MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is the area of a cardiod y = a(1+cosθ). |
| A. | \(\frac{3πa^2}{2} \) |
| B. | \(3πa^2 \) |
| C. | \(\frac{3πa^2}{4} \) |
| D. | \(\frac{3πa^2}{8} \) |
| Answer» B. \(3πa^2 \) | |
| 2. |
Calculate the area enclosed by parabolas x2 = y and y2 = x. |
| A. | \( \frac{1}{2} \) |
| B. | \( \frac{1}{3} \) |
| C. | \( \frac{1}{4} \) |
| D. | \( \frac{1}{6} \) |
| Answer» C. \( \frac{1}{4} \) | |
| 3. |
Evaluate the following integral by transforming into polar coordinates.\(\displaystyle\int_0^a \int_0^\sqrt{a^2-x^2} y\sqrt{x^2-y^2} dxdy \) |
| A. | \( \frac{a^4}{2} \) |
| B. | \( \frac{a^4}{3} \) |
| C. | \( \frac{a^4}{4} \) |
| D. | \( \frac{a^4}{5} \) |
| Answer» D. \( \frac{a^4}{5} \) | |
| 4. |
Evaluate \(\int_0^∞ \int_0^∞ e^{-(x^2+y^2 )} dxdy \) by changing into polar coordinates. |
| A. | \( \pi \) |
| B. | \( \frac{\pi}{2} \) |
| C. | \( \frac{\pi}{4} \) |
| D. | \( \frac{\pi}{8} \) |
| Answer» D. \( \frac{\pi}{8} \) | |
| 5. |
Evaluate ∫∫rsinθdrdθ over the cardiod r = a(1+cosθ) above the initial line. |
| A. | \(4 \frac{a^2}{3} \) |
| B. | \( \frac{a^2}{3} \) |
| C. | \(8 \frac{a^2}{3} \) |
| D. | \(4 \frac{a^2}{6} \) |
| Answer» B. \( \frac{a^2}{3} \) | |
| 6. |
Evaluate \(\int_0^∞ \int_0^{π/2} e^{-r^{2}} rdθdr \). |
| A. | \( \pi \) |
| B. | \( \frac{\pi}{2} \) |
| C. | \( \frac{\pi}{4} \) |
| D. | \( \frac{\pi}{8} \) |
| Answer» D. \( \frac{\pi}{8} \) | |
| 7. |
Evaluate ∫∫x2+y2 dxdy in the positive quadrant for which x+y |
| A. | \(\frac{1}{2} \) |
| B. | \(\frac{1}{3} \) |
| C. | \(\frac{1}{6} \) |
| D. | \(\frac{1}{12} \) |
| Answer» D. \(\frac{1}{12} \) | |
| 8. |
Evaluate ∫∫xy dxdy over the region bounded by x axis, ordinate x=2a and the curve x2=4ay. |
| A. | \(\frac{a^4}{3} \) |
| B. | \(\frac{a^4}{6} \) |
| C. | \(\frac{a^3}{3} \) |
| D. | \(\frac{a^2}{6} \) |
| Answer» B. \(\frac{a^4}{6} \) | |
| 9. |
Evaluate ∫xy dxdy over the positive quadrant of the circle x2+y2=a2. |
| A. | \(\frac{a^4}{8} \) |
| B. | \(\frac{a^4}{4} \) |
| C. | \(\frac{a^2}{8} \) |
| D. | \(\frac{a^2}{4} \) |
| Answer» B. \(\frac{a^4}{4} \) | |