MCQOPTIONS
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MCQOPTIONS
This section includes 48 Mcqs, each offering curated multiple-choice questions to sharpen your ENGINEERING SERVICES EXAMINATION (ESE) knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is the mixed triple product of three vectors? |
| A. | S.(PxQ) |
| B. | Sx(PxQ) |
| C. | S.(P.Q) |
| D. | Sx(P.Q) |
| Answer» B. Sx(PxQ) | |
| 2. |
The moment is the cross product of which two vectors? |
| A. | Force and Radius vectors |
| B. | Radius and Force vectors |
| C. | Force and Radius scalars |
| D. | Radius and Force scalars |
| Answer» C. Force and Radius scalars | |
| 3. |
The tendency of a force to rotate the body is called the moment of the force. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 4. |
The ___________ forces do not cause the rotation. |
| A. | Non-concurrent |
| B. | Concurrent |
| C. | Parallel |
| D. | Non-Parallel |
| Answer» C. Parallel | |
| 5. |
Which of them is not correct? |
| A. | j x j = 0 |
| B. | j x k = i |
| C. | j x i = k |
| D. | j x i = -k |
| Answer» D. j x i = -k | |
| 6. |
Which statement is true? (For three vectors P, Q and R) |
| A. | Associative law for cross product: (PxQ)xS = Px(QxS) |
| B. | Associative law for cross product: (PxQ)xS ≠ Px(QxS) |
| C. | Associative law for cross product: (PxQ)xS > Px(QxS) |
| D. | Associative law for cross product: (PxQ)xS < Px(QxS) |
| Answer» C. Associative law for cross product: (PxQ)xS > Px(QxS) | |
| 7. |
Which among the following is the distributive law for the cross product of three vectors? |
| A. | Px(Q+S) = (PxQ) + (PxS) |
| B. | Px(QxS) = (PxQ) + (PxS) |
| C. | Px(QxS) = (PxQ) x (PxS) |
| D. | Px(Q+S) = (PxQ) + (QxS) |
| Answer» B. Px(QxS) = (PxQ) + (PxS) | |
| 8. |
Commutative law is valid for the cross product of two vectors. (Commutative law: PxQ = QxP; for two vectors P and Q) |
| A. | True |
| B. | False |
| Answer» C. | |
| 9. |
Mathematically, for two vectors A and B of any magnitude, the cross product of both, i.e. AxB = given by: |
| A. | |A||B|sinØ |
| B. | |A||B| |
| C. | |A||B|cosØ |
| D. | |A||B|sin(180°+Ø) |
| Answer» B. |A||B| | |
| 10. |
What is the dot product of two vectors which are having a magnitude equal to unity and are making an angle of 45°? |
| A. | 0.707 |
| B. | -0.707 |
| C. | 1.414 |
| D. | -1.414 |
| Answer» B. -0.707 | |
| 11. |
What is (AxB).(BxA); or A = A1i + A2j + A3k and B = B1i + B2j + B3k? |
| A. | 0 |
| B. | A1B1A2B2i + A2B2A3B3j + A3B3A1B1k |
| C. | A1B1A1B2i + A2B2A3B2j + A3B3A1B3k |
| D. | A1B1A2B1i + A2B2A2B3j + A3B3A2B1k |
| Answer» B. A1B1A2B2i + A2B2A3B3j + A3B3A1B1k | |
| 12. |
What is multiplication law? |
| A. | A.B =B.A |
| B. | a(A.B) = A.(aB) |
| C. | A.(B+D) = (A.B) + (A.D) |
| D. | a(A.B) = AxB |
| Answer» C. A.(B+D) = (A.B) + (A.D) | |
| 13. |
What is Distributive law? |
| A. | A.B =B.A |
| B. | A.B =B.A |
| C. | A.(B+D) = (A.B) + (A.D) |
| D. | a(A.B) = AxB |
| Answer» D. a(A.B) = AxB | |
| 14. |
Which statement is right? |
| A. | Communitive law: A.B =B.A |
| B. | Multiplicative law: a(A.B) = Ax(aB) |
| C. | Multiplicative law: A.(B+D) = (A.B) + (A.D) |
| D. | Communitive law: a(A.B) = A.(aB) |
| Answer» B. Multiplicative law: a(A.B) = Ax(aB) | |
| 15. |
For two vectors A and B, what is A.B (if they have angle α between them)? |
| A. | |A||B| cosα |
| B. | |A||B| |
| C. | √(|A||B|) cosα |
| D. | |A||B| sinα |
| Answer» B. |A||B| | |
| 16. |
Which statement is correct about the vector F? |
| A. | F= Fcos β + Fcos α + Fcosγ |
| B. | F= Fsin β + Fcos α + Fcosγ |
| C. | F= Fcos β + Fsin α + Fcosγ |
| D. | F= Fcos β + Fcos α + Fsinγ |
| Answer» B. F= Fsin β + Fcos α + Fcosγ | |
| 17. |
We can add the force vectors directly. But with dividing each by it’s magnitude first. |
| A. | True |
| B. | False |
| Answer» C. | |
| 18. |
What is the x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F? |
| A. | B |
| B. | C |
| C. | Fcosα |
| D. | Fcosβ |
| Answer» D. Fcosβ | |
| 19. |
What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)? |
| A. | B/F |
| B. | C/F |
| C. | A/F |
| D. | 1 |
| Answer» D. 1 | |
| 20. |
What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C? |
| A. | Square root of the squares each A, B and C |
| B. | Square of the squares each A, B and C |
| C. | Cube root of the squares each A, B and C |
| D. | Cube of the squares each A, B and C |
| Answer» B. Square of the squares each A, B and C | |
| 21. |
Which statement is right for force vector F = Ai + Bj + Ck? |
| A. | In rectangular components representation of any vector we have vector F = Ai + Bj + Ck |
| B. | In rectangular components representation of any vector we have vector F = Ax + By + Cz |
| C. | In rectangular components representation of any vector we have vector F = Fx + Fy + Fz |
| D. | In rectangular components representation of any vector we have vector F = Fi + Fj + Fk |
| Answer» D. In rectangular components representation of any vector we have vector F = Fi + Fj + Fk | |
| 22. |
If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by? |
| A. | Xi + Yj + Zk |
| B. | Yi + Xj + Zk |
| C. | Zi + Yj + Xk |
| D. | Zi + Xj + Yk |
| Answer» E. | |
| 23. |
If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector? |
| A. | B units |
| B. | A units |
| C. | C units |
| D. | Square root of a sum of squares of the three, i.e. A, B and C |
| Answer» B. A units | |
| 24. |
In right handed coordinate system which axis is considered to be positive? |
| A. | The thumb is z-axis, fingers curled from x-axis to y-axis |
| B. | The thumb is x-axis, fingers curled from z-axis to y-axis |
| C. | The thumb is y-axis, fingers curled from x-axis to z-axis |
| D. | The thumb is z-axis, fingers curled from y-axis to x-axis |
| Answer» B. The thumb is x-axis, fingers curled from z-axis to y-axis | |
| 25. |
A vector can always have_____________ |
| A. | Only one component along any of the axis |
| B. | Only two components along any of the axis |
| C. | Only three components along any of the axis |
| D. | A unit vector along the direction perpendicular to its direction |
| Answer» D. A unit vector along the direction perpendicular to its direction | |
| 26. |
Which is true for the vector provided the only position coordinates given? |
| A. | (Final position coordinates + initial positions coordinates) gives the vector form of the vector |
| B. | (Final position coordinates – initial positions coordinates) gives the vector form of the vector |
| C. | (Initial positions coordinates – Final position coordinates) gives the vector form of the vector |
| D. | (Initial positions coordinates + Final position coordinates) gives the vector form of the vector |
| Answer» C. (Initial positions coordinates – Final position coordinates) gives the vector form of the vector | |
| 27. |
What if we multiply a scalar to the unit vector? |
| A. | The direction will change accordingly |
| B. | The magnitude will change accordingly |
| C. | The magnitude will not change accordingly |
| D. | The direction will change by a factor of square root of the scalar |
| Answer» C. The magnitude will not change accordingly | |
| 28. |
What is the difference between a position vector and unit vector? |
| A. | Position vector has magnitude = 1 and direction, while the unit vector has magnitude = 0 and no direction |
| B. | Position vector has magnitude = 0 and direction, while unit vector has magnitude = 0 and no direction |
| C. | Position vector has some magnitude and direction, while the unit vector has magnitude = 0 and no direction |
| D. | Position vector has some magnitude and direction, while the unit vector has magnitude = 1 and a specified direction |
| Answer» E. | |
| 29. |
Three vectors emerging from a point are always in a single plane. |
| A. | True |
| B. | False |
| Answer» C. | |
| 30. |
Two vectors emerging from a point are always in a single plane. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 31. |
The value cos-1(-3/7) + cos-1(2/7) + cos-1(6/7) is ____________ |
| A. | 215.4˚ |
| B. | 273.4˚ |
| C. | 188.4˚ |
| D. | 219.4˚ |
| Answer» E. | |
| 32. |
A force vector is along 4i – 4k direction and has a magnitude 100N and another force vector is along 4i +2j -4k and has a magnitude of 120N. What is the resultant of both forces? |
| A. | 80i + 40j – 80k N |
| B. | 80i – 40j – 80k N |
| C. | 151i + 40j – 80k N |
| D. | 151i+ 40j – 151k N |
| Answer» E. | |
| 33. |
The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB? |
| A. | The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). It has a magnitude of 750N. Which is the best Cartesian representation of the vector AB? |
| B. | -557i – 482j + 139k N |
| C. | -557i + 482j – 139k N |
| D. | 557i – 482j – 139k N |
| Answer» B. -557i – 482j + 139k N | |
| 34. |
The coordinate of the Force vector AB is A (2, 0, 2) and B (-2, 3.46, 3). What are its directions? |
| A. | -0.742i + 0.643j + 0.186k |
| B. | 0.742i – 0.643j – 0.186k |
| C. | -0.742i – 0.643j + 0.186k |
| D. | -0.742i + 0.643j – 0.186k |
| Answer» B. 0.742i – 0.643j – 0.186k | |
| 35. |
What is the magnitude of the vector, 12i – 8j – 24k? |
| A. | 18 |
| B. | 28 |
| C. | 38 |
| D. | 48 |
| Answer» C. 38 | |
| 36. |
Express the vector in the Cartesian Form, if the angle made by it with y and z axis is 60˚ and 45˚ respectively. Also, it makes an angle of α with the x-axis. The magnitude of the force is 200N. |
| A. | 100i + 100j + 141.4k N |
| B. | 100i – 100j + 141.4k N |
| C. | 100i + 100j – 141.4k N |
| D. | 100i – 100j – 141.4k N |
| Answer» B. 100i – 100j + 141.4k N | |
| 37. |
Every point on the force vector is having the same magnitude and the same direction as the whole force vector have. |
| A. | True |
| B. | False |
| Answer» C. | |
| 38. |
The resultant of three equal vectors having mutual angles being 120 degrees and being originated from a single point is zero. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 39. |
Force vector R is having a______________ |
| A. | Length of R and a specific direction |
| B. | Length of R |
| C. | A specific direction |
| D. | Length of magnitude equal to square root of R and a specific direction |
| Answer» B. Length of R | |
| 40. |
What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at the origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one? |
| A. | It is either in the 1st quadrant or in the 2nd quadrant |
| B. | It is either in the 1st quadrant or in the 3rd quadrant |
| C. | It is either in the 1st quadrant or in the 4th quadrant |
| D. | Only in the 1st quadrant |
| Answer» D. Only in the 1st quadrant | |
| 41. |
If two equal vector forces are mutually perpendicular then the resultant force is acting at which angle as compared to one of the vector? |
| A. | 45 degree |
| B. | 90 degree |
| C. | 180 degree |
| D. | 0 degree |
| Answer» B. 90 degree | |
| 42. |
The magnitude of the resultant of the two vectors is always_____________ |
| A. | Greater than one of the vector’s magnitude |
| B. | Smaller than one of the vector’s magnitude |
| C. | Depends on the angle between them |
| D. | Axis we choose to calculate the magnitude |
| Answer» D. Axis we choose to calculate the magnitude | |
| 43. |
Dividing the X-axis component and the Y-axis component of the of the vector making an angle with Y-axis α will give us. |
| A. | Cot α |
| B. | Tan α |
| C. | Sec α |
| D. | 1 |
| Answer» C. Sec α | |
| 44. |
A force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as: |
| A. | Rcosine (α) and Rsine(α) |
| B. | Rcosine (180-α) and Rsine(α) |
| C. | Rcosine (180-α) and Rsine(180+α) |
| D. | Rcosine (α) and Rsine(180+α) |
| Answer» B. Rcosine (180-α) and Rsine(α) | |
| 45. |
All the vectors quantities obey: |
| A. | Parallelogram law of addition |
| B. | Parallelogram law of multiplication |
| C. | Parallelogram law of addition of square root of their magnitudes |
| D. | Parallelogram law of addition of square of their magnitudes |
| Answer» B. Parallelogram law of multiplication | |
| 46. |
If a vector is multiplied by a scalar: |
| A. | Then its magnitude is increased by the square root of that scalar’s magnitude |
| B. | Then its magnitude is increased by the square of that scalar’s magnitude |
| C. | Then its magnitude is increased by the amount of that scalar’s magnitude |
| D. | You cannot multiply the vector with a scalar |
| Answer» D. You cannot multiply the vector with a scalar | |
| 47. |
For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents: |
| A. | Their magnitude’s square and direction of the line of action respectively |
| B. | Their magnitude and direction of the line of action respectively |
| C. | Magnitude’s square root and direction of the line of action respectively |
| D. | Magnitude’s square and the ratio of their lengths respectively |
| Answer» C. Magnitude’s square root and direction of the line of action respectively | |
| 48. |
Which of the following statement is true? |
| A. | A scalar is any physical quantity that can be completely specified by its magnitude |
| B. | A vector is any positive or negative physical quantity that can be completely specified by its magnitude |
| C. | A scalar is any physical quantity that requires both a magnitude and a direction for its complete description |
| D. | A scalar is any physical quantity that can be completely specified by its direction |
| Answer» B. A vector is any positive or negative physical quantity that can be completely specified by its magnitude | |