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:

There are 5 questions to complete.