MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Engineering Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Consider the curvature of the function f(x) = ex at x=0. The graph is scaled up by a factor of and the curvature is measured again at x=0. What is the value of the curvature function at x=0 if the scaling factor tends to infinity? |
| A. | a |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 2. |
The curvature function of some function is given to be k(x) = \(\frac{1}{[2+2x+x^2]^{\frac{3}{2}}}\) then which of the following functions could be f(x)? |
| A. | x2⁄2 + x + 101 |
| B. | x2⁄4 + 2x + 100 |
| C. | x2 + 13x + 101 |
| D. | x3 + 4x2 + 1019 |
| Answer» B. x2⁄4 + 2x + 100 | |
| 3. |
Given x = k1ea1t : y = k2ea2t it is observed that the curvature function obtained is zero. What is the relation between a1 and a2? |
| A. | a1 ≠ a2 |
| B. | a1 = a2 |
| C. | a1 = (a2)2 |
| D. | a2 = (a1)2 |
| Answer» C. a1 = (a2)2 | |
| 4. |
The curvature of a function depends directly on leading coefficient when x=0 which of the following could be f(x)? |
| A. | y = 323x3 + 4334x + 10102 |
| B. | y = x5 + 232x4 + 232x2 + 12344 |
| C. | y = ax5 + c |
| D. | y = 33x2 + 112345x + 8945 |
| Answer» E. | |
| 5. |
The curvature of the function f(x) = x3 – x + 1 at x = 1 is given by? |
| A. | ∣6⁄5∣ |
| B. | ∣3⁄5∣ |
| C. | \(\left |\frac{6}{5^{\frac{3}{2}}} \right |\) |
| D. | \(\left |\frac{3}{5^{\frac{3}{2}}} \right |\) |
| Answer» D. \(\left |\frac{3}{5^{\frac{3}{2}}} \right |\) | |
| 6. |
Let c(f(x)) denote the curvature function of given curve f(x). The value of c(c(f(x))) is observed to be zero. Then which of the following functions could be f(x). |
| A. | f(x) = x3 + x + 1 |
| B. | f(x)2 + y2 = 23400 |
| C. | f(x) = x19930 + x + 90903 |
| D. | No such function exist |
| Answer» C. f(x) = x19930 + x + 90903 | |
| 7. |
Find the curvature of the function f(x) = 3x3 + 4680x2 + 1789x + 181 at x = -520. |
| A. | 1 |
| B. | 0 |
| C. | ∞ |
| D. | -520 |
| Answer» C. ∞ | |
| 8. |
The curvature of a circle depends inversely upon its radius r. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 9. |
The curvature of the function f(x) = x2 + 2x + 1 at x = 0 is? |
| A. | 3⁄2 |
| B. | 2 |
| C. | \(\left |\frac{2}{5^{\frac{3}{2}}} \right |\) |
| D. | 0 |
| Answer» D. 0 | |
| 10. |
The curvature of a function f(x) is zero. Which of the following functions could be f(x)? |
| A. | ax + b |
| B. | ax2 + bx + c |
| C. | sin(x) |
| D. | cos(x) |
| Answer» B. ax2 + bx + c | |