must either pay a fine or go to prison."

PART II.

VII. Define Syllogism. It has been objected against the Sylicgistic theory, (a) that men reason from one particular case to another without the intervention of any universal proposition: (b) that the Syllogism involves the fallacy of begging the question. Explain fully the nature of these objections, and how they may be answered.

VIII. Give the special rules of Syllogism, and determine by a general process of reasoning what mood will violate the greatest number of rules. Why is the mood A E O useless!

G

IX. Construct Syllogisms in Cesare and Ferison, making S the minor term, M the middle, and P the major, and reduce them to the first figure. What is intended by the k in Baroko and Bokardo, and by the in Bramantip?

X. What form of arguments will fall most naturally into the second and third figure respectively? Show that in the second figure the conclusion is always negative, and in the third particular. In the valid moods does the quantity of any extreme ever vary in premiss and conclusion?

XI. What is a hypothetical Syllogism, and what rule is necessary for testing its validity? Show (giving an example) the nature of the fallacies involved in the violation of this rule.

WEDNESDAY, 22ND DEC., 10 A.M. TO 1 P.M.
SANSKRIT: GRAMMAR, &c.

(b) Conjugate to bind' in the Imperative and Aorist

Parasmai.

II. (a) State the rules of Grammar which have been observed in the formation of the compounds अनन्यजानि,

अमोघधन्वन्, and अर्धरात्र.

der of the last word?

What is the gen

(b) What is the force of the affix ता in जनता, of

दयस in नारीनितम्बइयम, and of मात्
श्रोत्रियसात्कृत्वा.

(c) Illustrate the use of कामं - पुन : by an example from

the books you have studied.