# 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 |

**Set Theory & Algebra**

**GATE CS 1999**

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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. |

**Probability**

**GATE CS 1999**

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Question 2 Explanation:

The first option is wrong since the Expected value need not be present in the data.
The second option is wrong since in the event where every value in the data is the same, the expected value is the same as every value. So, In this case, there is no value which is greater than the expected value.
The third option is correct, Since there must be some value which is either equal to or greater than the expected value. This is because it is impossible to have all the values less than the expected value as it is analogous to the mean. And the mean value is never greater than all the values of the data.

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 |

**Combinatorics**

**GATE CS 1999**

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Question 3 Explanation:

There are n zeros placed :
_0_0_0_....._0_
So, (n+1) gaps. Now we can place k 1's in those place n+1Ck ways.
Option (D) is correct.

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 |

**Regular languages and finite automata**

**GATE CS 1999**

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Question 5 |

Context free languages are closed under-

Union, Intersection | |

Union, Kleene closure | |

Intersection, Complement | |

Complement, Kleene closure |

**Context free languages and Push-down automata**

**GATE CS 1999**

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Question 5 Explanation:

Context free languages are closed under: Union, Concatenation and Kleene closure but not in Intersection and Complement.
Option (B) is correct.

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 |

**Context free languages and Push-down automata**

**GATE CS 1999**

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Question 7 |

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

x NAND x | |

x NOR x | |

x NAND 1 | |

x NOR 1 |

**Digital Logic & Number representation**

**GATE CS 1999**

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Question 8 |

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

a | |

b | |

c | |

d |

**Digital Logic & Number representation**

**GATE CS 1999**

**Logic functions and Minimization**

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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 |

**OS Memory Management**

**GATE CS 1999**

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Question 9 Explanation:

- Thread is handled by CPU.
- Virtual address space (it is a set of virtual memory addresses that a process can use) is associated with memory management.
- File System is used for disk management.
- Interrupt is a type of signal.

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 |

**OS CPU Scheduling**

**GATE CS 1999**

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Question 10 Explanation:

Nearest cylinder next is also known as shortest seek time first and in this algorithm many pages can be accessed in less amount of time.
So throughput will be high so this is optimal algorithm.
Option (B) is correct.

There are 70 questions to complete.