MCQOPTIONS
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MCQOPTIONS
This section includes 14 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 ( Gamma( frac{9}{4}) )? |
| A. | ( frac{5}{4} * frac{1}{4} * Gamma( frac{1}{4}) ) |
| B. | ( frac{9}{4} * frac{5}{4} * frac{1}{4} * Gamma( frac{1}{4}) ) |
| C. | ( frac{5}{4} * frac{1}{4} * Gamma( frac{5}{4}) ) |
| D. | ( frac{1}{4} * Gamma( frac{1}{4}) ) |
| Answer» B. ( frac{9}{4} * frac{5}{4} * frac{1}{4} * Gamma( frac{1}{4}) ) | |
| 5. |
What is the value of ( int_0^1 log(y)^8 dy )? |
| A. | 5! |
| B. | 6! |
| C. | 7! |
| D. | 8! |
| Answer» E. | |
| 6. |
What is the value of ( int_0^1 frac{x^2}{ sqrt{(1-x^4 )}} )? |
| A. | ( frac{2 sqrt{ pi} Gamma( frac{5}{4})}{ ( frac{1}{4})} ) |
| B. | ( frac{2 pi Gamma( frac{3}{4})}{ Gamma( frac{1}{4})} ) |
| C. | ( frac{2 sqrt{ pi} Gamma( frac{3}{4})}{ Gamma( frac{1}{4})} ) |
| D. | ( frac{2 sqrt{ pi} Gamma( frac{3}{4})}{ Gamma( frac{5}{4})} ) |
| Answer» D. ( frac{2 sqrt{ pi} Gamma( frac{3}{4})}{ Gamma( frac{5}{4})} ) | |
| 7. |
What is the value of the integral ( int_0^{ 2} sqrt{tan( ) } , d )? |
| A. | ( frac{ Gamma( frac{3}{4})^2}{ sqrt{ pi}} ) |
| B. | ( frac{ Gamma( frac{1}{4})^2}{ sqrt{ pi}} ) |
| C. | ( frac{ Gamma( frac{3}{4})^2}{ pi} ) |
| D. | ( frac{ Gamma( frac{1}{4})^2}{ pi} ) |
| Answer» B. ( frac{ Gamma( frac{1}{4})^2}{ sqrt{ pi}} ) | |
| 8. |
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} ) | |
| 9. |
What is the value of ( Gamma(5.5) )? |
| A. | ( displaystyle frac{11*9*7*5*3*1* sqrt{ pi}}{32} ) |
| B. | ( displaystyle frac{9*7*5*3*1* sqrt{ pi}}{32} ) |
| C. | ( displaystyle frac{9*7*5*3*1* sqrt{ pi}}{64} ) |
| D. | ( displaystyle frac{11*9*7*5*3*1* sqrt{ pi}}{64} ) |
| Answer» C. ( displaystyle frac{9*7*5*3*1* sqrt{ pi}}{64} ) | |
| 10. |
Is the given statement true or false?
|
| A. | True |
| B. | False |
| Answer» B. False | |
| 11. |
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) ) | |
| 12. |
Gamma function is said to be as Euler s integral of second kind. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 13. |
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 ) | |
| 14. |
(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 | |