1
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A memory less source emits n symbols each with a probability p. The entropy of the source as a function of n
A
increases as log n
B
decreases as log (1 / n)
C
increases as n
D
increases as n log n
2
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
Consider a Binary Symmetric Channel (BSC) with probability of error being 'p'. To transit a bit, say 1, we transmit a sequence of three 1s. The receiver will interpret the received sequence to represent 1 if at least two bits are 1. The probability that the transmitted bit will be received in error is
A
$${p^3} + 3{p^2}\left( {1 - p} \right)$$
B
$${p^3}$$
C
$${\left( {1 - p} \right)^3}$$
D
$${p^3} + {p^2}\left( {1 - p} \right)$$
3
GATE ECE 2008
MCQ (Single Correct Answer)
+1
-0.3
Step responses of a set of three second-order underdamped systems all have the same percentage overshoot. Which of the following diagrams represents the poles of the three systems?
A
GATE ECE 2008 Control Systems - Time Response Analysis Question 49 English Option 1
B
GATE ECE 2008 Control Systems - Time Response Analysis Question 49 English Option 2
C
GATE ECE 2008 Control Systems - Time Response Analysis Question 49 English Option 3
D
GATE ECE 2008 Control Systems - Time Response Analysis Question 49 English Option 4
4
GATE ECE 2008
MCQ (Single Correct Answer)
+2
-0.6
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at s=-2 and s=-4, and one simple zero at s=-1. A unit step u(t) is applied at the input of the system. At steady state, the output has constant value of 1. The impulse response of this system is
A
[exp(-2t) + exp(-4t)]u(t)
B
[-4exp(-2t) + 12exp(-4t) - exp(-t)]u(t)
C
[-4exp(-2t) + 12exp(-4t)]u(t)
D
[-0.5exp(-2t) + 1.5exp(-4t)]u(t)
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