Two houses are collinear with the base of a tower and are at distance 3 m and 12 m from the base of the tower. The angles of elevation from these two houses of the top of the tower are complementary. What is the height of the tower?

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2 .

A round balloon of unit radius subtends an angle of 90° at the eye of an observer standing at a point, say A. What is the distance of the centre of the balloon from the point A?

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3 .

If the area of a circle, inscribed in an equilateral triangle is 4$\pi$$cm^ 2$ , then what is the area of the triangle?

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4 .

The difference between the area of a square and that of an equilateral triangle on the same base is $1/over4$ $cm^ 2$ . What is the length of side of triangle?

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5 .

If the diameter of a wire is decreased by 10%, by how much per cent (approximately) will the length be increased to keep the volume constant?

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6 .

A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of C : H?

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7 .

In the given triangle, AB is parallel to PQ. AP = c, PC= b,PQ = a, AB= x. What is the value of x?

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8 .

What is the number of points in the plane of a $\Delta$ABC which are at equal distance from the vertices of the triangle?

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9 .

An obtuse angle made by a side of a parallelogram PQRS with other pair of parallel sides is 150°. If the perpendicular distance between these parallel sides (PQand SR) is 20 cm, what is the length of the side RQ?

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10 .

42 men take 25 days to dig a pond. If the pond would have to be dug in 14 days, then what is the number of men to be employed?

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