1
GATE CSE 2002
Subjective
+5
-0
(a) $$S = \left\{ { < 1,2 > ,\, < 2,1 > } \right\}$$ is binary relation on set $$A = \left\{ {1,2,3} \right\}$$. Is it irreflexive?
Add the minimumnumber of ordered pairs to $$S$$ to make it an $$\,\,\,\,\,$$equivalence relation. Give the modified $$S$$.

(b) Let $$S = \left\{ {a,\,\,b} \right\}\,\,\,\,$$ and let ▢ $$S$$ be the power set of $$S$$. Consider the binary relation $$'\underline \subset $$ (set inclusion)' on ▢ $$S$$. Draw the Hasse diagram corresponding to the lattice (▢$$(S)$$, $$\underline \subset $$)

2
GATE CSE 2002
Subjective
+2
-0
Obtain the eigen values of the matrix $$$A = \left[ {\matrix{ 1 & 2 & {34} & {49} \cr 0 & 2 & {43} & {94} \cr 0 & 0 & { - 2} & {104} \cr 0 & 0 & 0 & { - 1} \cr } } \right]$$$
3
GATE CSE 2002
MCQ (Single Correct Answer)
+2
-0.6
The function $$f\left( {x,y} \right) = 2{x^2} + 2xy - {y^3}$$ has
A
Only one stationary point at $$(0, 0)$$
B
Two stationary points at $$(0, 0)$$ and $$\left( {{1 \over 6},{{ - 1} \over 3}} \right)$$
C
Two stationary points at $$(0, 0)$$ and $$(1, -1)$$
D
no stationary points.
4
GATE CSE 2002
MCQ (Single Correct Answer)
+1
-0.3
Which of the following scheduling algorithms is non-preemptive?
A
Round Robin
B
First-In First-Out
C
Multilevel Queue Scheduling
D
Multilevel Queue Scheduling with Feedback
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