1
GATE ME 2007
MCQ (Single Correct Answer)
+2
-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?
A
$$E\left( {XY} \right) = E\left( X \right)E\left( Y \right)$$
B
$${\mathop{\rm cov}} \left( {X,Y} \right) = 0$$
C
$$Var\left( {X + Y} \right) = Var\left( X \right) + Var\left( Y \right)$$
D
$$\,E\left( {{X^2}{Y^2}} \right) = {\left( {E\left( X \right)} \right)^2}\,{\left( {E\left( Y \right)} \right)^2}$$
2
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ is
A
$${1 \over 2}\left( {\overrightarrow a - \overrightarrow b } \right) \bullet \left( {\overrightarrow a - \overrightarrow c } \right)$$
B
$${1 \over 2}\left| {\left( {\overrightarrow a - \overrightarrow b } \right) \times \left( {\overrightarrow a - \overrightarrow c } \right)} \right|$$
C
$${1 \over 2}\left| {\overrightarrow a \times \overrightarrow b \times \overrightarrow c } \right|$$
D
$${1 \over 2}\left( {\overrightarrow a \times \overrightarrow b } \right) \bullet \overrightarrow c $$
3
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
$$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$
A
$$0$$
B
$${1 \over 6}$$
C
$${1 \over 3}$$
D
$$1$$
4
GATE ME 2007
MCQ (Single Correct Answer)
+2
-0.6
If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.
A
$$4$$ (or) $$1$$
B
$$4$$ only
C
$$1$$ only
D
Undefined
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