1
GATE ECE 2014 Set 3
+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
$$\left[ {\matrix{ {5{e^{ - t}}} & { - 3{e^{ - 2t}}} \cr { - 5{e^{ - t}}} & { + 6{e^{ - 2t}}} \cr } } \right]$$
2
GATE ECE 2014 Set 3
+2
-0.6
In the circuit shown, 𝑊𝑊 and 𝑌𝑌 are MSBs of the control inputs. The output 𝐹𝐹 is given by
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
$$F = \,(\overline W + \overline X )\,\,\overline Y \,\overline Z$$
3
GATE ECE 2014 Set 3
+2
-0.6
If X and Y are inputs and the Difference (D = X – Y) and the Borrow (B) are the outputs, which one of the following diagrams implements a half-subtractor?
A
B
C
D
4
GATE ECE 2014 Set 3
+1
-0.3
The circuit shown in the figure is a
A
Toggle Flip Flop
B
JK Flip Flop
C
SR Latch
D
Master-Slave D Flip Flop
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