MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Fourier Analysis knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
What is the value of a0 if the function is f(x) = x3 in the interval 0 to 5? |
| A. | 25/4 |
| B. | 125/4 |
| C. | 625/4 |
| D. | 5/4 |
| Answer» D. 5/4 | |
| 2. |
In Parseval s formula for half range Fourier series, the formula contains l/2 multiplied with the square of individual coefficients. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 3. |
Find the value of ( frac{1}{1^4} + frac{1}{3^4} + frac{1}{5^4} + frac{1}{7^4} ) + .by finding the half range Fourier cosine series of the function f(x) = x in the interval 0<x<l. |
| A. | ( frac{ pi^4}{12} ) |
| B. | ( frac{ pi^4}{48} ) |
| C. | ( frac{ pi^4}{24} ) |
| D. | ( frac{ pi^4}{96} ) |
| Answer» E. | |
| 4. |
Find the value of ( frac{1}{1^2} + frac{1}{3^2} + frac{1}{5^2} + frac{1}{7^2} ) + .when finding the Half range Fourier sine series of the function f(x) = 1 in 0<x< . |
| A. | ( frac{ pi^2}{4} ) |
| B. | ( frac{ pi^2}{8} ) |
| C. | ( frac{ pi^2}{2} ) |
| D. | (3 frac{ pi^2}{8} ) |
| Answer» C. ( frac{ pi^2}{2} ) | |
| 5. |
In Parseval s relation of Half range Fourier cosine series expansion, which of the following terms doesn t appear? |
| A. | a<sub>0</sub> |
| B. | a<sub>n</sub> |
| C. | b<sub>n</sub> |
| D. | all terms appear |
| Answer» D. all terms appear | |
| 6. |
What is the formula for Parseval s relation in Fourier series expansion? |
| A. | ( int_{-l}^l (f(x))^2 dx=l[ frac{a_0^2}{2}+ _{n=1}^ (a_n^2+b_n^2 ) ] ) |
| B. | ( int_{-l}^l (f(x))^2 dx=l[ frac{a_0^2}{2}+ _{n=1}^ (a_n^2 ) ] ) |
| C. | ( int_{-l}^l (f(x))^2 dx=l 2 [ frac{a_0^2}{2}+ _{n=1}^ (a_n^2+b_n^2 ) ] ) |
| D. | ( l int_{-l}^l (f(x))^2 dx=[ frac{a_0^2}{2}+ _{n=1}^ (a_n^2+b_n^2 ) ] ) |
| Answer» B. ( int_{-l}^l (f(x))^2 dx=l[ frac{a_0^2}{2}+ _{n=1}^ (a_n^2 ) ] ) | |
| 7. |
Find bn when we have to find the half range sine series of the function x2 in the interval 0 to 3. |
| A. | -18 ( frac{cos(n )}{n } ) |
| B. | 18 ( frac{cos(n )}{n } ) |
| C. | -18 ( frac{cos(n pi 2)}{n } ) |
| D. | 18 ( frac{cos(n pi 2)}{n } ) |
| Answer» B. 18 ( frac{cos(n )}{n } ) | |
| 8. |
Find the half range sine series of the function f(x) = x, when 0<x< ( frac{ pi}{2} ) and ( -x) when ( frac{ pi}{2} )<x< . |
| A. | ( frac{8}{ pi}[ frac{sinx}{1^{2}} sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} sin frac{(7x)}{7^{2}} + ] ) |
| B. | ( frac{4}{ pi}[ frac{sinx}{1^{2}} + sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} + sin frac{(7x)}{7^{2}} + ] ) |
| C. | ( frac{8}{ pi}[ frac{sinx}{1^{2}} + sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} + sin frac{(7x)}{7^{2}} + ] ) |
| D. | ( frac{4}{ pi}[ frac{sinx}{1^{2}} sin frac{(3x)}{3^{2}} + sin frac{(5x)}{5^2} sin frac{(7x)}{7^{2}} + ] ) |
| Answer» E. | |
| 9. |
In half range cosine Fourier series, we assume the function to be _________ |
| A. | Odd function |
| B. | Even function |
| C. | Can t be determined |
| D. | Can be anything |
| Answer» C. Can t be determined | |
| 10. |
In half range Fourier series expansion, we know the nature of the function in its full time period. |
| A. | True |
| B. | False |
| Answer» C. | |