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 ( int_0^1 x^5 (1-x)^6 dx )? |
| A. | ( frac{1}{12*11*10*9*8*7} ) |
| B. | ( frac{1}{12*11*10*9*8} ) |
| C. | ( frac{1}{12*11*10*9*8*7*6} ) |
| D. | ( frac{1}{12*11*10*9*8*7*6*5} ) |
| Answer» D. ( frac{1}{12*11*10*9*8*7*6*5} ) | |
| 2. |
What is the value of ( beta( frac{9}{2},3) )? |
| A. | ( frac{16}{1287} ) |
| B. | ( frac{16}{1278} ) |
| C. | ( frac{14}{1287} ) |
| D. | ( frac{16}{127} ) |
| Answer» B. ( frac{16}{1278} ) | |
| 3. |
What is the value of ( int_0^ (sech x)^5 dx )? |
| A. | ( frac{3 pi}{80} ) |
| B. | ( frac{3 pi}{240} ) |
| C. | ( frac{3 pi}{16} ) |
| D. | ( frac{ pi}{240} ) |
| Answer» D. ( frac{ pi}{240} ) | |
| 4. |
Solve using the Beta function. ( int_0^1 x^{-2} (1-x)^{-3} dx. ) |
| A. | Can be solved using a Beta function with m = -1 and n = -2 |
| B. | Can be solved using a Beta function with m = 1 and n = -2 |
| C. | Can be solved using a Beta function with m = -1 and n = 2 |
| D. | Can t be solved using the Beta function |
| Answer» E. | |
| 5. |
What is the value of ( int_0^1 frac{(y^5+y^2)}{(1+y)^9} dy )? |
| A. | ( frac{1}{158} ) |
| B. | ( frac{2}{167} ) |
| C. | ( frac{1}{146} ) |
| D. | ( frac{1}{168} ) |
| Answer» E. | |
| 6. |
What is the value of ( int_0^1 frac{dx}{ sqrt{1+x^4}} )? |
| A. | ( beta( frac{1}{4}, frac{1}{2}) ) |
| B. | ( frac{1}{4 sqrt{2}} beta( frac{1}{4}, frac{1}{2}) ) |
| C. | ( frac{1}{3 sqrt{2}} beta( frac{1}{3}, frac{1}{2}) ) |
| D. | ( frac{1}{4 sqrt{3}} beta( frac{1}{4}, frac{1}{3}) ) |
| Answer» C. ( frac{1}{3 sqrt{2}} beta( frac{1}{3}, frac{1}{2}) ) | |
| 7. |
What is the value of ( int_0^ frac{1}{(1+y)^5} dy )? |
| A. | <sup>1</sup> <sub>2</sub> |
| B. | <sup>1</sup> <sub>3</sub> |
| C. | <sup>1</sup> <sub>4</sub> |
| D. | <sup>1</sup> <sub>5</sub> |
| Answer» D. <sup>1</sup> <sub>5</sub> | |
| 8. |
What is the value of ( int_0^{ /2} sqrt{sin d } + int_0^{ /2} sqrt{cos d } )? |
| A. | (8 sqrt{ pi} frac{ Gamma( frac{3}{4})}{ Gamma( frac{1}{4})} ) |
| B. | (4 sqrt{ pi} frac{ Gamma( frac{3}{4})}{ Gamma( frac{1}{4})} ) |
| C. | (8 sqrt{ pi} frac{ Gamma( frac{1}{4})}{ Gamma( frac{3}{4})} ) |
| D. | (4 sqrt{ pi} frac{ Gamma( frac{1}{4})}{ Gamma( frac{3}{4})} ) |
| Answer» B. (4 sqrt{ pi} frac{ Gamma( frac{3}{4})}{ Gamma( frac{1}{4})} ) | |
| 9. |
What is the value of ( beta( frac{1}{4}, frac{3}{4}) )? |
| A. | ( pi ) |
| B. | ( sqrt{2} pi ) |
| C. | ( sqrt{2 pi} ) |
| D. | ({2} pi ) |
| Answer» C. ( sqrt{2 pi} ) | |
| 10. |
What is the value of (3,2)? |
| A. | ( frac{1}{14} ) |
| B. | ( frac{1}{16} ) |
| C. | ( frac{1}{12} ) |
| D. | ( frac{1}{10} ) |
| Answer» D. ( frac{1}{10} ) | |
| 11. |
What is the value of ( beta(m, frac{1}{2}) )? |
| A. | (m, m) |
| B. | 2<sup>2m-1</sup> (m, m) |
| C. | 2<sup>2m+1</sup> (m, m) |
| D. | 2<sup>2m</sup> (m, m) |
| Answer» C. 2<sup>2m+1</sup> (m, m) | |
| 12. |
Which of the following is not the definition of Beta function? |
| A. | ( beta(m, n) = 2 int_0^1 x^{m-1} (1-x)^{n-1} dx (m>0, n>0) ) |
| B. | ( beta(m, n) = 2 int_0^{ /2}(sin u2061 )^{2m-1} (cos u2061 )^{2n-1} d ) |
| C. | ( beta(m, n) = int_0^ frac{y^{n+1}}{(1+y)^{m+n}} dy ) |
| D. | ( beta(m, n) = int_0^1 frac{x^{m-1}+x^{n-1}}{(1+x)^{m+n}} dx ) |
| Answer» B. ( beta(m, n) = 2 int_0^{ /2}(sin u2061 )^{2m-1} (cos u2061 )^{2n-1} d ) | |
| 13. |
Which of the following function is not called the Euler s integral of the first kind? |
| A. | ( beta(m, n) = int_0^1 x^{m-1} (1-x)^{n-1} dx (m>0, n>0) ) |
| B. | ( beta(m, n) = int_0^{ /2} (sin u2061 )^{2m-1} (cos u2061 )^{2n-1} d ) |
| C. | ( beta(m, n) = int_0^ frac{y^{n+1}}{(1+y)^{m+n}} dy ) |
| D. | ( beta(m, n) = 2 int_0^{ /2} (sin )^{2m-1} (cos u2061 )^{2n-1} d ) |
| Answer» C. ( beta(m, n) = int_0^ frac{y^{n+1}}{(1+y)^{m+n}} dy ) | |
| 14. |
(m, n) = (n, m). Is the statement true? |
| A. | True |
| B. | False |
| Answer» B. False | |