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ذجي تي : أني مجري نهر ياتي جي بيني وهي

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ذكر جي با با اها ماتري پیر صاحب فرمانو تر با با اها

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1. CookE, M.A., M.I., LL.D. ; GOVIND VITHAL KARKUPAY, B.A. [The black figures to the right indicate full marks.]

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375 of a guinea + ·54 of 8s. 3d. + ·027 of £2 15s. and re- 10 duce the result to the fraction of a guinea and a half.

3. A man owns of a ship and sells 3571428 of his share: 10 what fraction of the ship does he still own?

4. If the income tax be 6 pies in the rupee for the first 10 half of the year and 3 per cent. in the second, what is the gross income of a gentleman whose net annual receipts amount to Rs. 1454 1 anna ?

5. Five men do 6006 of a piece of work in 2:12 hours, 12 how long will 6 boys take to finish it, it being known that 3 men and 7 boys have done the whole piece of work in 3 hours?

6. If the difference between the simple and compound 10 interest on a sum of money for two years at

£5 18s. 93d.; find the sum.

per cent. be

7. When the three por cents were at 90, I found that by 10 selling out and investing in the four per cents at 95 I could improve my income by Rs. 243. What was the amount of my stock in the three per cents ?

8. A gardener plants an orchard with 5776 trees, and 8 arranges them so that the number of rows of trees equals the number of trees in each row. How many rows were there?

9. How many seconds will a train 184 feet in length, 12 travelling at the rate of 21 miles an hour, take in passing another train 223 feet long, proceeding in the same direction at the rate of 16 miles an hour?

10. Find the cube root of 1879080904.

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WEDNESDAY, 19TH NOVEMBER.

[2 P.M. TO 5 P.M.]

ALGEBRA.

T. COOKE, M.A., M.I., LL.D.; GOVIND VITHAL KARKURAY, B.A. [The black figures to the right indicate full marks.]

1. Explain the terms-inder, coeficient, like and unlike 4 quantities.

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6 (x2 + xy), 8 (ry — y2) and 10 (x2 - y2)

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6. Extract the square root of

4 x + 12 x3 y + 13 x2 y2 + 6 x y3 + y *.

7. Find the value of x from the equation

(x + 1) + f (x + 3) = } (x + 4) + 16.

8. Find the values of x and y from the equations

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9. The sum of two numbers is 100 and the greater is to 12 the less as 7 to 3; what are the numbers?

10. There is a number consisting of two digits whose sum 14 is 10, and if 72 be subtracted from it the digits will be inverted-what is the number?

THURSDAY, 20TH NOVEMBER.

[10 A.M. TO 1 P.M.]
EUCLID.

Professor KERO LAXUMAN CHHATRE; S. COOKE, B.A., L.C.E.

[The black figures to the right indicate full marks.]

1. When is a straight line said to be perpendicular to another straight line?

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Draw a straight line perpendicular to a given straight line of unlimited length, from a given point without it.

2. Show that if the square described on one of the sides of a triangle be equal to the sum of the squares described on the other two sides of it, the angle contained by these two sides is a right angle.

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3. In every triangle the square on the side subtending 12 an acute angle is less than the sum of the squares on the sides containing that angle, by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.

4. Show that the sum of the squares on the sides of a 10 triangle is equal to twice the square on half the base, together with twice the square on the straight line which joins the vertex to the middle point of the base.

5. Show that the sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals.

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6. From a given point without a circle, draw a straight 10 line which shall touch it.

7. If from any point without a circle there be drawn two 10 straight lines one of which cuts the circle and the other meets it, and if the rectangle contained by the whole line which cuts the circle and the part of it without the circle be equal to the square of the line which meets it, then the line which meets the circle shall be a tangent to it.

8. In the diameter of a circle produced determine a point 12 so that the tangent drawn from it to the circumference shall be of given length.

9. When is a circle said to be inscribed in a rectilineal figure?

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Can you inscribe a circle in any given rectilineal figure? 10. Inscribe a circle in a given triangle.

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THURSDAY, 20TH NOVEMBER.

[2 P.M. TO 5 P.M. ]

ELEMENTARY NATURAL SCIENCE.

Professor KERO LAXUMAN CHHATRE; S. COOKE, B.A., L.C.E. [The black figures to the right indicate full marks.]

1. Convert 40° Centigrade into its equivalent in Fahrenheit degrees.

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2. Convert 77° Fahrenheit into its equivalent in Centigrade degrees.

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3. Distinguish between a molecule and an atom.

4. State the law of multiple proportions, and give the 10 symbolic notation of the five oxides of nitrogen which are generally supposed to illustrate this law.

5. How is the atmosphere affected by green plants under 10 the influence of sunshine ?

6. Two sailors pull, one at each end of a rope, with a 5 force of 50 lbs. each; required the tension in the rope.

7. In testing the correctness of a balance a certain quan- 15 tity of rice was found to weigh 6 lbs. when put in one pan while it only weighed 4 lbs. when put in the other: required the true weight of the rice.

8. Calculate the amount of horizontal force necessary to 10 support a weight of 50 lbs. on an inclined plane whose height and base are respectively 25 and 30 yards.

9. Define the following astronomical terms:-
Equinoctial, declination, ecliptic, line of equinoxes, obliquity

of ecliptic.

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11. What is the average length of a degree of Latitude? 10 Where is it shortest, and why?

12. Explain, clearly, how the semi-diurnal tide is produced. 10

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