GATE EE 2005 | GATE EE Year Wise Previous Years Questions

GATE EE 2005

MCQ (Single Correct Answer)

-0.6

for the scalar field $$u = {{{x^2}} \over 2} + {{{y^2}} \over 3},\,\,$$ the magnitude of the gradient at the point $$(1,3)$$ is

$$\sqrt {{{13} \over 9}} $$

$$\sqrt {{9 \over 2}} $$

$$\sqrt 5 $$

$${{9 \over 2}}$$

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 $$(P)$$

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

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

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

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

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

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