1
GATE PI 2005
+1
-0.3
Two dice are thrown simultaneously. The probability that the sum of numbers on both exceeds $$8$$ is
A
$${4 \over {36}}$$
B
$${7 \over {36}}$$
C
$${9 \over {36}}$$
D
$${10 \over {36}}$$
2
GATE PI 2005
+1
-0.3
The life of a bulb (in hours) is a random variable with an exponential distribution $$\,\,f\left( t \right) = \alpha {e^{ - \alpha t}},0 \le t \le \infty .\,\,\,$$ The probability that its value lies $$b/w$$ $$100$$ and $$200$$ hours is
A
$$\,{e^{ - 100\alpha }} - {e^{ - 200\alpha }}$$
B
$${e^{ - 100}} - {e^{ - 200}}$$
C
$$\,{e^{ - 100\alpha }} + {e^{ - 200\alpha }}$$
D
$${e^{ - 100}} + {e^{ - 200}}$$
3
GATE PI 2005
+1
-0.3
The differential equation $${\left[ {1 + {{\left( {{{d\,y} \over {d\,x}}} \right)}^2}} \right]^3} = {C^2}{\left[ {{{{d^2}\,y} \over {d\,{x^2}}}} \right]^2}$$ is of
A
$${2^{nd}}$$ order and $${3^{rd}}$$ degree
B
$${3^{rd}}$$ order and $${2^{nd}}$$ degree
C
$${2^{nd}}$$ order and $${2^{nd}}$$ degree
D
$${3^{rd}}$$ order and $${3^{rd}}$$ degree
4
GATE PI 2005
+1
-0.3
The function $$w = u + iv = {1 \over 2}\log \left( {{x^2} + {y^2}} \right) + i{\tan ^{ - 1}}\left( {{y \over x}} \right)$$\$ is not analytic at the point.
A
(0, 0)
B
(0, 1)
C
(1, 0)
D
$$(2,\,\alpha )$$
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