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1. Find the value of the crop of wheat in a field 3 furlongs long and 2 furlongs wide, yielding 31 bushels per acre, when wheat is at 33s. 9d. a quarter.

2. Find the H.C.F. and L.C.M. of

a + 3a3 - 14a2 - 8a - 12 and

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a11a3 +26a2 + 2a - 24.

154, (x+4y) (4x − y) = 336.

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5. A man walking along a tramway from the terminus. meets two cars A, B at 12.10 and 12.18, respectively. On their way back they overtake him at 12.24 and 12.48, respectively. They travel at the same uniform rate, and each waits three minutes at the terminus before starting back. Find when the man left the terminus.

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8. Two arithmetic means between a certain pair of numbers are found, and are as 9: 17. Find the ratio of the harmonic mean and the geometric mean between the same two numbers.

9. A square map is divided into four equal squares. In how many ways can these be wrongly put together so as still to form one square?

10. If x is positive and n a positive whole number, prove that

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1. Find a point P in a given straight line AB, such that the rectangle AB. PB = AP2.

2. Show how to describe a regular figure of ten sides in a given circle.

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3. Define duplicate ratio,' and 'similar figures.' Prove that similar polygons can be divided into the same number of similar triangles, and that the ratio of their areas is the duplicate of that of a pair of corresponding sides.

4. If four straight lines are proportional, prove that the rectangle under the extremes is equal to the rectangle under

the means.

If the bisector of the angle A of a triangle meets the opposite side BC in X, prove that

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5. Construct a right-angled triangle being given the length of one of the sides and the ratio of the other side to the hypotenuse.

6. Express the trignometrical ratios of 180° - A and - A in terms of those of 4, showing how the results are arrived at.


sin 240°, tan 300°, and cosec (-135°).

7. If A, B, C are the angles of a triangle, prove that
sin 24 + sin 2B + sin 2 C = 4 sin A. sin B. sin C.
sin 24 sin 2B + sin 2 C

as a similar continued product.

8. Express cos 44 in terms of sin 4. Prove that

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9. Write down the expression for cos A in a triangle in terms of a, b, c.

If a = 3/2, b = 2√3, c = 3√3, find the angles

A and B.

10. If D is a point in the side BC of a triangle such that BD: DC:: m : n, prove that

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Find the angle which the median to the base of a triangle makes with the base, being given that the base angles are 30° and 15°.




1. Define the terms 'mass,' 'force,' and 'acceleration.' What is the relation between these three quantities?

2. What is a fluid? State the principle of Archimedes, and apply it to find the weight that a balloon of volume V will carry when filled with a gas of density p, the density of the air at the balloon being σ. The volume of the load is supposed negligible in comparison with that of the balloon.

3. Describe the mercury and the aneroid barometer. Explain the action of each.

4. Explain how sound is (a) produced, (b) carried to the ear of the hearer.

How might your explanations be verified?

5. Describe some practical method of finding the pitch of a note.

6. Describe a sonometer, and explain how it may be used to verify the formula

1 T

n =

21 m

What do the letters in the above formula mean?

7. Describe any form of photometer and explain how to use it.

8. How may it be shown that light travels in straight lines?

Explain, by diagrams, the production of complete and partial shadows.

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Where must the object be placed with respect to a concave mirror that the image may be virtual?

10. What is meant by the minimum deviation produced by a prism?

How would you measure it?




1. Mention some of the substances commonly used in thermometry, and discuss their relative advantages.

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2. Explain the terms water-equivalent,'' relative humidity,' absolute temperature.'

3. What is meant by 'coefficient of expansion'? Describe a method of finding it for the case of a solid.,

4. Describe any method of finding the dew-point.

5. Give some methods of magnetizing a piece of iron.


6. By what experiments would you show that electricity generally resides on the outside of conductors? Mention any exceptions to this that you know of.

Where do

7. Describe any form of electrical condenser. you consider the energy of a charged condenser to reside?

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8. When is a battery said to be polarized'? Describe one means of avoiding this defect.

9. Give the meaning of the terms-' ohm,' ' volt,'' ampère.' What is the connexion between them in the case of a steady current?

10. Describe some experiment illustrating electrolysis.

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