1
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
If $$P$$ and $$Q$$ are two random events, then which of the following is true?
A
Independence of $$P$$ and $$Q$$ implies that probability $$\,\,\left( {P \cap Q} \right) = 0\,\,$$
B
Probability $$\,\,\left( {P \cap Q} \right) \ge \,\,$$ probability $$(P)$$ $$+$$ probability $$(Q)$$
C
If $$P$$ and $$Q$$ are mutually exclusive then they must be independent
D
Probability $$\,\,\left( {P \cap Q} \right) \le \,\,$$ probability $$(P)$$
2
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
The solution of the first order differential equation $$\mathop x\limits^ \bullet \left( t \right) = - 3\,x\left( t \right),\,x\left( 0 \right) = {x_0}\,\,\,\,$$ is
A
$$x\left( t \right) = {x_0}\,{e^{ - 3\,t}}$$
B
$$x\left( t \right) = {x_0}\,{e^{ - 3\,}}$$
C
$$x\left( t \right) = {x_0}\,{e^{ - t\,3}}$$
D
$$x\left( t \right) = {x_0}\,{e^{ - t\,}}$$
3
GATE EE 2005
MCQ (Single Correct Answer)
+2
-0.6
For the equation $$\,\,\mathop x\limits^{ \bullet \bullet } \left( t \right) + 3\mathop x\limits^ \bullet \left( t \right) + 2x\left( t \right) = 5,\,\,\,$$ the solution $$x(t)$$ approaches the following values as $$t \to \infty $$
A
$$0$$
B
$$5/2$$
C
$$5$$
D
$$10$$
4
GATE EE 2005
MCQ (Single Correct Answer)
+1
-0.3
The conduction loss versus device current characteristic of a power $$MOSFET$$ is best approximated by
A
a parabola
B
a straight line
C
a rectangular hyperbola
D
an exponentially decaying function
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