# EC GATE 2014 PAPER 01 (Test 3)

Tag: ec gate 2014 paper 01
Q.1
For the following feedback system  The 2% settling time of the step response is required to be less than 2 seconds.

A. 3(1/s + 5)
B. 5((0.03/s) + 1)
C. 2(s + 4)
D. 4((s + 8) / (s + 3))
Explaination / Solution:
No Explaination.

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Q.2
A discrete time signal x[n] = sin (π2n) n being an integer, is
A. periodic with period π
B.  periodic with period π2
C. periodic with period π/2
D. not periodic
Explaination / Solution:

In the given options (A), (B) and (C), we have the periods respectively as
N1 = π

N2 = π2

N3 = π/3

None of the above period is an integer. Since, a discrete time signal has its period an integer. So, all the three options are incorrect. Hence, we are left with the option (D). i.e. the discrete time signal x[n] = sin (π2n) is not periodic.

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Q.3
The force on a point charge +q kept at a distance d from the surface of an infinite grounded metal plate in a medium of permittivity 𝜖 i
A. 0
B.  away from the plate
C.   towards the plate
D.   towards the plate
Explaination / Solution:

Consider the point charge +q and infinite surface as shown below.

We can replace the image charge by a negative equivalent charge -q placed at 2d distance from +q charge

Hence, the force experienced by +q charge is

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Q.4
For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z1 of the first section to the input impedance Z2 of the second section is
A. Z2 = Z1
B. Z2 = -Z1
C.

Z2 = Z1*

D.

Z2 = -Z1*

Explaination / Solution:

Consider the cascaded network shown below

Since, the output impedance of system 1 is Z1 and input impedance of system 2 is Z2. So, we have the equivalent circuit is

Now, we consider a circuit with internal impedance Zin and load impedance ZL

For maximum power transfer, the condition is

Zin* = Z2

Comparing this condition to cascaded system, we have the required condition for maximum power transfer as
Z1* = Z2

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Q.5
Consider the configuration shown in the figure which is a portion of a larger electrical network

For R = 1Ω and currents i1 = 2 A, i4 =- 1 A, i5 =- 4 A, which one of the following is TRUE ?
A. i6 = 5A
B. i3 = -4A
C. Data is sufficient to conclude that the supposed currents are impossible
D.  Data is insufficient to identify the currents i2i3 and i6
Explaination / Solution:

From the circuit, we have

i2 = i4 + i1

= -1 + 2
= 1A

i3 = i5 + i2

= -4 + 1
= -3A
i6 = i1 – i3
= 2 - (-3)
= 5A

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Q.6
A two-port network has scattering parameters given by  If the port-2 of the two port is short circuited, the S11 parameter for the resultant one
A.
B.
C.
D.
Explaination / Solution:
No Explaination.

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Q.7
A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is
A. (18 + j1.5) kVA
B. (18 - j1.5) kVA
C. (20 + j1.5) kVA
D. (20 - j1.5) kVA
Explaination / Solution:

Consider the circuit diagram for given problem as shown below

P1 = 10 kW

So, we obtain the complex power delivered to Z1 as

Again, the delivered power to load Zas

|s1|= 10 kVA

cos ϕ2 = 0.8, lagging

So, we obtain the complex power delivered to load Z2 as

Hence, the total complex power delivered by the source is

s1 + s2 = (10 – j7.5) + (8 + j6)

= (18 - j1.5) kVA

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Q.8
You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
A. 1/4
B. 1/3
C. 1/2
D. 2/3
Explaination / Solution:
No Explaination.

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Q.9
For matrices of same dimension M , N and scalar c, which one of these properties DOES NOT ALWAYS hold ?
A.

(MT)T = M

B.

(cM)T = c(M)T

C.

(M + N)T = MT + NT

D. MN = NM
Explaination / Solution:

Let the matrices

i.e. the property holds always

i.e. property does not hold always.

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Q.10
C is a closed path in the z -plane by |z| = 3 The value of the integral  is
A. -4π(1 + j2)
B. 4π(3 - j2)
C. -4π(3 + j2)
D. 4π(1 - j2)