EC GATE 2017 PAPER 01 - Online Test
Q1. In binary frequency shift keying (FSK), the given signal waveform are
u0 (t) = 5cos (20000 πt); 0 ≤ t ≤ T, and
u1 (t) = 5cos (22000 πt); 0 ≤ t ≤ T,
Where T is the bit-duration interval and t is in seconds. Both u0 (t) and u1 (t) are zero outside the interval 0 ≤ t ≤ T. With a matched filter (correlator) based receiver, the smallest positive value of T (in milliseconds) required to have u0 (t) and u1 (t) uncorrelated is
Answer : Option B
Explaination / Solution:
Q2. Let X(t) be a wide sense stationary random process with the power spectral density SX(f) as shown in Figure (a), where f is in Hertz (Hz). The random process X(t) is input to an ideal low pass filter with frequency response
As shown in Figure (b). The output of the lowpass filter is Y(t ).
Let E be the expectation operator and consider the following statements.
I. E( X(t)) = E(Y(t))
II. E( X2(t)) = E(Y2(t))
III. E(Y2(t)) = 2
Select the correct option:
Answer : Option A
Explaination / Solution:
Q3. A half wavelength dipole is kept in the x-y plane and oriented along 450 from the x-axis. Determine the direction of null in the radiation pattern for 0 ≤ ϕ ≤ π. Here the angle θ (0 ≤ θ ≤ π) is measured from the z-axis, and the angle ϕ (0 ≤ ϕ ≤ 2π) is measured from the x-axis in the x-y plane.
Answer : Option A
Explaination / Solution:
The null occurs along axis of the antenna which is θ = 900and ϕ= 450
Q4. The clock frequency of an 8085 microprocessor is 5 MHz. If the time required to execute an instruction is 1.4 μs, then the number of T-states needed for executing the instruction is
Answer : Option C
Explaination / Solution:
Q5. 
In the latch circuit shown, the NAND gates have non-zero, but unequal propagation delays. The present input condition is: P = Q = '0'. If the input condition is changed simultaneously to P = Q = '1', the outputs X and Y are
Answer : Option B
Explaination / Solution:
Unequal propagation delay
Case I: Case II:
Gate 1⟶2ns Gate 1⟶1nsec
Gate 2⟶1ns Gate 2⟶2nsec
Either x = 1, y = 0 or x = 0, y =1
Q6. 
A finite state machine (FSM) is implemented using the D flip-flops A and B, and logic gates, as shown in the figure below. The four possible states of the FSM are QA QB = 00,01,10 and 11.
Assume that XIN is held at a constant logic level throughout the operation of the FSM. When the FSM is initialized to the state QA QB = 00 and clocked, after a few clock cycles, it starts cycling through
Answer : Option D
Explaination / Solution:
In given diagram
When Xin = 0 2 State
When Xin =1 3 State
Q7. The following FIVE instructions were executed on an 8085 microprocessor.
MVI A, 33H
MVI B, 78H
ADD B
CMA
ANI 32H
The Accumulator value immediately after the execution of the fifth instruction is
Answer : Option B
Explaination / Solution:
MVI A, 33H A⟵33H
MVI B, 78H B⟵78H
ADD B B⟵ABH
CMA A⟵54H
ANI 32H A⟵10H
A⟶0011 0011 A⟶1010 1011 0101 0100
B⟶0111 1000 B⟶0101 0100 0011 0010
1010 1011 0001 0000
Q8.
Which one of the following gives the simplified sum of products expression for the Boolean function F =
m0 + m2 + m3 + m5, where m0,
m2, m3
and m5 are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
and m5 are minterms corresponding to the inputs A, B and C with A as the MSB and C as the LSB?
Answer : Option B
Explaination / Solution:
F =
m0 + m2 + m3 + m5, ⟶ minterm
Q9. 
Consider a single input single output discrete-time system with x[n] as input and y[n] as output, where the two are related as
Which one of the following statements is true about the system?
Answer : Option A
Explaination / Solution:
For an input-output relation if the present output depends on present and past input values then the given system is “Causal”.
For the given relation,
For n ranging from 0 to 10 present output depends on present input only.
At all other points present output depends on present and past input values.
Thus the system is “Causal”.
Stability
If x[n] is bounded for the given finite range of n i.e. 0 ≤ n ≤ 10 y[n] is also bounded.
Similarly x[n] - x[n-1] is also bounded at all other values of n
Thus the system is “stable”.
Q10. Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
I. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued
II. The complex Fourier series coefficients of x(3t) are {3ak} where k is integer valued
III. The fundamental angular frequency of x(3t) is 6𝜋 rad/s
For the three statements above, which one of the following is correct?
Answer : Option B
Explaination / Solution:
Fourier series coefficient ak is unaffected by scaling operating. Thus (I) is true and (II) is false.
T = 1sec for x(t) and if it compressed by '3' then the resultant period T = 1/3
Fundamental frequency = 2𝜋/T1= = 6𝜋 rad/sec
Thus (III) is correct.
