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
Question 6
Let L_1 be the set of all languages accepted by a PDA by final state and L_2 the set of all languages accepted by empty stack. Which of the following is true?
A
L_1 = L_2
B
L_1 \supset L_2
C
L_1 \subset L_2
D
None
Theory of Computation   Push-down Automata
Question 7
Which of the following expressions is not equivalent to \bar{x}?
A
x NAND x
B
x NOR x
C
x NAND 1
D
x NOR 1
Digital Logic   Boolean Algebra
Question 8
Which of the following functions implements the Karnaugh map shown below?

A
\bar{A}B + CD
B
D(C+A)
C
AD+\bar{A}B
D
(C+D) (\bar{C}+D) + (A+B)
Digital Logic   Boolean Algebra
Question 9
Listed below are some operating system abstractions (in the left column) and the hardware components (in the right column)
\small \begin{array}{cl|cl}\hline \text{(A)}& \text{Thread} & \text{1.}& \text{Interrupt} \\\hline \text{(B)}& \text{Virtual address space} & \text{2.}& \text{Memory} \\\hline \text{(C)} &\text{File system} & \text{3.} &\text{CPU} \\\hline \text{(D)} &\text{Signal} & \text{4.}& \text{Disk} \\\hline \end{array}
A
(A) - 2 (B) - 4 (C) - 3 (D) - 1
B
(A) - 1 (B) - 2 (C) - 3 (D) - 4
C
(A) - 3 (B) - 2 (C) - 4 (D) - 1
D
(A) - 4 (B) - 1 (C) - 2 (D) - 3
Operating System   Memory Management
Question 10
Which of the following disk scheduling strategies is likely to give the best throughput?
A
Farthest cylinder next
B
Nearest cylinder next
C
First come first served
D
Elevator algorithm
Operating System   Disk Scheduling
There are 10 questions to complete.

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