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1. If the sum of the sine and cosine of an angle is 1.2, find either, and find the angle.

2. If tan 20 3 tan 0, find tan 0 and 0.

3. Divide the arc 130° into two parts whose sines shall be to each other in the ratio of 3 to 5.

4. Or whose tangents shall be to each other in the same ratio.

5. Find the angles and area of a triangle whose sides are 586, 714, 649.

6. Given log 2.30103, log 3.47712, find the log of 7.2.

7. Give the steps by which the modulus of the common system of logarithms is calculated.

8. Of what series is the number e the sum ?-and what is this number to five places of decimals?

9. Solve the equation

x+3=√3x2 - 4x + 13.

1. If a railroad train goes I foot in 0.03 of a second, how many miles does it go in an hour?

2. In any triangle, how much is the square of a side opposite an acute angle less than the sum of the squares of the sides containing the angle? Prove this, and translate it into trigonometrical language.

3. Prove that the angle in a semicircle is right; and that the angle in a segment less than a semicircle is obtuse.

4. Prove that two triangles are equiangular if they have an angle in each equal, and the sides about the equal angles proportional.

5. The difference of two numbers is 5, and the difference of their squares 85; find the numbers.

6. The sum of two numbers is 9, and the sum of their squares 53; find the numbers.

7. Divide x2 + 3x + 4 into x1 - 5x3 +7x2 − 9x + 12. mainder?

Is there any re

8. What power of x do we obtain when we divide x by the square root of x-when we divide x3 by 23?-when we divide the cube root of x by x?

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8. If

and prove that



(x2 + a)p


should touch the curve

xn-1 dx



depends on (2+)-1

2. Prove that

3. Exhibit the five roots of the equation


depends on

4. If a, ẞ, y, d are the roots of the equation
ax +4bx3 + 6cx2 + 4dx+e=0,

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prove that

a3× {(a−y)(B-8) + (a− d) (B − y)} × {(a− ẞ) (y − d) + (a–d) (y-B)} × {(a−ß) (d− y) + (al− y) (8 −ẞ)} = −432 (ace + 2bcd — ad2 — eb2 — c3). 5. Find the locus of a point such that the tangents drawn from it to two conics may form an harmonic pencil.

6. Find the condition that the circle
(x − a)2+(y-ẞ)2 = r2

a2x2 + b2y2 = (x2 + y2)2.

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7. Prove that


(( 1 − 2m sin 0 + m2) ( 1 − 2m2 sin 0 + m1) ( 1 − 2m3 sin 0 + mo). . ad inf.\ + (1 + 2m2 sino +

(1 + 2m3 sin +

m sin 0


m3 sin 50

m3 sin 30
3(1-m3) ' 5(1− m3)

r = a, p2 + 2pq+2pr = b, p2 (q+r) = c,
√ p + √q + √r = 0,

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- ...

4pqr=√(a2-36) (b2 — 3ac).

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1. A weight is suspended by three cords to a fixed horizontal ring which passes through three loops, one at the extremity of each cord

a. Show that the cords cannot all be strained unless they are of equal length.

b. Determine the positions of equilibrium, distinguishing between those which are stable and those which are unstable.

c. Determine the positions of equilibrium in which the cord is, respectively, most likely and least likely to break.

2. A uniform beam is supported in a given horizontal position by a cord, attached to its extremities, and passing over two smooth pegs in the same horizontal line

a. Determine whether the probability that the pegs will break is increased or diminished by knotting the cord to them.

b. How is this conclusion modified if the pegs be rough?

3. A uniform rectangular board has one side in contact with a rough wall, and is supported by a string attached to the upper corner remote from the wall, passing over a pulley in the wall, situated vertically over the board, and sustaining a weight; determine the least value of the pressure against the wall.

4. A weight is attached by a cord to a fixed point; a second weight, equal to the first, is attached to it by an equal cord; show that the equations of the oscillations of the system so formed are of the form






5. Find the path of a particle on a smooth horizontal plane, the particle being attached to a point whose motion is rectilinear and uniform. 6. Determine the equation of the curve of quickest descent.



1. Determine the equation of the surface which, having a given superficial area, contains the greatest possible volume; and show that if it be a closed surface,

which will make

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where R, R' are the principal radii of curvature, P the perpendicular on the tangent plane, and ds the element of the superficial area.





2. Find the most general form of


A(= f(x, y, z, P, 9))

SSA (rt-s2) dxdy

capable of being reduced to single integrals, and show that the result may readily be verified without the aid of the Calculus of Variations.

3. Investigate the equation of the curve of quickest descent of a material particle in a medium resisting with a force represented by a given function of the velocity, gravity being the only acting force.

4. Explain the sign of substitution devised by Sarrus, and reduce according to this notation,

&SS Vdxdy


V = f (x, y, z, P, 1))

to the form in which it is immediately applicable to questions of maxima and minima.




1. Compare ordinary acute rheumatic fever with that form in which pus is deposited in and about the joint

(a). Symptoms and history.

(b). Results.

(c). Treatment.

2. What is implied by the term Febris Senilis?

3. Has nicotine been used as a remedial agent? In what disease would you think of employing it, and in what dose?

4. Explain the terms coction, lysis, and crisis, in reference to fever.

5. Explain the terms legitimate intermittent and false intermittent. Give examples of the two forms, and compare them as to the effect of anti-periodics, such as bark.

6. In what cases of true intermittent is quinine often found to fail? 7. Give Van der Kolk's views as to the nature and treatment of epilepsy.

8. Give your diagnosis in this case:- Orthopnoea; feeble, irregular pulse; cold extremities; systolic murmur at the base of the heart, traceable into the aorta; total absence of the second sound of the heart, which was not replaced by any murmur; the latter signs coming on a short time before death.

9. Give the most approved treatment for sunstroke.

10. Compare pericarditis with pleuritis, as to the period when stimulants are called for.



1. What are the organic peculiarities of those animals whose calorific function is most active?

2. What is Liebig's theory of animal heat?

3. What experiments, and by whom instituted, have thrown some doubt on the sufficiency of Liebig's theory to explain the phenomena of animal heat?

4. How does pathology seem to favour such doubt?

5. Explain the process of death by asphyxia.

6. While as a general rule the human subject will not bear submersion beyond a very limited time, a few cases have been recorded where animation has been restored after a much longer period of submersion. What physiological solution has been applied to explain these exceptional


7. What do you understand by vital capacity as applied to respiration? 8. What is the element in the individual that chiefly affects the vital capacity?

9. The relation that this element bears to the vital capacity admits of being expressed in a simple numerical form. What is it?

10. What are the symptoms of the Maladie de Duchesne? Where is the seat of the lesion on which it depends, and who first described the true seat of the disease?



1. Mention the circumstances which contra-indicate the operation of lithotomy.

2. Give the diagnosis of fungus of the bladder.

3. Describe the operations proposed for the cure of varicocele.

4. Enumerate the symptoms and dangers attending caries of the cervical vertebræ.

5. What are the characters of psoas abscess?

6. Mention the cases in which you would employ mercurial fumigations.

7. Describe the injury termed by Mr. Hey "internal derangement of the knee-joint."

3. Describe Hey's luxation of the thumb.

9. Describe Syme's amputation of the foot.

10. Mention Paget's account of the mode of formation of hæmatoma.



I. * How would you discover that a woman was in the first stage of labour?

*Each Candidate is expected to attempt this Question.

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