1
GATE CSE 2014 Set 1
Numerical
+2
-0
There are 5 bags labeled 1 to 5. All the coins in given bag have the same weight. Some bags have coins of weight 10 gm, other have coins of weight 11 gm. $${\rm I}$$ pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coin is _______ .
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2
GATE CSE 2014 Set 1
Numerical
+2
-0
A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)} and the set of all 3-pennants is {(2,1),(1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10-pennants is _________.
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3
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $$G = \left( {V,E} \right)$$ be a directed graph where $$V$$ is the set of vertices and $$E$$ the set of edges. Then which one of the following graphs has the same strongly connected components as $$G$$?
A
$${G_1} = \left( {V,\,\,{E_1}} \right)\,\,\,$$where $$\,\,{E_1} = \left\{ {\left( {u,v} \right) \notin E} \right\}$$
B
$${G_2} = \left( {V,\,\,{E_2}} \right)\,\,\,$$ where $$\,\,\,{E_2} = \left\{ {\left( {u,v} \right) \in E} \right\}$$
C
$${G_3} = \left( {V,\,\,{E_3}} \right)\,\,\,$$ where $$\,\,{E_3} = $$ {$${\left( {u,v} \right)\left| \, \right.}$$ there isa path of length $$ \le 2$$ from $$u$$ to $$v$$ in $$E$$}
D
$${G_4} = \left( {{V_4},\,\,{E_{}}} \right)\,\,\,$$ where $${{V_4}}$$ is the set of vertices in $$G$$ which are not isolated.
4
GATE CSE 2014 Set 1
Numerical
+1
-0
The maximum number of edges in a bipartite graph on $$12$$ vertices is _________.
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