MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Let f (x) = (x a) (x b) (x c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs? |
| A. | Both the roots in (a, b) |
| B. | At least one root in (a, b) and at least one root in (b, c) |
| C. | Both the roots in (b, c) |
| D. | Neither in (a, b) nor in (b, c) |
| Answer» C. Both the roots in (b, c) | |
| 2. |
Is Rolle s theorem valid for f(x) = x2 3x + 4 in the interval [1, 2]? |
| A. | Yes |
| B. | No |
| C. | Depends on x |
| D. | Data not sufficient |
| Answer» B. No | |
| 3. |
What will be the value of ( lim limits_{x rightarrow 1} x^{ frac{1}{1-x}} )? |
| A. | 1/e |
| B. | e |
| C. | 0 |
| D. | 1 |
| Answer» B. e | |
| 4. |
At which point does f(x) will attain local minima if f(x) = 0 x (t+1)(et 1)(t 2)(t + 4) dt? |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | -4 |
| Answer» C. 1 | |
| 5. |
If f(x) = |4x x2 3| when x [0, 4], then, which of the following is correct? |
| A. | x = 1 is the global maximum |
| B. | x = 2 is the global maximum |
| C. | x = 3 is the global maximum |
| D. | x = 0 is the global maximum |
| Answer» D. x = 0 is the global maximum | |
| 6. |
What is the value of ( )0 and 1 ? |
| A. | (0, 1) |
| B. | (1, 0) |
| C. | They are indeterminate form |
| D. | (1, 1) |
| Answer» D. (1, 1) | |
| 7. |
What will be the maximum area of an isosceles triangle inscribed in the ellipse x2/a2 + y2/b2 = 1 if its vertex at one end of the major axis? |
| A. | 3 3/4 ab sq units |
| B. | 3 3/2 ab sq units |
| C. | 3/2 ab sq units |
| D. | 3/4 ab sq units |
| Answer» B. 3 3/2 ab sq units | |
| 8. |
f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, -2 2 f(x) dx = -1348/15. Then what is the value of f(x)? |
| A. | x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x 55 |
| B. | x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x + 55 |
| C. | x<sup>4</sup> 8x<sup>3</sup> 22x<sup>2</sup> 24x 55 |
| D. | Data not sufficient |
| Answer» B. x<sup>4</sup> 8x<sup>3</sup> + 22x<sup>2</sup> 24x + 55 | |