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(2)

بند ر نے کہا سر زمین پهن مین ایک پاد شاه تها ملك اسكا مالا مال دولت لازوال - بخشند که تا و تخت - نیک سیرت - فرخنده بغت - جسد م مسائل کی صدا گو ش حق نیو ش مین در آی - و این احتياج پکاري مين براتی - یہان تک کہ لقب اسكا نزدیت و دور خدا دو ست مشہور ہوا ۔ ایک روز کوئي شخش آیا اور سوال کیا کہ اگر تو خدا دوست ہی تو الله تین دن ہے سلطنت کرنے دے ۔ یاد شاه نے فرمایا بسم الله - جو رکن سلطنت مسند نشنين حكومت حاضر تھے بتا کید آنهبن حکم ہوا کہ جو اسكي نافرماني کریگا مورد عتاب سلطاني يوگا - بهم فرما وه فرمانروا

اٹھا مسائل جابدتها حکمرانی کرنے لگا

(3)

شم

بای

نا قلان آثار راویان اخبار یعنی در ران تاریخ ملكك نے اس طرح تم کیا کم

جب داراب خلف من تنت نشین ہوا تو ایک عالم زير نگین ہوا - مگر فيلتوس قیصر روم نے اطاعت نكي - داراب نے ود لشکر اور ء جمع ظغ. پیکر جو مهندس عقل اور محاسب وام سے

گنا نگيا يکدا کیا ۔ اور قرے نے بهي اسباب درب سامان جنگ بژ کر و فر درست کرکے کوچ کیا - بعد از تلاقي عسکر ین و توازی صفین مرغ تي

صفدر ہوا اور شم زندگاني تم تدشة شمشیر ہوا آخرالامر نسیم فتح و ظفر عنایت ذو المذن سے وارت مل گشتاسپ اور بهمن كي طرف حلي قیصر کی شکست ہوئي ہوا بگڑ گئي اوس پڑگئي

(4)

پادشاه نے حکم کيا کم گو ہر سخن کي قدرت و قیمت هاری مهر با ني اور قدرداني کے بازار مین سب جنس سے زیاد ہي

لا تیرے پاس کیا ای پیر مرد نے ہاتھ جوڑ کر بهم التماس کیا کہ جہان پناه شک اور یقین میں چار انگل زیاد تفاوت نہین - چاہئے کہ جو که دیکهے سے مقرر ٹھي جانے اور جو کانون سے سنے اسکے بیچ اور جهو ته مين

شك اور شبهم رکھے کہ شاید دروغ ہو ۔ مصرع

سنے سے دیکھنے کا

بڑا اعتماد

ای

WEDNESDAY, 12TH FEB., 3 TO 5 P.M.

ORIGINAL COMPOSITION IN VERNACULAR LANGUAGE.

Write

I. A brief Essay on

Works of Fiction and their influence.

or

II. The story of the Play of Romeo and Juliet.

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

PURE MATHEMATICS.

W. A. PORTER, M.A.

I. Shew that the equation

(b - ) 4 (a - .) (c ) = 0. has real roots whatever be the values of a, b, c. Shew that the expression

(a k) x2 + (6 — k) x + (c - k) will have an invariable sign for all real values of «, 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 + ib) 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

2 + 3x + (1 – 3x)

+ (4

2 according to ascending powers of x.

IV. Assuming the formula

2C

x)}

+

+ &c.

e

2

log, (1 + x) prove that

n = 2

+ &c.

1 1 1 log, (n + 1) – loge

2n + ]

+ş (2n

3 (2n + 1)3 Given log, 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 proposi. tion 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 si Yl are drawn at right angles to a tangent, then Y and Yi are on the auxiliary circle and SY. $Y'

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 2 0 in terms of tan 0.

a-B If Sin (a + 0) Sin (B + 0) = m cos 2 0, shew that cos

+ m cos (a + b), a and B being different and less than . X. Given a = 19, b = 17, C 60° find the other angles.

Given log. 2 -301030, log. 3 = .4771213.

Log tan 5° 29' = 8:9822507.
Log tan 5° 30' : 8.9835769.

=

2

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, 0,,0g, the centres of the described circles touching AB, BC respectively, and R1, R2, R, the radii of the circles described about the triangles ABO,, AB0 g, and 00,, Og, shew that

R.: + R2

2

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THURSDAY, 13th FEB., 10 A.M. TO I P.M.

LOGIC.

C. H. PELLY. M.A,

1. 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.”
"This man was honest when he was young."
" There is a God."

“I hope to succeed." V. “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
(6) 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

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