HEC USAT-E (Pre-Engineering) Mathematics: Past Papers MCQs with Answers

Practise HEC USAT-E (Pre-Engineering) Mathematics past papers MCQs in sets of about 20 questions with instant answers and explanations. This page focuses on …

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HEC USAT-E (Pre-Engineering) Mathematics Past Papers sample MCQs

  1. Q1. Directrix of parabola x² = 12y is:

    • A) y = 3
    • B) y = -3
    • C) x = 3
    • D) x = -3

    Answer: y = -3

  2. Q2. Simplify the expression sin(π - x).

    • A) sin(x)
    • B) -sin(x)
    • C) cos(x)
    • D) -cos(x)

    Answer: sin(x)

  3. Q3. If x = 3/4 and y = 2/3, then x + y is?

    • A) 17/12
    • B) 5/7
    • C) 1/2
    • D) 3/2

    Answer: 17/12

  4. Q4. The range of y = sin(x) is

    • A) (-∞, ∞)
    • B) [-1, 1]
    • C) [0, 1]
    • D) (-1, 1)

    Answer: [-1, 1]

  5. Q5. The function f(x) = tan(x) is periodic with period

    • A) π
    • B) 2π
    • C) π/2
    • D) 3π/2

    Answer: π

  6. Q6. Cross product i × j = ?

    • A) k
    • B) -k
    • C) i
    • D) j

    Answer: k

  7. Q7. If sin(θ) = 1/2, find the value of θ in degrees.

    • A) 30°
    • B) 45°
    • C) 60°
    • D) 90°

    Answer: 30°

  8. Q8. If y = sin(3x), find dy/dx

    • A) 3cos(3x)
    • B) cos(3x)
    • C) -3cos(3x)
    • D) -cos(3x)

    Answer: 3cos(3x)

  9. Q9. A ladder is leaning against a wall, making an angle of 45° with the ground. If the length of the ladder is 10√2 m, find the height of the wall.

    • A) 10 m
    • B) 20 m
    • C) 15 m
    • D) 25 m

    Answer: 10 m

  10. Q10. What is the value of tan(60°)?

    • A) √3
    • B) 1/√3
    • C) 1
    • D) 2

    Answer: √3

  11. Q11. The angle of depression from the top of a cliff to a boat is 45°. If the height of the cliff is 100 m, find the distance between the cliff and the boat.

    • A) 100 m
    • B) 50 m
    • C) 200 m
    • D) 150 m

    Answer: 100 m

  12. Q12. A 1.8 m tall man is standing at some distance from a 31.8 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

    • A) 20√3 m
    • B) 30 m
    • C) 20 m
    • D) 57.6 / √3 m

    Answer: 57.6 / √3 m

  13. Q13. The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

    • A) 6 m
    • B) 5 m
    • C) 7 m
    • D) 8 m

    Answer: 6 m

  14. Q14. A tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle 30° with it. The distance between the foot of the tree to the point where the top touches the ground is 8 m. Find the height of the tree.

    • A) 8√3 m
    • B) 8 / √3 m
    • C) 16 m
    • D) 8 m

    Answer: 8√3 m

  15. Q15. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, find the height of the wall.

    • A) 15√3 / 2 m
    • B) 7.5 m
    • C) 15 / 2 m
    • D) 7.5√3 m

    Answer: 15 / 2 m

  16. Q16. The angle of elevation of a cloud from a point 60 m above a lake is 30° and the angle of depression of the reflection of the cloud in the lake is 60°. Find the height of the cloud.

    • A) 120 m
    • B) 60 m
    • C) 60√3 m
    • D) 120√3 m

    Answer: 120 m

  17. Q17. From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 20 m high building are 45° and 60° respectively. Find the height of the tower.

    • A) 20(√3 - 1) m
    • B) 20(√3 + 1) m
    • C) 14.64 m
    • D) 20 m

    Answer: 20(√3 - 1) m

  18. Q18. The angle of elevation of the top of a tower from a point 30 m away from its foot is 30°. Find the height of the tower.

    • A) 10√3 m
    • B) 30 / √3 m
    • C) 30√3 m
    • D) 17.32 m

    Answer: 10√3 m

  19. Q19. A 20m high building casts a shadow. If the sun's angle of elevation is 45°, find the shadow length.

    • A) 10 m
    • B) 20 m
    • C) 30 m
    • D) 40 m

    Answer: 20 m

  20. Q20. A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. 6 seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from the point where the angle of depression is 60°.

    • A) 3 seconds
    • B) 6 seconds
    • C) 9 seconds
    • D) 1 / 2 seconds

    Answer: 3 seconds

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