GATE EE 2005 | GATE EE Year Wise Previous Years Questions

GATE EE 2005

MCQ (Single Correct Answer)

-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 $$t \to \infty $$

$$0$$

$$5/2$$

$$5$$

$$10$$

GATE EE 2005

MCQ (Single Correct Answer)

-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

$$x\left( t \right) = {x_0}\,{e^{ - 3\,t}}$$

$$x\left( t \right) = {x_0}\,{e^{ - 3\,}}$$

$$x\left( t \right) = {x_0}\,{e^{ - t\,3}}$$

$$x\left( t \right) = {x_0}\,{e^{ - t\,}}$$

GATE EE 2005

MCQ (Single Correct Answer)

-0.6

A fair coin is tossed $$3$$ times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

$${1 \over 8}$$

$${1 \over 2}$$

$${3 \over 8}$$

$${3 \over 4}$$

GATE EE 2005

MCQ (Single Correct Answer)

-0.3

If $$P$$ and $$Q$$ are two random events, then which of the following is true?

Independence of $$P$$ and $$Q$$ implies that probability $$\,\,\left( {P \cap Q} \right) = 0\,\,$$

Probability $$\,\,\left( {P \cap Q} \right) \ge \,\,$$ probability $$(P)$$ $$+$$ probability $$(Q)$$

If $$P$$ and $$Q$$ are mutually exclusive then they must be independent

Probability $$\,\,\left( {P \cap Q} \right) \le \,\,$$ probability $$(P)$$

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