MCQOPTIONS
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MCQOPTIONS
This section includes 7 Mcqs, each offering curated multiple-choice questions to sharpen your Differential and Integral Calculus Questions and Answers knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Which among the following is the definition of Jacobian of u and v w.r.t x and y? |
| A. | \(J(\frac{x,y}{u,v})\) |
| B. | \(J(\frac{u,v}{x,y})\) |
| C. | \(\frac{∂(x,y)}{∂(u,v)} \) |
| D. | \(\frac{∂(u,x)}{∂(v,y)}\) |
| Answer» C. \(\frac{∂(x,y)}{∂(u,v)} \) | |
| 2. |
If u+v=ex cosy and u-v=ex sin y the value of \(J(\frac{u,v}{x,y})\) is ________ |
| A. | e2x |
| B. | \(\frac{e^2x}{2} \) |
| C. | \(\frac{-e^2x}{2} \) |
| D. | 0 |
| Answer» D. 0 | |
| 3. |
The application of Jacobians is significant in the evaluation of double integral of the form ∬f(x,y) dx dy and triple integral of the form ∭f(x,y,z)dx dy dz by transformation from one system of coordinate to the other. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 4. |
If x=rcosθ, y=rsinθ then the value of \(\frac{∂(x,y)}{∂(r,θ)}\) is ________ |
| A. | 1 |
| B. | 0 |
| C. | r |
| D. | \(\frac{1}{r}\) |
| Answer» D. \(\frac{1}{r}\) | |
| 5. |
If u=x+3y2-z3, v=4x2 yz, w=2z2-xy then \(\frac{∂(u,v,w)}{∂(x,y,z)} \) at (1,1,1). |
| A. | -184 |
| B. | -90 |
| C. | 20 |
| D. | 40 |
| Answer» B. -90 | |
| 6. |
Given \(u=\frac{yz}{x}, v=\frac{zx}{y}, w=\frac{xy}{z}\) then the value of \(\frac{∂(u,v,w)}{∂(x,y,z)}\) is ________ |
| A. | 4 |
| B. | -4 |
| C. | 0 |
| D. | 1 |
| Answer» B. -4 | |
| 7. |
The jacobian of p,q,r w.r.t x,y,z given p=x+y+z, q=y+z, r=z is ________ |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» C. 2 | |