MCQOPTIONS
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MCQOPTIONS
This section includes 5 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. |
What is the value of integral \(∭_Re^{{(x^2+y^2+z^2)}^{\frac{3}{2}}} \,dx \,dy \,dz \) where R is the region given by x2+y2+z2≤1? |
| A. | \(\frac{4π(e-1)}{3}\) |
| B. | \(\frac{4π(e^3-1)}{3}\) |
| C. | \(\frac{4π(e^2+1)}{3}\) |
| D. | \(\frac{8π(e+1)}{3}\) |
| Answer» B. \(\frac{4π(e^3-1)}{3}\) | |
| 2. |
The volume of the region R defined by inequalities 0≤z≤1, 0≤y+z≤2,0≤x+y+z≤3 is given by ______ |
| A. | 4 |
| B. | 6 |
| C. | 8 |
| D. | 1 |
| Answer» C. 8 | |
| 3. |
If ∭R xyz dx dy dz is solved using cylindrical coordinate where R is the region bounded by the planes x=0, y=0, z=0, z=1 & x2+y2=1 then what is the value of that integral? |
| A. | 1/24 |
| B. | 1/16 |
| C. | 1/4 |
| D. | 1/2 |
| Answer» C. 1/4 | |
| 4. |
For the below mentione figure ,conversion from cartesian coordinate ∭R f(x,y,z)dx dy dz to spherical polar with coordinates p(r,θ,∅) is given by ______ |
| A. | ∭R* f(r,θ,∅) sinθ dr dθ d∅ |
| B. | ∭R* f(r,θ,∅) r2 dr dθ d∅ |
| C. | ∭R* f(r,θ,∅) r2 cosθ dr dθ d∅ |
| D. | ∭R* f(r,θ,∅) r2 sinθ dr dθ d∅ |
| Answer» E. | |
| 5. |
For the below-mentioned figure, conversion from cartesian coordinate ∭R f(x,y,z)dx dy dz to cylindrical polar with coordinates p(ρ,∅,z) is given by ______ |
| A. | ∭R* f(ρ,∅,z) ρ dρ d∅ dz |
| B. | ∭R f(ρ,∅,z) dρ d∅ dz |
| C. | ∭R*f(ρ,∅,z) ρ∅ dρ d∅ dz |
| D. | ∭R f(ρ,∅,z) ρ2 dρ d∅ dz |
| Answer» B. ∭R f(ρ,∅,z) dρ d∅ dz | |