MCQOPTIONS
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MCQOPTIONS
This section includes 11 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. | <sup>1</sup> <sub>3</sub> |
| C. | Undefined |
| D. | <sup>1</sup> <sub>4</sub> |
| 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. | <sup>100!</sup> <sub>101</sub> |
| B. | <sup>99!</sup> <sub>101</sub> |
| C. | <sup>101</sup> <sub>100!</sub> |
| D. | <sup>1</sup> <sub>99!</sub> |
| Answer» B. <sup>99!</sup> <sub>101</sub> | |
| 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. |
Let f(x) = x9 ex then the ninth derivative of f(x) at x = 0 is given by? |
| A. | 9! |
| B. | 9! * e<sup>9</sup> |
| C. | 10! |
| D. | 21! |
| Answer» B. 9! * e<sup>9</sup> | |
| 7. |
f(x) = ( int_{0}^{ pi/2}sin(ax)da ) then the value of f(100)(0) is? |
| A. | a<sup>(100)</sup> sin(a) |
| B. | -a<sup>(100)</sup> sin(a) |
| C. | a<sup>(100)</sup> cos(a) |
| D. | 0 |
| Answer» E. | |
| 8. |
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}}) ) | |
| 9. |
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 | |
| 10. |
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. | <sup>3</sup> <sub>2</sub> |
| B. | <sup>1</sup> <sub>2</sub> |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 11. |
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)! * p<sup>q</sup> |
| Answer» D. (q 1)! * p<sup>q</sup> | |