EC GATE 2017 PAPER 01 - Online Test

Q1. Which of the following can be pole-zero configuration of a phase-lag controller (lag compensator)?
Answer : Option A
Explaination / Solution:

In phase lag compensator pole is near to j𝜔-axis,


Q2. Consider a stable system with transfer function

Where b1, ---, band a1, ---, aare real valued constants. The slope of the Bode log magnitude curve of G(s) converges to -60 dB/decade as 𝜔 ⟶ ∞. A possible pair of values for p and q is
Answer : Option A
Explaination / Solution:



Q3. Consider the following statements for continuous-time linear time invariant (LTI) systems. I. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. II. There is non causal and BIBO stable system with a pole in the right half of the complex plane. Which one among the following is correct?
Answer : Option D
Explaination / Solution:

If a system is non-causal then a pole on right half of the s-plane can give BIBO stable system. But for a causal system to be BIBO all poles must lie on left half of the complex plane.

Q4. A linear time invariant (LTI) system with the transfer function
 
is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K <  intersects the imaginary axis for K = 1.5. The closed loop system is stable for
Answer : Option A
Explaination / Solution:



Q5. Which one of the following options correctly describes the locations of the roots of the equation s+ s+ 1 = 0 on the complex plane?
Answer : Option C
Explaination / Solution:



Hence two roots contain RHS and two roots contain LHS plane.

Q6. The Nyquist plot of the transfer function

does not encircle the point (1+ j0) for K = 10 but does encircle the point (-1+ j0) for K = 100. Then the closed loop system (having unity gain feedback) is
Answer : Option B
Explaination / Solution:





Q7. Consider the following statement about the linear dependence of the real valued functions y1  = 1, y= x and y3 = x2over the field of real numbers.
I.   y1, yand y3 are linearly independent on -1 ≤ x ≤ 0
II.  y1, yand y3 are linearly dependent on 0 ≤ x ≤ 1
III. y1, yand y3 are linearly independent on 0 ≤ x ≤ 1
IV. y1, yand y3 are linearly dependent on -1 ≤ x ≤ 0
Which one among the following is correct?
Answer : Option B
Explaination / Solution:



Q8. Consider the 5 × 5 matrix

It is given that A has only one real eigen value. Then the real eigen value of A is
Answer : Option C
Explaination / Solution:




Q9. The rank of the matrix M =  is
Answer : Option C
Explaination / Solution:



Q10. A periodic signal x(t) has a trigonometric Fourier series expansion  
If  we can conclude that
Answer : Option A
Explaination / Solution:

If x(t) = -x(-t) the given periodic signal is odd symmetric. For an odd symmetric signal an = 0 for all n.
If x(t) = -x(t- π/𝜔0),  π/𝜔T0/2 where T0 is fundamental period then the given condition satisfies half-wave symmetry.
For half-wave symmetrical signal all coefficients an and bn are zero for even value of n.