MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Ordinary Differential Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is the value of the integral \(\int_0^∞ \frac{1}{c^x} dx\)? |
| A. | \(\frac{1}{logc} \) |
| B. | \(\frac{2}{logc} \) |
| C. | \(\frac{\pi}{logc} \) |
| D. | \(\frac{1}{2logc} \) |
| Answer» B. \(\frac{2}{logc} \) | |
| 2. |
What is the value of \(\int_0^∞ \frac{1}{(1+x^4 )} dx\)? |
| A. | \(\frac{\sqrt{2} \pi}{4} \) |
| B. | \(\frac{\sqrt{3} \pi}{6} \) |
| C. | \(\frac{\sqrt{2} \pi}{6} \) |
| D. | \(\frac{\sqrt{3} \pi}{4} \) |
| Answer» B. \(\frac{\sqrt{3} \pi}{6} \) | |
| 3. |
\(\Gamma(m) * \Gamma(1-m) = \frac{\pi}{sin(m\pi)}\). Check if the statement is True or False? |
| A. | True |
| B. | False |
| Answer» B. False | |
| 4. |
What is the value of \(\int_0^∞ e^{-x^2} dx\)? |
| A. | \( \sqrt{\pi} \) |
| B. | \(\frac{\sqrt{\pi}}{\sqrt{2}} \) |
| C. | \(\frac{\sqrt{\pi}}{2} \) |
| D. | \(\frac{\pi}{2} \) |
| Answer» D. \(\frac{\pi}{2} \) | |
| 5. |
Is the given statement true or false?\(\displaystyle\beta(m, n) = \frac{\Gamma(m).\Gamma(n)}{\Gamma(m+n)}\) |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
What is the value of \(\Gamma\left(\frac{1}{2}\right)\)? |
| A. | \(\sqrt{\pi}\) |
| B. | \(\left(\frac{\sqrt{\pi}}{\sqrt{2}}\right)\) |
| C. | \(\left(\frac{\sqrt{\pi}}{2}\right)\) |
| D. | \(\frac{\pi}{2}\) |
| Answer» B. \(\left(\frac{\sqrt{\pi}}{\sqrt{2}}\right)\) | |
| 7. |
Gamma function is said to be as Euler’s integral of second kind. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 8. |
Which of the following is not a definition of Gamma function? |
| A. | \(\Gamma(n) = n!\) |
| B. | \(\Gamma(n) = \int_{0}^{\infty} x^{n-1} e^{-x}dx\) |
| C. | \(\Gamma(n+1) = n\Gamma(n)\) |
| D. | \(\Gamma(n) = \int_{0}^{1} log \left({1 \atop y}\right)^{n-1}\) |
| Answer» B. \(\Gamma(n) = \int_{0}^{\infty} x^{n-1} e^{-x}dx\) | |
| 9. |
Γ(n+1) = n! can be used when ____________ |
| A. | n is any integer |
| B. | n is a positive integer |
| C. | n is a negative integer |
| D. | n is any real number |
| Answer» C. n is a negative integer | |