MCQOPTIONS
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MCQOPTIONS
This section includes 8 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_G(X)_=_LN(X)_‚ÄÖ√Ñ√∂‚ÀÖ√Ñ‚ÀÖ√´_X_‚ÄÖ√Ñ√∂‚ÀÖ√Ë‚ÀÖ¬®_1_THEN_THE_HUNDREDTH_DERIVATIVE_AT_X_=_1_IS?$# |
| A. | <sup>100!</sup>‚ÅÑ<sub>101</sub> |
| B. | <sup>99!</sup>‚ÅÑ<sub>101</sub> |
| C. | <sup>101</sup>‚ÅÑ<sub>100!</sub> |
| D. | <sup>1</sup>‚ÅÑ<sub>99!</sub> |
| Answer» B. <sup>99!</sup>‚Äö√Ñ√∂‚àö√ñ‚àö√´<sub>101</sub> | |
| 2. |
The first, second and third derivatives of a cubic polynomial f(x) at x = 1 , are 13, 23 and 33 respectively. Then the value of f(0) + f(1) – 2f(-1) i?# |
| A. | 76 |
| B. | 86 |
| C. | 126 |
| D. | 41.5 |
| Answer» E. | |
| 3. |
The following moves are performed on g(x) |
| A. | Pick (x<sub>0</sub>, y<sub>0</sub>) on g(x) and travel toward the left/right to reach the y = x line. Now travel above/below to reach g(x). Call this point on g(x) as (x<sub>1</sub>, y<sub>1</sub>) |
| B. | Let the new position of (x<sub>0</sub>, y<sub>0</sub>)be (x<sub>0</sub>, y<sub>1</sub>) |
| C. | and a new function is got. Again these steps may be repeated on new function and another function is obtained. It is observed that, of all the functions got, at a certain point (i.e. after finite number of moves) the n<sup>th</sup> derivatives of the intermediate function are constant, and the curve passes through the origin. Then which of the following functions could be g(x) |
| D. | y = √1 – x<sup>2</sup> |
| Answer» E. | |
| 4. |
Let f(x) = x9 ex then the ninth derivative of f(x) at x = 0 is given by |
| A. | 9 |
| B. | 11 |
| C. | 10 |
| D. | 21 |
| Answer» B. 11 | |
| 5. |
f(x) = ∫0 π⁄2 sin(ax)da then the value of f(100)(0) is$ |
| 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. | |
| 6. |
Let f(x) = 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 | |
| 7. |
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>‚ÅÑ<sub>2</sub> |
| B. | <sup>1</sup>‚ÅÑ<sub>2</sub> |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 8. |
The pth derivative of a qth degree monic polynomial, where p, q are positive integers and 2p4 + 3pq3‚ÅÑ2 = 3q3‚ÅÑ2 + 2qp3 is given by |
| A. | Cannot be generally determined |
| B. | (q – 1)! |
| C. | (q)! |
| D. | (q – 1)! * p<sup>q</sup> |
| Answer» D. (q ‚Äö√Ñ√∂‚àö√ë‚àö¬® 1)! * p<sup>q</sup> | |