HEC HAT-1 (Engineering / IT / Math / Physics) Quantitative Reasoning: Practice MCQs with Answers

HEC HAT-1 (Engineering / IT / Math / Physics) Quantitative Reasoning Practice sample MCQs

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. What is the latus rectum of the parabola y² = 8x?

   • A) 4
   • B) 8
   • C) 12
   • D) 16

   Answer: 8

3. Q3. Directrix of parabola x² = 12y is:

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

   Answer: y = -3

4. Q4. If sin^-1 (x) = π/6, then x is

   • A) 1/2
   • B) -1/2
   • C) 1
   • D) Not defined

   Answer: 1/2

5. Q5. If y = 1/x, then dy/dx = ?

   • A) -1/x²
   • B) 1/x²
   • C) -1/x
   • D) 1/x

   Answer: -1/x²

6. Q6. If f(x) = x²e^x, then f'(x) =

   • A) x²e^x + 2xe^x
   • B) x²e^x - 2xe^x
   • C) 2xe^x
   • D) x²e^x

   Answer: x²e^x + 2xe^x

7. Q7. Simplify the expression sin(π - x).

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

   Answer: sin(x)

8. Q8. 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

9. Q9. The number 121 is divisible by?

   • A) 3
   • B) 7
   • C) 11
   • D) 13

   Answer: 11

10. Q10. What is the magnitude of vector a = 3i - 4j + 12k?

    • A) 13
    • B) sqrt(109)
    • C) sqrt(13)
    • D) 14

    Answer: 13

11. Q11. For the equation 2x² - 3x + 1 = 0, the sum of the roots is

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

    Answer: 3 / 2

12. Q12. For the quadratic equation x² - 3x + 2 = 0, the sum of roots is?

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

    Answer: 3

13. Q13. The sum of the first n odd numbers is n². If the sum is 49, then n = ?

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

    Answer: 7

14. Q14. The range of y = sin(x) is

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

    Answer: [-1, 1]

15. Q15. The function f(x) = tan(x) is periodic with period

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

    Answer: π

16. Q16. Simplify: sin(3x)/sin(x) - cos(3x)/cos(x)

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

    Answer: 2

17. Q17. Cross product i × j = ?

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

    Answer: k

18. Q18. If a = (1, 2) and b = (3, -1), find a · b.

    • A) 5
    • B) 1
    • C) 2
    • D) 0

    Answer: 1

19. Q19. 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

20. Q20. 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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