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. |
Consider the vertical cone. The minimum value of the function in the region f(x,y) = c is? |
| A. | constant |
| B. | 1 |
| C. | 0 |
| D. | -1 |
| Answer» B. 1 | |
| 2. |
f(x, y)=\(10y(10y-1)+(\frac{x^3sin(x^2)tan(x^3)}{(x-1)^3})-100y^2\). Find the critical points |
| A. | (0,0) |
| B. | (1,1) |
| C. | (2,22) |
| D. | None exist |
| Answer» E. | |
| 3. |
let s(1) be the set of all critical points of f1(x, y) = g1(x).g2(y) and s(2) be the set of critical points of f2(g1(x), g2(y)) Which of the following is the right relation between s(1) and s(2), given that minimum number of elements in s(1) is 2. |
| A. | s(1) = s(2) |
| B. | s(1) ≠ s(2) |
| C. | s(1) ∩ s(2) ≠ 0 |
| D. | depends on the functions |
| Answer» C. s(1) ∩ s(2) ≠ 0 | |
| 4. |
A man travelling onf(x, y) = sin(xy). His shadow passing through the origin in a straight line (sun travels with him overhead).What is the slope of the line travelling on which would lead him to the lowest elevation. |
| A. | There isn’t such a line |
| B. | 1 |
| C. | -1 |
| D. | .What is the slope of the line travelling on which would lead him to the lowest elevation.a) There isn’t such a lineb) 1c)-1d) 0 |
| Answer» B. 1 | |
| 5. |
The point (0,0) in the domain of f(x, y) = sin(xy) is a point of ___________ |
| A. | Saddle |
| B. | Minima |
| C. | Maxima |
| D. | Constant |
| Answer» E. | |
| 6. |
f(x, y) = sin(x).cos(y) Which of the following is a critical point? |
| A. | (Π⁄4, Π⁄4) |
| B. | (- Π⁄4, Π⁄4) |
| C. | (0, Π⁄2) |
| D. | (0, 0) |
| Answer» D. (0, 0) | |
| 7. |
The critical point exist for the function f(x, y) = xn + xn-1 y +……+yn at (0,0). |
| A. | True |
| B. | False |
| Answer» C. | |
| 8. |
Consider the f(x, y) = x2 + y2 – a. For what values of a do we have critical points for the function. |
| A. | independent of a |
| B. | for any real number except zero |
| C. | a ∊ (0, +∞) |
| D. | a ∊ (-1, 1) |
| Answer» B. for any real number except zero | |