1
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
Voltage phasors at the two terminals of a transmission line of length $$70$$ km have a magnitude of $$1.0$$ per unit but are $$180$$ degrees out of phase. Assuming that the maximum load current in the line is $$1/5$$th of minimum $$3$$-phase fault current. Which one of the following transmission line protection schemes will NOT pick up for this condition?
A
Distance protection using mho relays with zone-$$1$$ set to $$80$$% of the line impedance.
B
Directional over current protection set to pick up at $$1.25$$ times the maximum load current
C
Pilot relaying system with directional comparison scheme
D
Pilot relaying system with segregated phase comparison scheme.
2
GATE EE 2008
MCQ (Single Correct Answer)
+1
-0.3
A signal $${e^{ - \alpha t}}\,\sin \left( {\omega t} \right)$$ is the input to a real Linear Time Invariant system. Given $$K$$ and $$\phi $$ are constants, the output of the system will be of the form $$K{e^{ - \beta t}}\,\sin \,\left( {\upsilon t + \phi } \right)$$ where
A
$$\beta $$ need not be equal to $$\alpha $$ but $$\upsilon $$ equal to
B
$$\upsilon $$ need not be equal to $$\omega $$ but $$\beta $$ equal to $$\alpha $$
C
$$\beta $$ equal to $$\alpha $$ and $$\upsilon $$ equal to $$\omega $$
D
$$\beta $$ need not be equal to $$\alpha $$ and $$\upsilon $$ need not be equal to $$\omega $$
3
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
The transfer function of a linear time invariant system is given as $$G\left( s \right) = {1 \over {{s^2} + 3s + 2}}.$$ The steady state value of the output of this system for a unit impulse input applied at time instant $$t=1$$ will be
A
$$0$$
B
$$0.5$$
C
$$1$$
D
$$2$$
4
GATE EE 2008
MCQ (Single Correct Answer)
+2
-0.6
A signal $$x\left( t \right) = \sin c\left( {\alpha t} \right)$$ where $$\alpha $$ is a real constant $$\left( {\sin \,c\left( x \right) = {{\sin \left( {\pi x} \right)} \over {\pi x}}} \right)$$ is the input to a linear Time invariant system whose impulse response $$h\left( t \right) = \sin c\left( {\beta t} \right)$$ where $$\beta $$ is a real constant. If $$\min \left( {\alpha ,\,\,\beta } \right)$$ denotes the minimum of $$\alpha $$ and $$\beta $$, and similarly $$\max \left( {\alpha ,\,\,\beta } \right)$$ denotes the maximum of $$\alpha $$ and $$\beta $$, and $$K$$ is a constant, which one of the following statements is true about the output of the system?
A
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\min \left( {\alpha ,\,\,\beta } \right)$$
B
It will be of the form $$K$$ $$sinc$$$$\left( {\gamma t} \right)$$ where $$\gamma = \,\max \left( {\alpha ,\,\,\beta } \right)$$
C
It will be of the form $$K$$ $$\sin c\left( {\alpha t} \right)$$
D
It cannot be a $$sinc$$ type of signal
EXAM MAP