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 |
| 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 |
| 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. | a0 |
| B. | an |
| C. | bn |
| 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 \( \frac{cos(nπ)}{nπ} \) |
| B. | 18 \( \frac{cos(nπ)}{nπ} \) |
| C. | -18 \( \frac{cos(n \pi⁄2)}{nπ} \) |
| D. | 18 \( \frac{cos(n \pi⁄2)}{nπ} \) |
| Answer» B. 18 \( \frac{cos(nπ)}{nπ} \) | |
| 8. |
Find the half range sine series of the function f(x) = x, when 0 |
| 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. | |