ECAT (Engineering College Admission): Mathematics MCQs with Answers

Question 1

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

Accepted Answer

8

Answer

4

Answer

12

Answer

16

Question 2

If sin^-1 (x) = π/6, then x is

Accepted Answer

1/2

Answer

-1/2

Answer

1

Answer

Not defined

Question 3

If y = 1/x, then dy/dx = ?

Accepted Answer

-1/x²

Answer

1/x²

Answer

-1/x

Answer

1/x

Question 4

If f(x) = x²e^x, then f'(x) =

Accepted Answer

x²e^x + 2xe^x

Answer

x²e^x - 2xe^x

Answer

2xe^x

Answer

x²e^x

Question 5

The number 121 is divisible by?

Accepted Answer

11

Answer

3

Answer

7

Answer

13

Question 6

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

Accepted Answer

13

Answer

sqrt(109)

Answer

sqrt(13)

Answer

14

Question 7

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

Accepted Answer

3 / 2

Answer

-3 / 2

Answer

1 / 2

Answer

2 / 3

Question 8

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

Accepted Answer

7

Answer

5

Answer

6

Answer

8

Question 9

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

Accepted Answer

1

Answer

5

Answer

2

Answer

0

Question 10

The angle of elevation of a tower from a point on the ground is 30°. At a point on the horizontal line passing through the foot of the tower and 100 m nearer to the tower, the angle of elevation is found to be 60°. Find the height of the tower.

Accepted Answer

86.6 m

Answer

50√3 m

Answer

100√3 m

Answer

200 m

Question 11

A tower is 100√3 m high. Find the angle of elevation of its top when observed from a point 100 m away from its foot.

Accepted Answer

60°

Answer

45°

Answer

30°

Answer

90°

Question 12

The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.

Accepted Answer

16.67 m

Answer

50/3 m

Answer

25 m

Answer

30 m

Question 13

From the top of a 100 m high cliff, the angles of depression of two ships on the sea are 30° and 60°. If one ship is exactly behind the other on the same side of the cliff, find the distance between the ships.

Accepted Answer

115.47 m

Answer

100√3 / 3 m

Answer

200 / √3 m

Answer

230.94 m

Question 14

The angle of elevation of the top of a vertical tower from a point A on the ground is 60°. From a point B, 20 m vertically above A, the angle of elevation is 45°. Find the height of the tower.

Accepted Answer

47.32 m

Answer

30 + 10√3 m

Answer

20 + 20√3 m

Answer

60 m

Question 15

A tree is broken by the wind and its top touches the ground making an angle of 30° with the ground. If the length of the broken part is 20 m, find the height of the tree.

Accepted Answer

20(√3 + 1)/√3 m

Answer

30 m

Answer

20√3 m

Answer

10√3 m