# EC GATE 2009 (Test 4)

Tag: ec gate 2009
Q.1
The ROC of z -transform of the discrete time sequence A. 1/3< |Z| < 1/2
B.  |Z| > 1/2
C. |Z| < 1/2
D. 2<|Z| < 3
Explaination / Solution: Taking z transform we have Workspace
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Q.2
Two infinitely long wires carrying current are as shown in the figure below. One wire is in the y - z plane and parallel to the y axis. The other wire is in the x - y plane and parallel to the x - axis. Which components of the resultingmagnetic field are non-zero at the origin ? A. x,y,z components
B. x,y components
C. y, z components
D. x,z components
Explaination / Solution:

Due to 1 A current wire in x - y plane, magnetic field be at origin will be in x direction.
Due to 1 A current wire in y - z plane, magnetic field be at origin will be in z direction.
Thus x and z component is non-zero at origin.

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Q.3
If a vector field is related to another vector field through which of the following is true? (Note : C and SC refer to any closed contour and any surface whose boundary is C . )
A. B. C. D. Explaination / Solution:

Hence (B) is correct option. Workspace
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Q.4
A magnetic field in air is measured to be What current distribution leads to this field ?
[Hint : The algebra is trivial in cylindrical coordinates.]

A. B. C. D. Explaination / Solution: Workspace
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Q.5
In the interconnection of ideal sources shown in the figure, it is known that the 60 V source is absorbing power. Which of the following can be the value of the current source I ?
A. 10A
B. 13A
C. 15A
D. 18A
Explaination / Solution:

Circuit is as shown below Since 60 V source is absorbing power. So, in 60 V source current flows from + to - ve direction So,
I + I1 = 12
I = 12 - I1
I is always less then 12 A So, only option (A) satisfies this conditions.

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Q.6
If the transfer function of the following network is A. R/4

B. R/2
C. R
D. 2R
Explaination / Solution: Workspace
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Q.7
The built-in potential of the junction
A. is 0.70 V
B. is 0.76 V
C. is 0.82 V
D. Cannot be estimated from the data given
Explaination / Solution:

We know that Workspace
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Q.8
The order of the differential equation A. 1
B. 2
C. 3
D. 4
Explaination / Solution:

The highest derivative terms present in DE is of 2nd order.

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Q.9
A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?
A.

(1/2)2

B.

10 C2(1/2)

C.

(1/2)10

D.

10 C2(1/2)10

Explaination / Solution:

Number of elements in sample space is 210   Only one element  "H,H,T,T,T,T,T,T,T,T, is event. Thus probability is 1/210
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Q.10 A. B. C. D.   