1
GATE PI 2005
+2
-0.6
A cast steel slab of dimension $$30 \times 20 \times 5\,\,cm$$ is poured horizontally using a side riser. The riser is cylindrical in shape with diameter and height, both equal to $$D.$$ The freezing ratio of the moulds is
A
$$8D/75$$
B
$$4D/75$$
C
$$75/8D$$
D
$$75/4D$$
2
GATE PI 2005
+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
$$-10$$
3
GATE PI 2005
+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
4
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
$${10 \over {36}}$$
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