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.
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1. The perpendicular bisector of any chord of a circle

May or may not pass through the center of the circle

Does not pass through the center of the circle

None of these

Passes through the center of the circle

2. The magnitude of a vector can never be

Positive

Zero

Negative

None of these

3. An example of vector quantity is

Force

Energy

Work

Power

4. A vector with magnitude one is called

Constant vector

Zero vector

Unit vector

Null vector

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

6. The vector quantity in the following is

Energy

Impulse

Distance

Temperature

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

√290

√297

√279

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

√845/2

√184

√676

10.

11. 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

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

13. [k – i, i – j, j – k] = ?

-1

14. 3j . k x i

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

√2

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

A parabola

A st. line

A circle

An ellipse

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

Directrices

Branches

Nappes

Vertices

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

√450

√150

200

√50

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

30°

90°

45°

60°

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

None of these

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

Focal axis

Conjugate axis

Minor axis

Major axis

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

√89

√76

√74

23. An example of scalar quantity is

Power

Velocity

Acceleration

Force

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

√41

½ √17

½ √14

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

5/√17 (– i + 3j – 10k)

6/√17 (– i + 3j – 10k)

5/√110 (– i – 3j – 10k)

5/√17 (– i – 3j – 10k)

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26.

27. The scalar quantity in the following is

Speed

Velocity

Torque

Force

28.

29. The scalar quantity in the following is

Velocity

Density

Force

Displacement

30. The vector quantity in the following is

Energy

Angular acceleration

Temperature

Distance

31. The unit vector along z-axis is

k̂

None of these

32. The scalar quantity in the following is

Displacement

Time

Force

Velocity

33. The conic is a parabola if

None of these

e > 1

e < 1

e = 1

34. The direction cosines of y-axis are

1, 0, 0

0, 1, 0

0, 0, 1

1, 1, 1

35. Which is not a vector

Density

Electrified intensity

Weight

Displacement

36. The scalar quantity in the following is

Acceleration

Velocity

Force

Pressure

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

√3

38.

39. a x b = b x c = c x a if

a = b + c

a = b = c

a + b + c = 0

Both b and c

40. An example of scalar quantity is

Kinetic energy

Force

Acceleration

Weight

41. A vector of magnitude zero is called

Free vector

None of these

Null vector

Position vector

42. 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

43. An example of scalar quantity is

Force

Velocity

Energy

Acceleration

44. 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/3

π/4

π/2

π/6

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

Constant

Variable

Scalar

Vector

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

19/9

8/19

19/8

9/19

47. An example of vector quantity is

Energy

Power

Work

Acceleration

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

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

2 – dimensional space

One – dimensional

3 – dimensional space

None of these

50. 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

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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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Danial Malik

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ECAT Math Vectors

ECAT Math Vectors Chapter Online Test

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