1
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
Consider a weighted complete graph $$G$$ on the vertex set $$\left\{ {{v_1},\,\,\,{v_2},....,\,\,\,{v_n}} \right\}$$ such that the weight of the edge $$\left( {{v_i},\,\,\,\,{v_j}} \right)$$ is $$2\left| {i - j} \right|$$. The weight of a minimum spanning tree of $$G$$ is
A
$$n - 1$$
B
$$2n - 2$$
C
$$\left( {\matrix{ n \cr 2 \cr } } \right)$$
D
$${n^2}$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices and has minimum total weight is a
A
Hamiltonian cycle
B
grid
C
hypercube
D
tree
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the set S = {a, b, c, d}. Consider the following 4 partitions $$\,{\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}$$ on $$S:\,{\pi _1} = \left\{ {\overline {a\,b\,c\,d} } \right\},\,{\pi _2} = \left\{ {\overline {a\,b\,} ,\,\overline {c\,d} } \right\},\,{\pi _3} = \left\{ {\overline {a\,b\,c\,} ,\,\overline d } \right\},\,{\pi _4} = \left\{ {\overline {a\,} ,\,\overline b ,\,\overline c ,\,\overline d } \right\}.$$ Let $$ \prec $$ be the partial order on the set of partitions $$S' = \{ {\pi _1},\,{\pi _2},\,{\pi _3},\,{\pi _4}\} $$ defined as follows: $${\pi _i} \prec \,\,{\pi _j}$$ if and only if $${\pi _i} $$ refines $${\pi _j}$$. The poset diagram for $$(S',\, \prec )$$ is
A
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 41 English Option 1
B
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 41 English Option 2
C
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 41 English Option 3
D
GATE CSE 2006 Discrete Mathematics - Set Theory & Algebra Question 41 English Option 4
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Let S = {1, 2, 3,....., m} , m > 3. Let $${X_1},\,....,\,{X_n}$$ be subsets of S each of size 3. Define a function f from S to the set of natural numbers as, f (i) is the number of sets $${X_j}$$ that contain the element i. That is $$f(i) = \left\{ {j\left| i \right.\,\, \in \,{X_j}} \right\}\left| . \right.$$

Then $$\sum\limits_{i - 1}^m {f\,(i)} $$ is

A
3m
B
3n
C
2m + 1
D
2n + 1
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