GATE CS 1999

Question 1

The number of binary relations on a set with n elements is:

• n²
• 2^n
• 2^n²
• None of the above

Question 2

Suppose that the expectation of a random variable X is 5. Which of the following statement is True?  

• There is a simple point at which X has the value 5.
• There is a simple point at which X has value greater than 5.
• There is a simple point at which X has a value greater than or equal to 5.
• None of the above.

Question 3

The number of binary strings of n zeros and k ones such that no two ones are adjacent is:

• a
• b
• c
• d

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:

• n states
• n+1 states
• n+2 states
• None of the above

Question 5

Context free languages are closed under-

• Union, Intersection
• Union, Kleene closure
• Intersection, Complement
• Complement, Kleene closure

Question 6

Let L_D  be the set of all languages accepted by a PDA by final state and L_F  the set of all languages accepted by empty stack. Which of the following is true?

• a
• b
• c
• d

Question 7

Which of the following expressions is not equivalent to X‾  ?

• x NAND x
• x NOR x
• x NAND 1
• x NOR 1

Question 8

Which of the following function implements the Karnaugh map shown below?

• a
• b
• c
• d

Question 9

Listed below are some operating system abstractions (in the left column) and the hardware components or mechanism (in the right column) that they are abstractions of. Which of the following matching of pairs is correct?

A. Thread                      1. Interrupt
B. Virtual address space       2. Memory
C. File system                 3. CPU
D. Signal                      4. Disk

• A-2, B-4, C-3, D-1
• A-1, B-2, C-3, D-4
• A-3, B-2, C-4, D-1
• A-4, B-1, C-2, D-3

Question 10

Which of the following disk strategies is likely to give the best throughput?

• Farthest cylinder next
• Nearest cylinder next
• First come first served
• Elevator algorithm