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 _______ .

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 _________.

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 $$G$$?

Consider the statement
"Not all that glitters is gold"
Predicate glitters$$(x)$$ is true if $$x$$ glitters and
predicate gold$$(x)$$ is true if $$x$$ is gold.

Which one of the following logical formulae represents the above statement?