MCQOPTIONS
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MCQOPTIONS
This section includes 14 Mcqs, each offering curated multiple-choice questions to sharpen your Signals & Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The Fourier transform of the signal te-t u(t) is _____________ |
| A. | ( frac{1}{1+ ^2} ) |
| B. | ( frac{-1}{1+ ^2} ) |
| C. | ( frac{1}{(1+j )^2} ) |
| D. | ( frac{1}{(1-j )^2} ) |
| Answer» D. ( frac{1}{(1-j )^2} ) | |
| 2. |
The Fourier transform of the signal te-3|t-1| is _____________ |
| A. | ( frac{6e^{-j }}{9+ ^2} frac{12j e^{-j }}{9+ ^2} ) |
| B. | ( frac{6e^{-j }}{9+ ^2} ) |
| C. | ( frac{12j e^{-j }}{9+ ^2} ) |
| D. | ( frac{6e^{-j }}{9+ ^2} + frac{12j e^{-j }}{9+ ^2} ) |
| Answer» B. ( frac{6e^{-j }}{9+ ^2} ) | |
| 3. |
The Fourier transform of the signal e-t+2 u (t-2) is ___________ |
| A. | ( frac{e^{-2j }}{1-2 } ) |
| B. | ( frac{e^{2j }}{1+2 } ) |
| C. | ( frac{e^{-2j }}{1+2 } ) |
| D. | ( frac{e^{2j }}{1-2 } ) |
| Answer» D. ( frac{e^{2j }}{1-2 } ) | |
| 4. |
The inverse Laplace transform of F(s) = ( frac{e^{-3s}}{s(s^2+3s+2)} ) is ______________ |
| A. | {0.5 + 0.5e<sup>-2(t+3)</sup>-e<sup>-(t+3)</sup>} u (t+3) |
| B. | {0.5 + 0.5e<sup>-2(t-3)</sup>-e<sup>-(t-3)</sup>} u (t-3) |
| C. | {0.5 0.5e<sup>-2(t-3)</sup>-e<sup>-(t-3)</sup>} u (t-3) |
| D. | 0.5 + 0.5e<sup>-2t</sup>-e<sup>-t</sup>) |
| Answer» C. {0.5 0.5e<sup>-2(t-3)</sup>-e<sup>-(t-3)</sup>} u (t-3) | |
| 5. |
The Laplace transform of the function 6e5tcos(2t) e7t is ______________ |
| A. | ( frac{6(s-5)}{(s-5)^2+4} frac{1}{s-7} ) |
| B. | ( frac{6(s-5)}{(s-5)^2+4} + frac{1}{s-7} ) |
| C. | ( frac{6(s+5)}{(s+5)^2+4} frac{1}{s-7} ) |
| D. | ( frac{6(s+5)}{(s+5)^2+4} + frac{1}{s-7} ) |
| Answer» B. ( frac{6(s-5)}{(s-5)^2+4} + frac{1}{s-7} ) | |
| 6. |
A band pass signal extends from 1 KHz to 2 KHz. The minimum sampling frequency that is needed to retain all information of the sampled signal is ___________ |
| A. | 1 KHz |
| B. | 2 KHz |
| C. | 3 KHz |
| D. | 4 KHz |
| Answer» C. 3 KHz | |
| 7. |
The Laplace transform of the function e-2tcos(3t) + 5e-2tsin(3t) is ____________ |
| A. | ( frac{(s+2)-15}{(s+2)^2-9} ) |
| B. | ( frac{(s+2)+15}{(s+2)^2-9} ) |
| C. | ( frac{(s+2)+15}{(s+2)^2+9} ) |
| D. | ( frac{(s+2)-15}{(s+2)^2+9} ) |
| Answer» D. ( frac{(s+2)-15}{(s+2)^2+9} ) | |
| 8. |
The inverse Laplace transform of F(s) = ( frac{2}{s+c}e^{-bs} ) is _____________ |
| A. | 2e<sup>-k (t+b)</sup> u (t+b) |
| B. | 2e<sup>-k (t-b)</sup> u (t-b) |
| C. | 2e<sup>k (t-b)</sup> u (t-b) |
| D. | 2e<sup>k (t-b)</sup> u (t+b) |
| Answer» C. 2e<sup>k (t-b)</sup> u (t-b) | |
| 9. |
The Inverse Fourier transform of the signal e-2| | is ____________ |
| A. | ( frac{2}{ (4+t^2)} ) |
| B. | ( frac{1}{2 (4+t^2)} ) |
| C. | ( frac{1}{ (4+t^2)} ) |
| D. | ( frac{1}{(4+t^2)} ) |
| Answer» B. ( frac{1}{2 (4+t^2)} ) | |
| 10. |
The Fourier transform of the signal e-4|t| is ____________ |
| A. | ( frac{8}{16+ ^2} ) |
| B. | ( frac{-8}{16+ ^2} ) |
| C. | ( frac{4}{16+ ^2} ) |
| D. | ( frac{-4}{16+ ^2} ) |
| Answer» B. ( frac{-8}{16+ ^2} ) | |
| 11. |
The Fourier transform of signal e-2t u(t-3) is ___________ |
| A. | ( frac{e^{-3(2-j )}}{2-j } ) |
| B. | ( frac{e^{-3(2+j )}}{2+j } ) |
| C. | ( frac{e^{3(2-j )}}{2-j } ) |
| D. | ( frac{e^{3(2+j )}}{2+j } ) |
| Answer» C. ( frac{e^{3(2-j )}}{2-j } ) | |
| 12. |
The input and output of an LTI system are x (t) = e-3t u (t) and y (t) = e-t u (t). The differential equation which characterizes the system is ___________ |
| A. | ( frac{dy(t)}{dt} + y(t) = frac{dx(t)}{dt} + 3x(t) ) |
| B. | ( frac{dy(t)}{dt} + 2y(t) = frac{dx(t)}{dt} + 3x(t) ) |
| C. | ( frac{dy(t)}{dt} y(t) = frac{dx(t)}{dt} + 3x(t) ) |
| D. | ( frac{dy(t)}{dt} 2y(t) = frac{dx(t)}{dt} + 3x(t) ) |
| Answer» B. ( frac{dy(t)}{dt} + 2y(t) = frac{dx(t)}{dt} + 3x(t) ) | |
| 13. |
Given, X (ej ) = ( frac{(b-a) e^{j }}{e^{-j2 }-(a+b) e^{j } + ab} ), |b|<1<|a|
|
| A. | b<sup>n</sup> u [n] + a<sup>n</sup> u [n-1] |
| B. | b<sup>n</sup> u [n] a<sup>n</sup> u [-n-1] |
| C. | b<sup>n</sup> u [n] + a<sup>n</sup> u [-n-1] |
| D. | b<sup>n</sup> u [n] a<sup>n</sup> u [n+1] |
| Answer» D. b<sup>n</sup> u [n] a<sup>n</sup> u [n+1] | |
| 14. |
The Fourier transform of u (t) is B (j ) and the Laplace transform of u (t) is A(s). Which of the following is correct? |
| A. | B(j ) = A(s) |
| B. | A(s) = ( frac{1}{s} ) but B(j ) ( frac{1}{j } ) |
| C. | A(s) ( frac{1}{s} ) but B(j ) ( frac{1}{j } ) |
| D. | A(s) ( frac{1}{s} ) but B(j ) = ( frac{1}{j } ) |
| Answer» C. A(s) ( frac{1}{s} ) but B(j ) ( frac{1}{j } ) | |