2. Find the number of products of the type (i) abc, (ii) a3b2c, (iii) a2bc out of 6 letters.

4. Find the amount at 52% per annum compound interest, payable half-yearly for 12 years, of $6000.

In how many years would this sum double itself? (Tables are provided).

5. Expand in ascending powers of x to tour terms

in the expansion of this fraction in ascending powers of x.

7. Prove that loge(1+x)=x/1—x2/2+ . when x is numerically less than 1.

Calculate log. 9/10 to five decimal places.

FACULTY OF PRACTICAL SCIENCE.

TRIGONOMETRY I.

1. The sides of a triangle are 8".246; 11".714 and 9".126. Find: (a) The area of the triangle. (b) Its circumradius. (Use contracted multiplication and division of decimals, giving answer correct to three decimal places).

2. A surveyor running a line due west, alters his direction to N.W. at a point P. He continues N.W. to a point Q, x miles from P and then changes his direction so as to return to his original east and west line at R, the distance RP being y miles.

If y=2x, find the direction from Q to R to the nearest second.

3. Develop either one of the following formulae :

(b) sin(A+B)=sin A.cos B+cos A. sin B.

4. (a) Define a logarithm.

(b) Find the value of—

1st. log 625.

V5

2nd. I cosec 118° 19′ 18′′.

3rd. when I tan 0-7.90827.

(c) Find the number of digits in the integral part of

(1.037) 10000

(d) Find the number of ciphers between the decimal point and the first significant figure of (.8047) 100.

5. Find the value of K when:-

K='42089-3 +5

12843

+ 3

sin 18′ 18′′. 4

(*0482) tan 212° 17′ 36′′

6. Two vessels A and B leave a harbour at the same time. The course of A is W. 20° 18′ 14′′ S. and that of B is S.E. 5° 8′ 42′′ S. If the speeds of the vessels are 18.3 and 21.62 miles per hour, respectively, find their distance apart four hours after leaving port. (Use logarithms throughout and give the answers in miles correct to four decimal places). 7. Prove that:

FACULTY OF PRACTICAL SCIENCE.

GEOMETRY I.

Candidates may try either 6 or 8.

1. (a) Prove that similar triangles are to one another as the squares on homologous sides.

(b) Apply this to show that the ratio of the area of a circle to its diameter is a constant.

2. (a) A stream is 200' wide and the soundings taken every 40' are 0.0, 8.0, 10.5, 12.2, 9.8, 0.0. Find the area of the cross-section.

(b) Given a line of length a, construct the line of length a√5.

3. The diagonals of a field are 236' and 342'; they intersect at an angle of 60. Find the area of the field.

4. Prove that a triangular prism may be divided into three equal pyramids.

5. A steel tank in the form of the frustum of a cone is 10' high, the top is 16' in diameter, and the bottom of the frustum is 12' in diameter,; the bottom of the tank is a spherical cap which is 4' deep. The material used is 1⁄2" steel plate. Find the weight of the tank alone and also its capacity in cu. feet. (A cubic ft. steel weighs 490 lbs.)

6. State and prove Pappus' theorem for volumes formed by a moving area, and apply it to find the centre of gravity of a semicircle.