1
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $$X$$ be a real - valued random variable with $$E\left[ X \right]$$ and $$E\left[ {{X^2}} \right]$$ denoting the mean values of $$X$$ and $${{X^2}}$$, respectively. The relation which always holds true is
A
$${\left( {E\left[ X \right]} \right)^2} > E\left[ {X{}^2} \right]$$
B
$$E\left[ {X{}^2} \right] \ge {\left( {E\left[ X \right]} \right)^2}$$
C
$$E\left[ {X{}^2} \right] = {\left( {E\left[ X \right]} \right)^2}$$
D
$$E\left[ {X{}^2} \right] > {\left( {E\left[ X \right]} \right)^2}$$
2
GATE ECE 2014 Set 1
Numerical
+1
-0
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _______.
Your input ____
3
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
$$C$$ is a closed path in the $$z-$$plane given by
$$\left| z \right| = 3.$$ The value of the integral
$$\oint\limits_c {{{{z^2} - z + 4j} \over {z + 2j}}dz} $$ is
A
$$ - 4\pi \left( {1 + j2} \right)$$
B
$$4\pi \left( {3 - j2} \right)$$
C
$$ - 4\pi \left( {3 + j2} \right)$$
D
$$4\pi \left( {1 - j2} \right)$$
4
GATE ECE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A system is described by the following differential equation, where $$u(t)$$ is the input to the system and $$y(t)$$ is the output of the system. $$$\mathop y\limits^ \bullet \left( t \right) + 5y\left( t \right) = u\left( t \right)$$$

When $$y(0)=1$$ and $$u(t)$$ is a unit step function, $$y(t)$$ is

A
$$0.2 + 0.8{e^{ - 5t}}$$
B
$$0.2 - 0.2{e^{ - 5t}}$$
C
$$0.8 + 0.2{e^{ - 5t}}$$
D
$$0.8 - 0.8{e^{ - 5t}}$$
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