ECAT (Engineering College Admission) Mathematics: Practice MCQs with Answers

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Sample ECAT (Engineering College Admission) Mathematics practice 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. 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

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