MCQOPTIONS
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MCQOPTIONS
This section includes 15 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. |
The extreme value of the function f(x1, x2,….. xn)=\(\frac{x_1}{2^0}+\frac{x_2}{2^1}+……+\frac{x_n}{2^{n-1}}\) With respect to the constraint Σmi=1 (xi)2 = 1 where m always stays lesser than n and as m,n tends to infinity is? |
| A. | 1 |
| B. | \(\frac{2}{3\sqrt{3}}\) |
| C. | 2 |
| D. | 1 ⁄ 2 |
| Answer» C. 2 | |
| 2. |
The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid is? |
| A. | Increases |
| B. | Decreases |
| C. | Invariant |
| D. | The scaling of Astroid is irrelevant |
| Answer» B. Decreases | |
| 3. |
Consider the points closest to the origin on the planes x + y + z = a. |
| A. | The closest point travels farther as a is increased |
| B. | The closest point travels nearer as a is increased |
| C. | The closest point is independent of a as a is not there in the expression of the gradient. |
| D. | Varies as a2, away from the origin. |
| Answer» B. The closest point travels nearer as a is increased | |
| 4. |
Find the points on the plane x + y + z = 9 which are closest to origin. |
| A. | (3,3,3) |
| B. | (2,1,3) |
| C. | (2,2,2) |
| D. | (3,4,1) |
| Answer» B. (2,1,3) | |
| 5. |
Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region. |
| A. | Maximum value is invariant |
| B. | Maximum value decreases |
| C. | Maximum value increases and minimum value goes lesser |
| D. | minimum value goes higher |
| Answer» D. minimum value goes higher | |
| 6. |
Which one of these is the right formula for the Lagrange multiplier with more than one constraint? |
| A. | ∇f = (μ)2 * ∇g1 + ∇g2 |
| B. | Cannot be applied to more than one constraint function. |
| C. | ∇f = μ * ∇g1 + λ * ∇g2 |
| D. | ∇f = μ * ∇g1 + ∇g2 |
| Answer» D. ∇f = μ * ∇g1 + ∇g2 | |
| 7. |
Maximize the function x + y – z = 1 with respect to the constraint xy=36. |
| A. | 0 |
| B. | -8 |
| C. | 8 |
| D. | No Maxima exists |
| Answer» E. | |
| 8. |
In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function. |
| A. | True |
| B. | False |
| Answer» C. | |
| 9. |
The span of a Astroid is increased along both the x and y axes equally. Then the maximum value of: z = x + y along the Astroid |
| A. | Increases |
| B. | Decreases |
| C. | Invariant |
| D. | The scaling of Astroid is irrelevant |
| Answer» B. Decreases | |
| 10. |
Consider the points closest to the origin on the planes x + y + z =a. |
| A. | The closest point travels farther as <b>a</b> is increased |
| B. | The closest point travels nearer as <b>a</b> is increased |
| C. | The closest point is independent of <b>a</b> as <b>a</b> is not there in the expression of the gradient. |
| D. | Varies as <b>a<sup>2</sup></b>, away from the origin. |
| Answer» B. The closest point travels nearer as <b>a</b> is increased | |
| 11. |
Find the points on the plane x + y + z = 9 which are closest to origin. |
| A. | (3,3,3) |
| B. | (2,1,3) |
| C. | (2,2,2) |
| D. | (3,4,1) |
| Answer» B. (2,1,3) | |
| 12. |
Maximum value of a 3-d plane is to be found over a circular region. Which of the following happens if we increase the radius of the circular region. |
| A. | Maximum value is invariant |
| B. | Maximum value decreases |
| C. | Maximum value increases and minimum value goes lesser |
| D. | minimum value goes higher |
| Answer» D. minimum value goes higher | |
| 13. |
Which one of these is the right formula for the Lagrange multiplier with more than one constraint. |
| A. | ∇f = (μ)<sup>2</sup> * ∇<sub>g1</sub> + ∇<sub>g2</sub> |
| B. | Cannot be applied to more than one constraint function. |
| C. | ∇f = μ * ∇<sub>g1</sub> + λ * ∇<sub>g2</sub> |
| D. | ∇f = μ * ∇<sub>g1</sub> +∇<sub>g2</sub> |
| Answer» D. ‚Äö√Ñ√∂‚àö‚Ć‚àö¬∞f = ‚âà√≠¬¨‚à´ * ‚Äö√Ñ√∂‚àö‚Ć‚àö¬∞<sub>g1</sub> +‚Äö√Ñ√∂‚àö‚Ć‚àö¬∞<sub>g2</sub> | |
| 14. |
Maximize the function x + y – z = 1 with respect to the constraint xy=36.$ |
| A. | 0 |
| B. | -8 |
| C. | 8 |
| D. | No Maxima exists |
| Answer» E. | |
| 15. |
In a simple one-constraint Lagrange multiplier setup, the constraint has to be always one dimension lesser than the objective function. |
| A. | True |
| B. | False |
| Answer» C. | |