EC GATE 2015 PAPER 01 - Online Test
Q1. Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?
Answer : Option D
Explaination / Solution:
No Explaination.
Q2. 
A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as
The minimum decision error probability is
Answer : Option D
Explaination / Solution:
Given the conditional density function of R as
Decision error probability that receiver decides 0 for a transmitted bit 1 is
fR/1 (r =
0) = 1/6
Again, the decision error probability that receiver decides 1 for a transmitted bit 0 is
fR/0 (r = 1) = 1/4
Hence, the minimum decision error probability is
fR/1 (r = 0) = 1/6
Q3. Two sequences [a, b, c] and [A, B, C ] are related as.
If another sequence [p, q , r ] is derived as,
then the relationship between the sequences [p, q , r ] and [a, b, c] is
Answer : Option C
Explaination / Solution:
Given relation is
Comparing it with the DFT concept of taking fourier transform by matrix form. We may calculate that here we are taking the 3 order DFT of [a b c]T whose
transformed output is [A B C]T . So,
Again, we consider the equation (1),
Since, the relation between cube roots of unity is given as
So, we solve the matrix equation as
Again, we consider the equation (2),
In above equation, we apply elementary row operation as
Hence, we can conclude that
[p q r] =[c a b]
Q4. The solution of the differential equation 
is
is
Answer : Option B
Explaination / Solution:
We have the differential equation,
Given equation is linear constant coefficient differential equation. Let
Q5. Which one of the following graphs describes the function 
Answer : Option B
Explaination / Solution:
This condition is satisfied by the graph shown in option (B).
