GATE ME 2007 | GATE ME Year Wise Previous Years Questions

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GATE ME 2007

MCQ (Single Correct Answer)

-0.3

The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is

$$ - \infty \le x \le \propto $$

$$ - \infty \le x \le 1$$

$$x < 1,x > 1$$

$$ - 2 \le x \le 2$$

GATE ME 2007

MCQ (Single Correct Answer)

-0.6

Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ variance $$\left( {{V_{ar}}} \right)$$ and covariance $$\left( {{C_{ov}}} \right)$$ given below is FALSE?

$$E\left( {XY} \right) = E\left( X \right)E\left( Y \right)$$

$${\mathop{\rm cov}} \left( {X,Y} \right) = 0$$

$$Var\left( {X + Y} \right) = Var\left( X \right) + Var\left( Y \right)$$

$$\,E\left( {{X^2}{Y^2}} \right) = {\left( {E\left( X \right)} \right)^2}\,{\left( {E\left( Y \right)} \right)^2}$$

GATE ME 2007

MCQ (Single Correct Answer)

-0.6

The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is

$${1 \over 2}\left( {\overrightarrow a - \overrightarrow b } \right) \bullet \left( {\overrightarrow a - \overrightarrow c } \right)$$

$${1 \over 2}\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a - \overrightarrow c } \right)} \right|$$

$${1 \over 2}\left| {\overrightarrow a \times \overrightarrow b \times \overrightarrow c } \right|$$

$${1 \over 2}\left( {\overrightarrow a \times \overrightarrow b } \right) \bullet \overrightarrow c $$

GATE ME 2007

MCQ (Single Correct Answer)

-0.6

$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$

$$0$$

$${1 \over 6}$$

$${1 \over 3}$$

$$1$$

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