Home/ECAT/ECAT Mathematics Vectors Chapter Online Test

ECAT Mathematics Vectors Chapter Online Test

Danial MalikLast Updated: April 18, 2025

ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

Total Questions:	50
Time Allowed:	20 Minutes
Total Marks:	50
How to Attempt Test:	Please choose the right Option in MCQ-type question.
Test Helpful For:	ECAT Entry Test Mathematics Online Test Interview Questions about Mathematics All Universities Entrance Test Recruitments Tests

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1. The vector quantity in the following is

Energy

Impulse

Distance

Temperature

2. The line through the center and perpendicular to the transverse axis is called the

Major axis

Conjugate axis

Focal axis

Minor axis

3. A vector of magnitude zero is called

Null vector

Position vector

Free vector

None of these

4. The cosine of the angle between the vector a and b where a = I + 2j – k , b = -I + j – 2k is

√3/2

1/√2

6. The scalar quantity in the following is

Time

Velocity

Force

Displacement

7. If V = [2, 1, 3] and w = [–1, 4, 0] then |V – 2w| =

√74

√89

√76

8. The scalar quantity in the following is

Density

Velocity

Displacement

Force

9. If u = [3, -4], then {u} = ?

√2

10. The conic is a parabola if

None of these

e = 1

e < 1

e > 1

11. The direction cosines of y-axis are

1, 1, 1

1, 0, 0

0, 0, 1

0, 1, 0

12.

13. The projection of a = i – 2j + k along b = 4i – 4j + 7k is

19/8

19/9

9/19

8/19

14. The modulus of the sum of three mutually perpendicular unit vectors is

√3

15. The area of a parallelogram whose adjacent sides are represented by 3i k and I + 2j is

½ √14

√41

½ √17

16. The set R³ = {x, y, z): x, y, zε R} is called the

3 – dimensional space

None of these

One – dimensional

2 – dimensional space

17. 3j . k x i

18. The locus of the point of intersection of tangents to an ellipse at two points, sum of whose eccentric angles is constant is

A st. line

A circle

An ellipse

A parabola

19. The scalar quantity in the following is

Velocity

Pressure

Force

Acceleration

20. The value of 3j. (^k + ^i) = ?

None of these

21. The perpendicular bisector of any chord of a circle

May or may not pass through the center of the circle

None of these

Passes through the center of the circle

Does not pass through the center of the circle

22. An example of scalar quantity is

Force

Acceleration

Velocity

Energy

23. A force f = 2i + 4j - 2k is applied at P(2, 3, -1) its moment about A(1, 0, 3) is as coterminous edges is

24.

25. A vector with magnitude one is called

Constant vector

Zero vector

Null vector

Unit vector

Page 2 of 2

26. If the vector 2i + 4j – 7k and 2i + 6j + xk are perpendicular then x = ?

27. If the distance of a point on the ellipse x²/6 + y²/2 = 1 from the center is 2, then the eccentric angle is

π/2

π/3

π/4

π/6

28. The vector quantity in the following is

Temperature

Distance

Energy

Angular acceleration

29. a x b = b x c = c x a if

a = b = c

Both b and c

a + b + c = 0

a = b + c

30. An example of scalar quantity is

Kinetic energy

Force

Weight

Acceleration

31. If the angle between two vectors with magnitude 6 and 2 is 60° then their scalar product is

32. The volume of the tetrahedron that has a = I + 2j + 3k, b = 3i + j + 2k and c = 2i + 3j + k as its vertices is

33.

34. If 1 and 1 are x and y –components of a vector, then its angle with x – axis is

45°

30°

90°

60°

35. An example of vector quantity is

Acceleration

Power

Energy

Work

36. The perimeter a triangle formed by 3i + 4j + 5k, 4i -3j -5k and 7i + j is

√50

200

√150

√450

37. The unit vector along z-axis is

k̂

None of these

38. The scalar quantity in the following is

Velocity

Speed

Torque

Force

39. An example of scalar quantity is

Acceleration

Velocity

Force

Power

40. The two different parts of the hyperbola are called its

Vertices

Nappes

Branches

Directrices

41.

42. A vector of magnitude 5 and perpendicular to a = i + 3j-k and b = 3i –j is

6/√17 (– i + 3j – 10k)

5/√17 (– i – 3j – 10k)

5/√110 (– i – 3j – 10k)

5/√17 (– i + 3j – 10k)

43. [k – i, i – j, j – k] = ?

-1

44. Which is not a vector

Displacement

Density

Weight

Electrified intensity

45. If a and b are two non – zero vectors the component of b along a is

√2/3

√3/2

2/3

None of these

46. The area enclosed by the triangle ABC whose vertices are A(1, 2, -3) B (0,0,0) and c (2, 4, 7) is

√676

√184

√845/2

47. If u = -I + 2j + 4k and V = 2i –j + 4k are two adjacent sides of a parallelogram then area of parallelogram is

√290

√279

√297

48. An example of vector quantity is

Power

Force

Work

Energy

49. The physical quantity which is completely specified by its magnitude only is called

Constant

Vector

Scalar

Variable

50. The magnitude of a vector can never be

Zero

None of these

Negative

Positive

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Danial MalikLast Updated: April 18, 2025

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ECAT Mathematics Vectors Chapter Online Test

ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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