1) Let A and B be any two arbitrary events then which one of the following is true ?

1. P( A intersection B) = P(A). P(B)
2. P(A union B) = P(A) + P(B)
3. P(AB) = P(A intersection B). P(B)
4. P(A union B) >= P(A) + P(B)

2) If X and Y be the sets. Then the set ( X – Y) union (Y- X) union (X intersection Y ) is equal to?

1. X union Y
2. X^c union Y^c
3. X intersection Y
4. X^c intersection Y^c

3) If G is an undirected planer graph on n vertices with e edges then ?

1. e<=n
2. e<=2n
3. e<=3n
4. None of these

4) Which of the following statement is false ?

1. G is connected and is circuitless
2. G is connected and has n edges
3. G is minimally connected graph
4. G is circuitless and has n-1 edges

5) Probability that two randomly selected cards from a set of two red and two black cards are of same color is ?

1. 1 / 2
2. 1 / 3
3. 2 / 3
4. None of these

6) The number of circuits that can be created by adding an edge between any two vertices in a tree is ?

1. Two
2. Exactly one
3. At least two
4. None

7) In a tree between every pair of vertices there is ?

1. Exactly one path
2. A self loop
3. Two circuits
4. n number of paths

8) The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is ?

1. 8
2. 3
3. 9
4. 12

9) Context free languages are closed under ?

1. union, intersection
2. Intersection , complement
3. union , kleene star
4. Complement , kleene star

10) Let R be a symmetric and transitive relation on a set A. Then ?

1. R is reflexive and hence a partial order
2. R is reflexive and hence an equivalence relation
3. R is not reflexive and hence not an equivalence relation
4. None of above