MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics 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. |
If, A and B are arbitrary constants then what will be the differential equation of y = Ax + B/x? |
| A. | x<sup>2</sup> d<sup>2</sup> y/dx<sup>2</sup> xdy/dx + y = 0 |
| B. | x<sup>2</sup> d<sup>2</sup> y/dx<sup>2</sup> + xdy/dx + y = 0 |
| C. | x<sup>2</sup> d<sup>2</sup> y/dx<sup>2</sup> + xdy/dx y = 0 |
| D. | x<sup>2</sup> d<sup>2</sup> y/dx<sup>2</sup> xdy/dx y = 0 |
| Answer» D. x<sup>2</sup> d<sup>2</sup> y/dx<sup>2</sup> xdy/dx y = 0 | |
| 3. |
Which of the following is the valid differential equation x = a cos( t + )? |
| A. | d<sup>2</sup>x/dt<sup>2</sup> x = 0 |
| B. | d<sup>2</sup>x/dt<sup>2</sup> + x = 0 |
| C. | d<sup>2</sup>x/dt<sup>2</sup> <sup>2</sup>x = 0 |
| D. | d<sup>2</sup>x/dt<sup>2</sup> + <sup>2</sup>x = 0 |
| Answer» E. | |
| 4. |
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<sup>-x</sup> |
| B. | y = 4xe<sup>x</sup> |
| C. | y = -4xe<sup>-x</sup> |
| D. | y = -4xe<sup>x</sup> |
| Answer» B. y = 4xe<sup>x</sup> | |
| 5. |
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 = e<sup>x</sup> sin3x + Ax + B |
| B. | y = e<sup>2x</sup> sin3x + Ax + B |
| C. | y = e<sup>2x</sup> sin3x + A |
| D. | Data inadequate |
| Answer» C. y = e<sup>2x</sup> sin3x + A | |
| 6. |
What will be the required solution of d2y/dx2 3dy/dx + 4y = 0? |
| A. | Ae<sup>-4x</sup> + Be<sup>-x</sup> |
| B. | Ae<sup>4x</sup> Be<sup>-x</sup> |
| C. | Ae<sup>4x</sup> + Be<sup>-x</sup> |
| D. | Ae<sup>4x</sup> + Be<sup>x</sup> |
| Answer» D. Ae<sup>4x</sup> + Be<sup>x</sup> | |
| 7. |
If y = t(x) be a differentiable function x R, then which of the following is always true? |
| A. | d<sup>2</sup>y/dx<sup>2</sup> (dy/dx)<sup>3</sup> = 0 |
| B. | d<sup>2</sup>y/dx<sup>2</sup> + (dy/dx)<sup>3</sup> d<sup>2</sup>x/dy<sup>2</sup> = 0 |
| C. | d<sup>2</sup>y/dx<sup>2</sup> (dx/dy)<sup>3</sup> = 0 |
| D. | d<sup>2</sup>y/dx<sup>2</sup> + (dy/dx)<sup>3</sup> = 0 |
| Answer» C. d<sup>2</sup>y/dx<sup>2</sup> (dx/dy)<sup>3</sup> = 0 | |
| 8. |
What is the differential equation of all parabolas whose directrices are parallel to the x-axis? |
| A. | d<sup>3</sup>x/dy<sup>3</sup> = 0 |
| B. | d<sup>3</sup>y/(dx<sup>3</sup> + d<sup>2</sup>y/dx<sup>2</sup>) = 0 |
| C. | d<sup>3</sup>y/dx<sup>3</sup> = 0 |
| D. | d<sup>2</sup>y/dx<sup>2</sup> = 0 |
| Answer» D. d<sup>2</sup>y/dx<sup>2</sup> = 0 | |
| 9. |
What is thedifferential equation whose solution represents the family y = ae3x + bex? |
| A. | d<sup>2</sup>y/dx<sup>2</sup> 3dy/dx + 4y = 0 |
| B. | d<sup>2</sup>y/dx<sup>2</sup> 4dy/dx + 3y = 0 |
| C. | d<sup>2</sup>y/dx<sup>2</sup> + 4dy/dx + 3y = 0 |
| D. | d<sup>2</sup>y/dx<sup>2</sup> 4dy/dx 3y = 0 |
| Answer» C. d<sup>2</sup>y/dx<sup>2</sup> + 4dy/dx + 3y = 0 | |
| 10. |
Which one of the following is correct if we differentiate the equation xy = aex + be-x two times? |
| A. | x(d<sup>2</sup>y/ dx) + 2(dy/dx) = xy |
| B. | x(d<sup>2</sup>y/ dx) 2(dy/dx) = xy |
| C. | 3x(d<sup>2</sup>y/ dx) + 2(dy/dx) = xy |
| D. | x(d<sup>2</sup>y/ dx) + 2(dy/dx) = 2xy |
| Answer» B. x(d<sup>2</sup>y/ dx) 2(dy/dx) = xy | |