1
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
Consider p(s) = s3 + $${a_2}$$s2 + $${a_1}$$s + $${a_0}$$ with all real coefficients. It is known that its derivative p'(s) has no real roots. The number of real roots of p(s) is
A
0
B
1
C
2
D
3
2
GATE ECE 2018
Numerical
+2
-0.67
For a unity feedback control system with the forward path transfer function

$$G(s) = {K \over {s\left( {s + 2} \right)}}$$

The peak resonant magnitude Mr of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.
Your input ____
3
GATE ECE 2018
MCQ (Single Correct Answer)
+2
-0.67
The state equation and the output equation of a control system are given below:

$$\mathop x\limits^. = \left[ {\matrix{ { - 4} & { - 1.5} \cr 4 & 0 \cr } } \right]x + \left[ {\matrix{ 2 \cr 0 \cr } } \right]u,$$

$$y = \left[ {\matrix{ {1.5} & {0.625} \cr } } \right]x.$$

The transfer function representation of the system is
A
$${{3s + 5} \over {{s^2} + 4s + 6}}$$
B
$${{3s - 1.875} \over {{s^2} + 4s + 6}}$$
C
$${{4s + 1.5} \over {{s^2} + 4s + 6}}$$
D
$${{6s + 5} \over {{s^2} + 4s + 6}}$$
4
GATE ECE 2018
MCQ (Single Correct Answer)
+1
-0.33
A function F(A, B, C) defined by three Boolean variables A, B and C when expressed as sum of products is given by

F = $$\overline A .\overline B .\overline C + \overline A .B.\overline C + A.\overline B .\overline C $$

where, $$\overline A $$, $$\overline B $$, and $$\overline C $$ are the complements of the respective variables. The product of sums (POS) form of the function F is
A
F = (A + B + C)(A + $$\overline B $$ + C)($$\overline A $$ + B + C)
B
F = ($$\overline A $$ + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)
C
F = (A + B + $$\overline C $$)(A + $$\overline B $$ + $$\overline C $$)($$\overline A $$ + B + $$\overline C $$)($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + $$\overline B $$ + $$\overline C $$)
D
F = ($$\overline A $$ + $$\overline B $$ + C)($$\overline A $$ + B + C)(A + $$\overline B $$ + C)(A + B + $$\overline C $$)(A + B + C)
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