1. Find the area of the quadrilateral whose vertices are (-1,6), (-3,-9), (5,-8), and (3,9).
2. If the lines x+y+2 = 0, 2x-y+3 = 0 and x+my-3 = 0 are concurrent, find the value of m.
3. If sinθ = cosθ where θ is an acute angle, find the value of
4. A light-house was observed from two points in a line with it, but on opposite sides of it. The distance between the points is 120 meters. If the angle of elevation are 30° and 45°, find the height of the light-house.
5. The scores of a batsman are 38, 70, 48, 34, 42, 56. Find the Standard deviation.
6. Two dices are thrown. What is the probability of getting the same number on both the dices or the total of the number on the faces being 9?
7. A hollow cylinder has a total surface area of 1320 square centimeters. If its internal diameter is 8 centimeters and height is 7 centimeters, find its external radius.
8. A semi-circular plate of tin has a diameter of 40 centimeters. It is made into an open conical vessel by bringing the radii together and soldering. Find the capacity of the vessel.
9. A cylindrical boiler 2 meters high and 3.5 meters in diameter has a hemispherical lid. Find the volume of the interior of the boiler including the part covered by the lid.
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