1
GATE ECE 2014 Set 4
Numerical
+2
-0
Parcels from sender $$S$$ to receiver $$R$$ pass sequentially through two post - offices. Each post - office has a probability $${1 \over 5}$$ of losing an incoming parcel, independently of all other parcels. Given that a parcel is lost, the probability that it was lost by the second post - office is _________.
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2
GATE ECE 2014 Set 4
Numerical
+1
-0
Let $$X$$ be a zero mean unit variance Gaussian random variable. $$E\left[ {\left| X \right|} \right]$$ is equal to ______
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3
GATE ECE 2014 Set 4
Numerical
+2
-0
With initial values $$\,\,\,y\left( 0 \right) = y'\left( 0 \right) = 1,\,\,\,$$ the solution of the differential equation $$\,\,{{{d^2}y} \over {d{x^2}}} - 4{{dy} \over {dx}} + 4y = 0\,\,$$ at $$x=1$$ is ________.
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4
GATE ECE 2014 Set 4
MCQ (Single Correct Answer)
+1
-0.3
If $$a$$ and $$b$$ are constants, the most general solution of the differential equation $$\,{{{d^2}x} \over {d{t^2}}} + 2{{dx} \over {dt}} + x = 0$$ is
A
$$a{e^{ - t}}$$
B
$$a{e^{ - t}} + bt{e^{ - t}}$$
C
$$a{e^t} + bt{e^{ - t}}$$
D
$$a{e^{ - 2t}}$$
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