1
GATE ECE 2014 Set 3
Numerical
+1
-0
The input $$-3\mathrm e^{2\mathrm t}\;\mathrm u\left(\mathrm t\right)$$, where u(t) is the unit step function, is applied to a system with transfer function $$\frac{s-2}{s+3}$$. If the initial value of the output is -2, then the value of the output at steady state is __________.
Your input ____
2
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus? GATE ECE 2014 Set 3 Control Systems - Root Locus Diagram Question 2 English
A
$$\frac{s+1}{\left(s+2\right)\left(s+4\right)\left(s+7\right)}$$
B
$$\frac{s+4}{\left(s+1\right)\left(s+2\right)\left(s+7\right)}$$
C
$$\frac{s+7}{\left(s+1\right)\left(s+2\right)\left(s+4\right)}$$
D
$$\frac{\left(s+1\right)\left(s+2\right)}{\left(s+4\right)\left(s+7\right)}$$
3
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$
For $${x_0} = \left[ {\matrix{ 1 \cr { - 1} \cr } } \right],x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} \cr { - {e^{ - t}}} \cr } } \right]$$ and for $${x_0} = \left[ {\matrix{ 0 \cr 1 \cr } } \right],x\left( t \right) = \left[ {\matrix{ {{e^{ - t}}} & { - {e^{ - 2t}}} \cr { - {e^{ - t}}} & { + 2{e^{ - 2t}}} \cr } } \right]$$ when $${x_0} = \left[ {\matrix{ 3 \cr 5 \cr } } \right],x\left( t \right)$$ is
A
$$\left[ {\matrix{ { - 8{e^{ - t}}} & { + 11{e^{ - 2t}}} \cr {8{e^{ - t}}} & { - 22{e^{ - 2t}}} \cr } } \right]$$
B
$$\left[ {\matrix{ {11{e^{ - t}}} & { - 8{e^{ - 2t}}} \cr { - 11{e^{ - t}}} & { + 16{e^{ - 2t}}} \cr } } \right]$$
C
$$\left[ {\matrix{ {3{e^{ - t}}} & { - 5{e^{ - 2t}}} \cr { - 3{e^{ - t}}} & { + 10{e^{ - 2t}}} \cr } } \right]$$
D
$$\left[ {\matrix{ {5{e^{ - t}}} & { - 3{e^{ - 2t}}} \cr { - 5{e^{ - t}}} & { + 6{e^{ - 2t}}} \cr } } \right]$$
4
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
In the circuit shown, 𝑊𝑊 and 𝑌𝑌 are MSBs of the control inputs. The output 𝐹𝐹 is given by GATE ECE 2014 Set 3 Digital Circuits - Combinational Circuits Question 24 English
A
$$F = \,W\overline X + \overline W X + \overline Y \,\overline Z $$
B
$$F = \,W\overline X + \overline W X + \overline Y \,Z$$
C
$$F = \,W\overline X \,\overline Y + \overline W X\,\overline Y $$
D
$$F = \,(\overline W + \overline X )\,\,\overline Y \,\overline Z $$
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