MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 12 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. |
Let f(x)=\(\frac{ln(1-x)}{e^x}\). Find the third derivative at x = 0. |
| A. | 4 |
| B. | 1⁄3 |
| C. | Undefined |
| D. | 1⁄4 |
| Answer» C. Undefined | |
| 2. |
Find the value of S=\(\sum_{n=1}^\infty \frac{(-1)^{n+1} \times (2n-1)^3}{(2n-1)!}\) using nth derivatives. |
| A. | – 2 * sin(1) |
| B. | 3 * sin(1) |
| C. | 3 * cos(1) |
| D. | – 3 * cos(1) |
| Answer» B. 3 * sin(1) | |
| 3. |
Let f(x) = ln(x3 – 3x2 – 16x – 12) , then the 1729th derivative at x = 234 is? |
| A. | (1728!)\(\times(\frac{1}{228^{1729}}+\frac{1}{236^{1729}}+\frac{1}{235^{1729}})\) |
| B. | (-1728!)\(\times(\frac{1}{228^{1729}}+\frac{1}{236^{1729}}+\frac{1}{235^{1729}})\) |
| C. | (1728!)\(\times(\frac{1}{228^{1729}}+\frac{1}{236^{1728}}+\frac{1}{235^{1729}})\) |
| D. | (-1729!)\(\times(\frac{1}{228^{1729}}+\frac{1}{236^{1729}}+\frac{1}{235^{1729}})\) |
| Answer» B. (-1728!)\(\times(\frac{1}{228^{1729}}+\frac{1}{236^{1729}}+\frac{1}{235^{1729}})\) | |
| 4. |
Let g(x) = ln(x) ⁄ x – 1 Then the hundredth derivative at x = 1 is? |
| A. | 100!⁄101 |
| B. | 99!⁄101 |
| C. | 101⁄100! |
| D. | 1⁄99! |
| Answer» B. 99!⁄101 | |
| 5. |
The first, second and third derivatives of a cubic polynomial f(x) at x = 1, are 13, 23 and 33 respectively. Then the value of f(0) + f(1) – 2f(-1) is? |
| A. | 76 |
| B. | 86 |
| C. | 126 |
| D. | 41.5 |
| Answer» E. | |
| 6. |
The following moves are performed on g(x).(i) Pick (x0, y0) on g(x) and travel toward the left/right to reach the y = x line. Now travel above/below to reach g(x). Call this point on g(x) as (x1, y1)(ii) Let the new position of (x0, y0)be (x0, y1)This is performed for all points on g(x) and a new function is got. Again these steps may be repeated on new function and another function is obtained. It is observed that, of all the functions got, at a certain point (i.e. after finite number of moves) the nth derivatives of the intermediate function are constant, and the curve passes through the origin. Then which of the following functions could be g(x) |
| A. | y = \(\sqrt{1 – x^2}\) |
| B. | xy3⁄2 + y = constant |
| C. | x9 y3⁄2 + y6 x3⁄2 = constant |
| D. | x7 y 8 + 4y = constant |
| Answer» E. | |
| 7. |
Let f(x) = x9 ex then the ninth derivative of f(x) at x = 0 is given by? |
| A. | 9! |
| B. | 9! * e9 |
| C. | 10! |
| D. | 21! |
| Answer» B. 9! * e9 | |
| 8. |
f(x) = \(\int_{0}^{\pi/2}sin(ax)da\) then the value of f(100)(0) is?a) a(100) sin(a)b) -a(100) sin(a)c) a(100) cos( |
| A. | a(100) sin(a) |
| B. | -a(100) sin(a) |
| C. | a(100) cos(a) |
| D. | 0 |
| Answer» E. | |
| 9. |
Let f(x) = ln(x2 + 5x + 6) then the value of f(30)(1) is given by? |
| A. | (29!)\((\frac{1}{3^{30}}+\frac{1}{4^{30}})\) |
| B. | (-29!)\((\frac{1}{3^{30}}+\frac{1}{4^{30}})\) |
| C. | (30!)\((\frac{1}{3^{30}}+\frac{1}{4^{30}})\) |
| D. | (-30!)\((\frac{1}{3^{30}}+\frac{1}{4^{30}})\) |
| Answer» C. (30!)\((\frac{1}{3^{30}}+\frac{1}{4^{30}})\) | |
| 10. |
Let f(x) = \(\frac{sin(x)}{x – 54}\), then the value of f(100)(54) is given by? |
| A. | Undefined |
| B. | 100 |
| C. | 10 |
| D. | 0 |
| Answer» B. 100 | |
| 11. |
The first and second derivatives of a quadratic Polynomial at x = 1 are 1 and 2 respectively. Then the value of f(1) – f(0) Is given by? |
| A. | 3⁄2 |
| B. | 1⁄2 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 12. |
The pth derivative of a qth degree monic polynomial, where p, q are positive integers and 2p4 + 3pq3⁄2 = 3q3⁄2 + 2qp3 is given by? |
| A. | Cannot be generally determined |
| B. | (q – 1)! |
| C. | (q)! |
| D. | (q – 1)! * pq |
| Answer» D. (q – 1)! * pq | |