GATE CSE 1999


Question 1
Suppose that the expectation of a random variable X is 5. Which of the following statements is true?
A
There is a sample point at which X has the value 5.
B
There is a sample point at which X has value greater than 5.
C
There is a sample point at which X has a value greater than equal to 5.
D
None of the above
Discrete Mathematics   Probability Theory
Question 2
The number of binary relations on a set with n elements is:
A
n^2
B
2^n
C
2^{n^2}
D
None of the above
Discrete Mathematics   Relation


Question 3
The number of binary strings of n zeros and k ones in which no two ones are adjacent is
A
^{n-1}C_k
B
^nC_k
C
^nC_{k+1}
D
None of the above
Discrete Mathematics   Combination
Question 4
Consider the regular expression (0 + 1) (0+1) ... n times. The minimum state finite automaton that recognizes the language represented by this regular expression contains
A
n states
B
n+1 states
C
n+2 states
D
None of the above
Theory of Computation   Finite Automata
Question 5
Context-free languages are closed under:
A
Union, intersection
B
Union, Kleene closure
C
Intersection, complement
D
Complement, Kleene closure
Theory of Computation   Context Free Language


There are 5 questions to complete.

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