# EC GATE 2007 (Test 7)

Tag: ec gate 2007
Q.1
Consider a linear system whose state space representation is x(t) = Ax(t). If the initial state vector of the system is then the system response is If the itial state vector of the system changes to the system response becomes The system matrix A is

A. B. C. D. Explaination / Solution:
No Explaination.

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Q.2
If C is code curve enclosing a surface S , then magnetic field intensity , the current density and the electric flux density are related by
A. B. C. D. Explaination / Solution: Workspace
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Q.3
It is given that X, X .... XM at M non-zero, orthogonal vectors. The dimension of the vector space spanned by the 2M vectors X, X, ....XM, - X, - X, ..... - Xis
A. 2M
B. M+
C. M
D.  dependent on the choice of X, X, ...XM
Explaination / Solution:

For two orthogonal vectors, we require two dimensions to define them and similarly for three orthogonal vector we require three dimensions to define them. 2M vectors are basically M orthogonal vector and we require M dimensions to define them.

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Q.4
The field (in A/m) of a plane wave propagating in free space is given by The time average power flow density in Watts is
A. η0/100
B. 100/η0
C. D. 50/η0
Explaination / Solution: Workspace
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Q.5
The RC circuit shown in the figure is A. a low-pass filter
B. a high-pass filter
C. a band-pass filter
D. a band-reject filter
Explaination / Solution:

At ω3, capacitor acts as short circuited and circuit acts as shown in fig below At ω0, capacitor acts as open circuited and circuit look like as shown in fig below So frequency response of the circuit is as shown in fig and circuit is a Band pass filter. Workspace
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Q.6
Two series resonant filters are as shown in the figure. Let the 3-dB bandwidth of Filter 1 be B1 and that of Filter 2 be B2. the value B1/Bis A. 4
B. 1
C. 1/2
D. 1/4
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Q.7
For the circuit shown in the figure, the Thevenin voltage and resistance looking into X − Y are A. B. C. D. 4 V, 2 Ω
Explaination / Solution:

Here Vth is voltage across node also. Applying nodal analysis we get Workspace
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Q.8
In the circuit shown, vC is 0 volts at t = 0 sec. For t > 0, the capacitor current iC(t), where t is in seconds is given by A. 0.50 exp(− 25t) mA
B. 0.25 exp(− 25t) mA
C. 0.50 exp(− 12.5t) mA
D. 0.25 exp(− 6.25t) mA
Explaination / Solution:  Workspace
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Q.9
In the ac network shown in the figure, the phasor voltage VA (in Volts) is A. 0
B. C. D. Explaination / Solution: Workspace
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Q.10
For the Zener diode shown in the figure, the Zener voltage at knee is 7 V, the knee current is negligible and the Zener dynamic resistance is 10 Ω. If the input voltage (Vi) range is from 10 to 16 V, the output voltage (V0) ranges from A. 7.00 to 7.29 V
B. 7.14 to 7.29 V
C. 7.14 to 7.43 V
D. 7.29 to 7.43 V  