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1.
What is the maximum number of different Boolean functions involving n Boolean variables?
2.
Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of k colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of k that satisfies this requirement ?
3.
How many onto (or surjective) functions are there from an n-element (n >= 2) set to a 2-element set?
4.
What is the possible number of reflexive relations on a set of 5 elements?
5.
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is
6.
Let G be a simple graph with 20 vertices and 100 edges. The size of the minimum vertex cover of G is 8. Then, the size of the maximum independent set of G is
7.
The 2n vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of connected components in G is:
8.
If G is a forest with n vertices and k connected components, how many edges does G have?
9.
The 2n vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6 . Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements. The number of vertices of degree zero in G is:
10.
A cycle on n vertices is isomorphic to its complement. The value of n is _____.