EC GATE 2013 - Online Test
Q1. Three capacitors C1, C2 and C3 whose values are 10 μF , 5 μF , and 2 μF respectively, have breakdown voltages of 10 V, 5 V and 2 V respectively. For the
interconnection shown below, the maximum safe voltage in Volts that can be
applied across the combination, and the corresponding total charge in μC stored
in the effective capacitance across the terminals are respectively
Answer : Option C
Explaination / Solution:
No Explaination.
Q2. There are four chips each of 1024 bytes connected to a 16 bit address bus as
shown in the figure below, RAMs 1, 2, 3 and 4 respectively are mappped to
addresses
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. The open-loop transfer function of a dc motor is given a 
When connected in feedback as shown below, the approximate value of Ka that
will reduce the time constant of the closed loop system by one hundred times as
compared to that of the open-loop system is
When connected in feedback as shown below, the approximate value of Ka that
will reduce the time constant of the closed loop system by one hundred times as
compared to that of the open-loop system is
Answer : Option C
Explaination / Solution:
No Explaination.
Q4. The signal flow graph for a system is given below. The transfer function Y(s)/U(s) for this system is
Answer : Option A
Explaination / Solution:
No Explaination.
Q5.
The minimum eigen value of the following matrix is
Answer : Option A
Explaination / Solution:
For, a given matrix [A] the eigen value is calculated as 
where 
gives the eigen values of matrix. Here, the minimum eigen value among the given options is 
We check the characteristic equation of matrix for this eigen value
where gives the eigen values of matrix. Here, the minimum eigen value among the given options is We check the characteristic equation of matrix for this eigen value= 3(60 - 49h- 5(25 - 14)+ 2)35 - 24h
= 33 - 55 + 22
= 0
Hence, it satisfied the characteristic equation and so, the minimum eigen value is
Q6. A polynomial 
with all coefficients positive has
with all coefficients positive has
Answer : Option D
Explaination / Solution:
Given, the polynomial 
Since, all the coefficients are positive so, the roots of equation is given by
f(x) = 0
It will have at least one pole in right hand plane as there will be least one sign change from (a1) to (a0) in the Routh matrix 1st column. Also, there will be a corresponding pole in left hand plane
i.e.; at least one positive root (in R.H.P)
and at least one negative root (in L.H.P)
Rest of the roots will be either on imaginary axis or in L.H.P
Q7. Let 
, and h(t) is a filter matched to g(t). if g(t) is applied as input to h(t) then the Fourier transform of the output is
, and h(t) is a filter matched to g(t). if g(t) is applied as input to h(t) then the Fourier transform of the output is
Answer : Option D
Explaination / Solution:
The matched filter is characterized by a frequency response that is given as
Q8. Let U and V be two independent zero mean Gaussain random variables of variances 1/4 and 1/9 respectively. The probability 
is
is
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. Let A be an m × n matrix and B an n × m matrix. It is given that determinant (Im + AB) = determinant (In + BA), where Ik is the k × k identity
matrix. Using the above property, the determinant of the matrix given below is
Answer : Option B
Explaination / Solution:
Consider the given matrix be
From the given property
Q10. A system described by the differential equation 
Let
x(t) be a rectangular pulse given by
Let
x(t) be a rectangular pulse given byAssuming that y(0) = 0 and dy/dt = 0 at t = 0, the Laplace transform of y(t) is
Answer : Option B
Explaination / Solution:
No Explaination.
