x, y be two acute angles, x + y < 90� and sin(2x - 20�) = cos(2y + 20�), the val

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x, y be two acute angles, x + y < 90� and sin(2x - 20�) = cos(2y + 20�), the value of tan(x + y) is
Options
A. ?3
B. 1/?3
C. 1
D. 2+?2

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Area problems

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1. In a circle, a diameter AB and a chord PQ (which is not a diameter) intersect each other at X perpendicularly. If AX : BX = 3 : 2 and the radius of the circle is 5 cm, then the length of chord PQ is
Options
A. 2?13 cm
B. 5?3 cm
C. 4?6 cm
D. 6?5 cm

3. In an isosceles triangle, the length of each equal side is twice the length of the third side. The ratio of areas of the isosceles triangle and an equilateral triangle with same perimeter is
Options
A. 30?5 : 100
B. 32?5 : 100
C. 36?5 : 100
D. 42?5 : 100

4. A piece of wire 132 cm long is bent successively in the shape of an equilateral triangle, a square and a circle. Then area will be longest in shape of
Options
A. Circle
B. Equilateral triangle
C. Square
D. Equal in all the shapes

5. The ratio between the area of a square and that of a circle, when the length of a side of the square is equal to that of the diameter of the circle, is (take ?=22/7)
Options
A. 14 : 11
B. 28 : 11
C. 7 : 22
D. 22 : 7

6. Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be
Options
A. 0.13 m
B. 0.4 m
C. 0.3 m
D. 0.41 m

7. The radii of two concentric circles are 68 cm and 22 cm. The area of the closed figure bounded by the boundaries of the circles is
Options
A. 4140? sq.cm.
B. 4110? sq.cm.
C. 4080? sq.cm.
D. 4050? sq.cm.

9. In a trapezium ABCD, AB and DC are parallel sides and ? ADC = 90�. If AB = 15 cm, CD = 40 cm and diagonal AC = 41 cm. Then the area of the trapezium ABCD is
Options
A. 245 cm2
B. 240 cm2
C. 247.5 cm2
D. 250 cm2

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