EC GATE 2009 - Online Test
Q1.
What are the minimum numbers of NOT gates and 2 - input OR gates required to design the logic of the driver for this 7 - Segment display
Answer : Option D
Explaination / Solution:
As shown in previous solution 2 NOT gates and 3-OR gates are required.
Q2. The built-in potential of the junction
Answer : Option B
Explaination / Solution:
We know that
Q3. The order of the differential equation
Answer : Option B
Explaination / Solution:
The highest derivative terms present in DE is of 2nd order.
Q4. The feedback configuration and the pole-zero locations of 
are shown below. The root locus for negative values of k , i.e. for -3 < k < 0, has breakaway/break-in points and angle of departure at pole P (with respect to the
positive real axis) equal to
are shown below. The root locus for negative values of k , i.e. for -3 < k < 0, has breakaway/break-in points and angle of departure at pole P (with respect to thepositive real axis) equal to
Answer : Option B
Explaination / Solution:
The characteristic equation is
Q5. An LTI system having transfer function 
and input x(t) = sin(t + 1) is in steady state. The output is sampled at a rate ws rad/s to obtain the final output {x(k)}. Which of the following is true ?
and input x(t) = sin(t + 1) is in steady state. The output is sampled at a rate ws rad/s to obtain the final output {x(k)}. Which of the following is true ?
Answer : Option A
Explaination / Solution:
No Explaination.
Q6. The unit step response of an under-damped second order system has steady state value of -2. Which one of the following transfer functions has theses properties ?
Answer : Option B
Explaination / Solution:
For under-damped second order response
Q7. 
The Nyquist plot of a stable transfer function G(s) is shown in the figure are interested in the stability of the closed loop system in the feedback configuration shown.
Which of the following statements is true ?
Answer : Option B
Explaination / Solution:
The plot has one encirclement of origin in clockwise direction. Thus G(s) has a zero is in RHP.
Q8. 
The Nyquist plot of a stable transfer function G(s) is shown in the figure are interested in the stability of the closed loop system in the feedback configuration shown.
The gain and phase margins of G(s) for closed loop stability are
Answer : Option C
Explaination / Solution:
The Nyzuist plot intersect the real axis ate - 0.5. Thus
G. M. =- 20 log x =- 20 log 0.5 = 6.020 dB
And its phase margin is 90◦c
Q9. A fair coin is tossed 10 times. What is the probability that only the first two tosses will yield heads?
Answer : Option C
Explaination / Solution:
Number of elements in sample space is 210 Only one element "H,H,T,T,T,T,T,T,T,T, is event. Thus probability is 1/210
Q10. 
Answer : Option C
Explaination / Solution:
We have
