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 scalar quantity in the following is

Displacement

Velocity

Force

Time

2. The scalar quantity in the following is

Force

Velocity

Acceleration

Pressure

3. The conic is a parabola if

e < 1

e > 1

e = 1

None of these

5. [k – i, i – j, j – k] = ?

-1

6. An example of scalar quantity is

Force

Acceleration

Weight

Kinetic energy

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

√41

½ √14

½ √17

8. An example of vector quantity is

Power

Work

Energy

Force

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

10.

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

Conjugate axis

Major axis

Minor axis

Focal axis

12. The direction cosines of y-axis are

0, 1, 0

0, 0, 1

1, 1, 1

1, 0, 0

13. The vector quantity in the following is

Distance

Temperature

Energy

Impulse

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

Constant

Scalar

Vector

Variable

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

Vertices

Branches

Directrices

Nappes

16. a x b = b x c = c x a if

Both b and c

a = b = c

a + b + c = 0

a = b + c

17.

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

1/√2

√3/2

19. 3j . k x i

20. 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

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

√150

200

√50

√450

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

√279

√297

√290

23. The unit vector along z-axis is

k̂

None of these

24. The perpendicular bisector of any chord of a circle

None of these

Does not pass through the center of the circle

Passes through the center of the circle

May or may not pass through the center of the circle

25.

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26. An example of scalar quantity is

Velocity

Power

Force

Acceleration

27. The vector quantity in the following is

Distance

Angular acceleration

Energy

Temperature

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

2/3

√2/3

√3/2

None of these

29. A vector of magnitude zero is called

Free vector

None of these

Position vector

Null vector

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

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

None of these

32. A vector with magnitude one is called

Null vector

Constant vector

Zero vector

Unit vector

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

√74

√76

√89

34. 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

An ellipse

A circle

A parabola

35. The scalar quantity in the following is

Speed

Force

Velocity

Torque

36. 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/√17 (– i + 3j – 10k)

5/√110 (– i – 3j – 10k)

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

2 – dimensional space

None of these

One – dimensional

3 – dimensional space

38. 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/4

π/3

π/6

π/2

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

90°

60°

45°

30°

40. An example of vector quantity is

Energy

Work

Acceleration

Power

41. 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

√845/2

√184

42. Which is not a vector

Electrified intensity

Density

Weight

Displacement

43. The scalar quantity in the following is

Velocity

Density

Force

Displacement

44. An example of scalar quantity is

Energy

Acceleration

Velocity

Force

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

46. The magnitude of a vector can never be

Positive

None of these

Negative

Zero

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

9/19

19/8

19/9

8/19

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

√3

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

√2

50.

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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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