Question 1 |

Consider the following two statements about the function f(x)=|x|:

P. f(x) is continuous for all real values of x

Q. f(x) is differentiable for all real values of x

Which of the following is TRUE?

P. f(x) is continuous for all real values of x

Q. f(x) is differentiable for all real values of x

Which of the following is TRUE?

P is true and Q is false. | |

P is false and Q is true. | |

Both P and Q are true. | |

Both P and Q are false. |

Question 1 Explanation:

Question 2 |

Let S be a set of n elements. The number of ordered pairs in the largest and the
smallest equivalence relations on S are:

n and n | |

n^{2} \; and \; n | |

n^{2} \; and \; 0 | |

n and 1 |

Question 2 Explanation:

Question 3 |

What is the maximum number of different Boolean functions involving n Boolean
variables?

n^{2} | |

2^{n} | |

2^{2^{n}} | |

2^{n^{2}} |

Question 3 Explanation:

Question 4 |

Let G be the non-planar graph with the minimum possible number of edges. Then G has

9 edges and 5 vertices | |

9 edges and 6 vertices | |

10 edges and 5 vertices | |

10 edges and 6 vertices |

Question 4 Explanation:

Question 5 |

Consider the DAG with V = {1,2,3,4,5,6}, shown below.

Which of the following is NOT a topological ordering?

Which of the following is NOT a topological ordering?

1 2 3 4 5 6 | |

1 3 2 4 5 6 | |

1 3 2 4 6 5 | |

3 2 4 1 6 5 |

Question 5 Explanation:

Question 6 |

Which of the following problems is undecidable?

Membership problem for CFGs. | |

Ambiguity problem for CFGs. | |

Finiteness problem for FSAs. | |

Equivalence problem for FSAs. |

Question 6 Explanation:

Question 7 |

Which of the following is TRUE?

Every subset of a regular set is regular. | |

Every finite subset of a non-regular set is regular. | |

The union of two non-regular sets is not regular. | |

Infinite union of finite sets is regular. |

Question 7 Explanation:

Question 8 |

How many 3-to-8 line decoders with an enable input are needed to construct a 6-
to-64 line decoder without using any other logic gates?

7 | |

8 | |

9 | |

10 |

Question 8 Explanation:

Question 9 |

Consider the following Boolean function of four variables:

f (w, x, y, z)=\Sigma(1,3,4,6,9,11,12,14)

The function is:

f (w, x, y, z)=\Sigma(1,3,4,6,9,11,12,14)

The function is:

independent of one variables | |

independent of two variables. | |

independent of three variables. | |

dependent on all the variables |

Question 9 Explanation:

Question 10 |

Consider a 4-way set associative cache consisting of 128 lines with a line size of
64 words. The CPU generates a 20-bit address of a word in main memory. The
number of bits in the TAG, LINE and WORD fields are respectively:

9, 6, 5 | |

7, 7, 6 | |

7, 5, 8 | |

9, 5, 6 |

Question 10 Explanation:

There are 10 questions to complete.