(2)

بندر نے کہا سر زمین یمن مین ایک پاد شاه تها

ملك اسكا مالا مال دولت لا زوال - بخشنده تا

لم

و تخت ـ نيك سيرت - فرخنده بخت - جسد سائل کی صدا گوش حق نیوش مین در آئی ـ و پین احتياج بكاري مين برائي - يہاں تک کہ لقب اسکا نزدیک و دور خدا دوست مشہور ہوا - ایک روز کوئي شخش آیا اور سوال کیا کہ اگر تو خدا دوست هی تو لله تین دن مجھے سلطنت کرنے دے - یادشاه نے فرمایا:بسم الله - جو رکن سلطنت مسند نشنین حکومت حاضر تهم بتاكيد انهين حكم ہوا کہ جو اسكي نافرماني کریگا مورد عذاب سلطانی ہوگا ۔ يهم فرما وه فرمانروا انها سائل جابيتها حکمرانی کرنے لگا *

عجم

(3)

نا قلان آثار راویان اخبار یعنی در ران تاریخ ملک نے اس طرح رقم کیا ای که جب داراب خلف بهمن تخت نشین ہوا تو ایک عالم زیر نگین ہوا ۔ مگر فيلقوس قيصر روم نے اطاعت نكي ـ داراب نے وہ لشکر اور مجمع ظفر پیکر جو مهندس عقل اور محاسب گرا نگیا یکجا کیا ۔ اور قیصر نے بهي اسباب حرب مامان جنگ بڑا کرو فر درست کر کے کوچ

و ہم سے

کیا

بعد از تلاقي عسكرین و توازی صفین مرغ تیر

سفیر ہوا اور شب زندگاني ته تیشه شمشیر ہوا - آخر الامر نسيم فتح و ظفر عنایت ذو المذن سے وارث ملک گشتاسب اور بہمن کي طرف چلي قيصر كي شکست ہوئي ہوا بكركدي اوس پڑگئي *

(4)

پادشاہ نے حکم کیا کم گوہر سخن کي قدرت و قیمت هماری مہربانی اور قدرداني کے بازار مین سب جنس سے زیاد ہي لا تیرے پاس کیا ہی پیر مرد نے ہاتھ جوڑ کر یہ التماس کیا کہ جہان پنا شک اور یقین میں چار انگل زیاد تفاوت نہین ـ چاہئے کہ جو کچھ دیکھے اُسے مقرر ٹھیک جانے اور جو کانون سنے اسکے بیچ اور جھوتھ مین شک اور شبهم

رکھے کہ شاید دروغ ہو

مصرع

سنے سے دیکھنے کا

has real roots whatever be the values of a, b, c.

Shew that the expression

(a−k) x2 + (b − k) x + (c — k)

will have an invariable sign for all real values of x, if k have any value outside certain limits.

II. In the expansion of (1 + x) n where n is a positive integer, determine the circumstances in which (1) the terms increase from beginning to end, (2) there are two consecutive terms equal.

999
2

In the expansion of (1 +) find the first term that is less than the preceding one, and also the first term that is negative.

III. Find the first two terms in the expansion of

Given loge

3 = 1·098612, find log, 10 to 5 places of decimals.

e

V. State the circumstances in which two parallelograms are to each other (1) in the same ratio as two of their sides, (2) in the duplicate ratio of two of their sides; and illustrate each case by the figure formed by drawing parallels to the sides of a parallelogram through any point in a diagonal.

Give the method employed in one of the propositions of the sixth book for finding two lines which are to each other as any two given rectilineal figures, and show how it may be done more easily when the given figures are similar.

VI. 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.

Point out four planes that are considered in the proof of this proposition, and their inclinations to each other.

VII. State in order the properties of the parabola that have to be proved (starting from the definition) in establishing the proposition that if chords be drawn in a parabola parallel to a tangent they will all be bisected by the line drawn parallel to the axis through the point of contact of the tangent.

VIII. If from the foci S and S' of an ellipse SY and S1 Y1 are drawn at right angles to a tangent, then Y and Y1 are on the auxiliary circle and SY. S1 Y1 BC2.

=

Given the major axis of an ellipse in magnitude and position and a tangent in position, find its point of contact with the ellipse.

IX Express cos 20 in terms of tan 0.

XI. Express the radius of the circle inscribed in a triangle in terms of one side and the adjacent angles.

If O be the centre of the circle inscribed in the triangle ABC, 01, 02, the centres of the described circles touching AB, BC respectively, and R1, R2, R, the radii of the circles described about the triangles ABO1, ABО, and 00, 0, shew that

THURSDAY, 13TH FEB., 10 A.M. TO 1 P.M.

LOGIC.

C. H. PELLY. M.A.

I. What do you understand by 'Logical Reasoning'? How would you reply to the charge brought against Aristotle that "in his Treatises of Ethics, Politics, &c., he argues like a rational creature and never attempts to bring his own system into practice ?"

II. What is meant by Generalization? Show that Abstraction does not necessarily imply Generalization though Generalization implies Abstraction ?

III. State and define the three operations of the mind which are immediately concerned in Argument.

IV. Resolve the following sentences into Logical Propositions :"The Romans conquered."

V.

"This man was honest when he was young."

"There is a God."

"I hope to succeed."

"Reduce the rules, commonly given by Logicians, by which all Categorical Syllogisms are to be tried, to six, and show from them that

(a) nothing can be proved from two particular premises

(b) if one of the premises be particular the conclusion must be particular.

VI. Show why all syllogisms in the second figure must have negative conclusions ?

VII. State the following argument in a syllogism of the first figure?

“No lawyers should be appointed to judicial offices in India who do not understand some of the native languages. None but men partly educated in India understand any of the native languages, therefore no lawyers who have been educated altogether in England should be raised to the Indian bench."

R