1
GATE EE 2006
MCQ (Single Correct Answer)
+1
-0.3
$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency
$$\omega = 2\pi \left( {2k} \right)/T;\,\,k = 1,2,........$$ Also, no sine terms are present. Then $$x(t)$$ satisfies the equation
A
$$x\left( t \right) = - x\left( {t - T} \right)$$
B
$$x\left( t \right) = x\left( {T - t} \right) = - x\left( { - t} \right)$$
C
$$x\left( t \right) = x\left( {T - t} \right) = - x\left( {t - T/2} \right)$$
D
$$x\left( t \right) = x\left( {t - T} \right) = - x\left( {t - T/2} \right)$$
2
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
The RMS value of the voltage v(t) = 3 + 4cos(3t) is
A
$$\sqrt{17}\;V$$
B
5 V
C
7 V
D
$$\left(3\;+\;2\sqrt2\right)\;\mathrm V$$
3
GATE EE 2002
MCQ (Single Correct Answer)
+1
-0.3
Fourier Series for the waveform, $$f(t)$$ shown in Fig. is
A
$${8 \over {{\pi ^2}}}\left[ {\sin \left( {\pi t} \right) + {1 \over 9}\sin \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$
B
$${8 \over {{\pi ^2}}}\left[ {\sin \left( {\pi t} \right) - {1 \over 9}\cos \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$
C
$${8 \over {{\pi ^2}}}\left[ {\cos \left( {\pi t} \right) + {1 \over 9}\cos \left( {3\,\pi t} \right) + {1 \over {25}}\cos \left( {5\,\pi t} \right) + ........} \right]$$
D
$${8 \over {{\pi ^2}}}\left[ {\cos \left( {\pi t} \right) - {1 \over 9}\sin \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$
4
GATE EE 2002
MCQ (Single Correct Answer)
+1
-0.3
What is the $$rms$$ value of the voltage waveform shown in Fig?
A
$$200/\pi \,V$$
B
$$100/\pi \,V$$
C
$$200$$ $$V$$
D
$$100$$ $$V$$
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