1
GATE ECE 2014 Set 3
+2
-0.6
Assuming that the Op-amp in the circuit shown is ideal, V0 is given by
A
$${5 \over 2}{V_1} - 3{V_2}$$
B
$$2{V_1} - {5 \over 2}{V_2}$$
C
$$- {3 \over 2}{V_1} + {7 \over 2}{V_2}$$
D
$$- 3{V_1} + {{11} \over 2}{V_2}$$
2
GATE ECE 2014 Set 3
+1
-0.3
Consider an FM signal $$f\left(t\right)\;=\;\cos\left[2{\mathrm{πf}}_\mathrm c\mathrm t\;+\;{\mathrm\beta}_1\sin\;2{\mathrm{πf}}_1\mathrm t\;+\;{\mathrm\beta}_2\sin\;2{\mathrm{πf}}_2\mathrm t\right]$$ . The maximum deviation of the instantaneous frequency from the carrier frequency fc is
A
$$\beta_1f_1+\;\beta_2f_2$$
B
$$\beta_1f_2+\;\beta_2f_1$$
C
$$\beta_1+\;\beta_2$$
D
$$f_1+\;f_2$$
3
GATE ECE 2014 Set 3
+2
-0.6
Let $$X(t)$$ be a wide sense stationary $$(WSS)$$ random procfess with power spectral density $${S_x}\left( f \right)$$. If $$Y(t)$$ is the process defined as $$Y(t) = X(2t - 1)$$, the power spectral density $${S_y}\left( f \right)$$ is .
A
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j\pi f}}$$
B
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j\pi f/2}}$$
C
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right)$$
D
$${S_y}\left( f \right) = {1 \over 2}{S_x}\left( {{f \over 2}} \right){e^{ - j2\pi f}}$$
4
GATE ECE 2014 Set 3
Numerical
+2
-0
A real band-limited random process $$X( t )$$ has two -sided power spectral density $${S_x}\left( f \right) = \left\{ {\matrix{ {{{10}^{ - 6}}\left( {3000 - \left| f \right|} \right)Watts/Hz} & {for\left| f \right| \le 3kHz} \cr 0 & {otherwise} \cr } } \right.$$\$

Where f is the frequency expressed in $$Hz$$. The signal $$X( t )$$ modulates a carrier cos $$16000$$ $$\pi t$$ and the resultant signal is passed through an ideal band-pass filter of unity gain with centre frequency of $$8kHz$$ and band-width of $$2kHz$$. The output power (in Watts) is ______.

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