PAF Initial Test Mathematics: Most Important MCQs with Answers

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Sample PAF Initial Test Mathematics most important questions

1. Q1. A tower subtends an angle of 30° at a point on the same level as the foot of the tower. At a second point, h m above the first, the depression of the foot of the tower is 60°. The height of the tower is

   • A) h/3 m
   • B) 3h m
   • C) h m
   • D) h/2 m

   Answer: h/3 m

2. Q2. For the quadratic equation x² - 3x + 2 = 0, the sum of roots is?

   • A) 3
   • B) -3
   • C) 2
   • D) -2

   Answer: 3

3. Q3. Simplify: sin(3x)/sin(x) - cos(3x)/cos(x)

   • A) 2
   • B) -2
   • C) 1
   • D) -1

   Answer: 2

4. Q4. A tower stands at the center of a circular park. The angle of elevation of the top of the tower at a point on the circumference is 30°. If the radius is 100 m, find the height of the tower.

   • A) 100 / √3 m
   • B) 100√3 m
   • C) 50√3 m
   • D) 200 / √3 m

   Answer: 100 / √3 m

5. Q5. The angle of elevation of a cloud from a point 100 m above a lake is 30° and the angle of depression of its reflection is 60°. Find the height of the cloud.

   • A) 200 m
   • B) 100 m
   • C) 150 m
   • D) 250 m

   Answer: 200 m

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