1
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
The eigen values of the matrix $$M$$ given are $$15, 3,$$ and $$0.$$
$$M = \left[ {\matrix{ 8 & { - 6} & 2 \cr { - 6} & 7 & { - 4} \cr 2 & { - 4} & 3 \cr } } \right],$$ the value of the determinant of a matrix is
A
$$20$$
B
$$10$$
C
$$0$$
D
$$-10$$
2
GATE PI 2005
MCQ (Single Correct Answer)
+1
-0.3
Which one of the following is Not associated with vector calculus?
A
Stoke's theorem
B
Gauss Divergence theorem
C
Green's theorem
D
Kennedy's theorem
3
GATE PI 2005
MCQ (Single Correct Answer)
+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
$${10 \over {36}}$$
4
GATE PI 2005
MCQ (Single Correct Answer)
+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
$${e^{ - 100}} + {e^{ - 200}}$$
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