MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What will be the value of C if C the constant of the coefficient of the solution of the given equation (D + 1)2y = 0 given y = 2 loge 2 when x = loge 2 and y = (4/3) loge3 when x = loge3? |
| A. | 2 |
| B. | -2 |
| C. | -4 |
| D. | 4 |
| Answer» D. 4 | |
| 2. |
Which of the following is the valid differential equation x = a cos(αt + β)? |
| A. | d2x/dt2 – αx = 0 |
| B. | d2x/dt2 + αx = 0 |
| C. | d2x/dt2 – α2x = 0 |
| D. | d2x/dt2 + α2x = 0 |
| Answer» E. | |
| 3. |
What is the solution of the given equation (D + 1)2y = 0 given y = 2 loge 2 when x = loge 2 and y = (4/3) loge3 when x = loge3? |
| A. | y = 4xe-x |
| B. | y = 4xex |
| C. | y = -4xe-x |
| D. | y = -4xex |
| Answer» B. y = 4xex | |
| 4. |
What will be the general solution of the differential equation d2y/dx2 = e2x(12 cos3x – 5 sin3x)? (here, A and B are integration constant) |
| A. | y = ex sin3x + Ax + B |
| B. | y = e2x sin3x + Ax + B |
| C. | y = e2x sin3x + A |
| D. | Data inadequate |
| Answer» C. y = e2x sin3x + A | |
| 5. |
What will be the required solution of d2y/dx2 – 3dy/dx + 4y = 0? |
| A. | Ae-4x + Be-x |
| B. | Ae4x – Be-x |
| C. | Ae4x + Be-x |
| D. | Ae4x + Bex |
| Answer» D. Ae4x + Bex | |
| 6. |
If y = t(x) be a differentiable function ᵾ x € R, then which of the following is always true? |
| A. | d2y/dx2 – (dy/dx)3 = 0 |
| B. | d2y/dx2 + (dy/dx)3 d2x/dy2 = 0 |
| C. | d2y/dx2 – (dx/dy)3 = 0 |
| D. | d2y/dx2 + (dy/dx)3 = 0 |
| Answer» C. d2y/dx2 – (dx/dy)3 = 0 | |
| 7. |
What is thedifferential equation whose solution represents the family y = ae3x + bex? |
| A. | d2y/dx2 – 3dy/dx + 4y = 0 |
| B. | d2y/dx2 – 4dy/dx + 3y = 0 |
| C. | d2y/dx2 + 4dy/dx + 3y = 0 |
| D. | d2y/dx2 – 4dy/dx – 3y = 0 |
| Answer» C. d2y/dx2 + 4dy/dx + 3y = 0 | |
| 8. |
Which one of the following is correct if we differentiate the equation xy = aex + be-x two times? |
| A. | x(d2y/ dx) + 2(dy/dx) = xy |
| B. | x(d2y/ dx) – 2(dy/dx) = xy |
| C. | 3x(d2y/ dx) + 2(dy/dx) = xy |
| D. | x(d2y/ dx) + 2(dy/dx) = 2xy |
| Answer» B. x(d2y/ dx) – 2(dy/dx) = xy | |