EC GATE 2014 PAPER 01 - Online Test
Q1. 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
Answer : Option C
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
Q2. The digital logic shown in the figure satisfies the given state diagram when Q1 is
connected to input A of the XOR gate.
Suppose the XOR gate is replaced by an XNOR gate. Which one of the following
options preserves the state diagram ?
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. 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 ?
Answer : Option A
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
Q4. 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
If the
port-2 of the two port is short circuited, the S11 parameter for the resultant one
Answer : Option B
Explaination / Solution:
No Explaination.
Q5. 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
Answer : Option B
Explaination / Solution:
Consider the circuit diagram for given problem as shown below
Load delivered to Z1 is
P1 = 10 kW
cos ϕ1
= 0.8, leading
So, we obtain the complex power delivered to Z1 as
Again, the delivered power to load Z2 as
|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
Q6. Consider the feedback system shown in the figure. The Nyquist plot of G (s) is
also shown. Which one of the following conclusions is correct ?
Answer : Option D
Explaination / Solution:
Given the feedback system and the Nyquist plot of G (s)is
For the given system, we have the open loop transfer function as
G (s) = KG (s)
Considering the open loop system G (s) is stable, we have no open loop poles in
right half plane
P = 0
From Nyquist theorem, we know that
N = P - Z
Where N is the number of encirclements of (-1 + j0), P is number of open loop
poles in right half plane, Z is number of closed loop poles in right half plane. For
stability, we must have
Z = 0
N = 0, if closed loop system is stable
N ≠ 0, if closed loop system is unstable
observing the Nyquist plot, we conclude that the plot of KG(s) encircles (-1 + j0)
if K> 1
Hence, N ≠ 0 for sufficient large and positive value of K . Thus, the closedsystem
is unstable for sufficiently large and positive K .
Q7. For the following feedback system 
The 2% settling time of the
step response is required to be less than 2 seconds.
The 2% settling time of the
step response is required to be less than 2 seconds.
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. 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
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. For matrices of same dimension M , N and scalar c, which one of these properties DOES NOT ALWAYS hold ?
Answer : Option D
Explaination / Solution:
Let the matrices
i.e. the property holds always
i.e. property does not hold always.
Q10. C is a closed path in the z -plane by |z| = 3 The value of the integral 
is
is
Answer : Option C
Explaination / Solution:
Integral,
So, we have the singularity
z j + 2 = 0
z =- 2j
Since, z = -2j lies inside |z| = 3. Therefore, using cauchy’s integral, we get
