Question 1 |

If g(x)=1-x and h(x)=\frac{x}{x-1}, then \frac{g(h(x))}{h(g(x))} is:

\frac{h(x)}{g(x)} | |

\frac{-1}{x} | |

\frac{g(x)}{h(x)} | |

\frac{x}{(1-x)^{2}} |

Question 1 Explanation:

Question 2 |

\lim_{x\rightarrow \infty }x^{1/x} is

\infty | |

0 | |

1 | |

Not defined |

Question 2 Explanation:

Question 3 |

Match the following:

P-iii, Q-ii, R-iv, S-i | |

P-i, Q-ii, R-iv, S-iii | |

P-ii, Q-iii, R-iv, S-i | |

P-ii, Q-i, R-iii, S-iv |

Question 3 Explanation:

Question 4 |

Which one of the following is the recurrence equation for the worst case time complexity of the Quicksort algorithm for sorting n ( \geq2) numbers? In the recurrence equations given in the options below, c is a constant.

T(n)=2T(n/2)+cn | |

T(n)=T(n-1)+T(1)+cn | |

T(n)=2T(n-1)+cn | |

T(n)=T(n/2)+cn |

Question 4 Explanation:

Question 5 |

The height of a tree is the length of the longest root-to-leaf path in it. The maximum and minimum number of nodes in a binary tree of height 5 are

63 and 6, respectively | |

64 and 5, respectively | |

32 and 6, respectively | |

31 and 5, respectively |

Question 5 Explanation:

Question 6 |

Match the following:

P-ii, Q-iii, R-i, S-iv | |

P-iii, Q-iv, R-ii, S- i | |

P-iii, Q-i, R-iv, S-ii | |

P-iii, Q-i, R-ii, S-iv |

Question 6 Explanation:

Question 7 |

Which of the following is/are correct inorder traversal sequence(s) of binary search tree(s)?

I. 3, 5, 7, 8, 15, 19, 25

II. 5, 8, 9, 12, 10, 15, 25

III. 2, 7, 10, 8, 14, 16, 20

IV. 4, 6, 7, 9 18, 20, 25

I. 3, 5, 7, 8, 15, 19, 25

II. 5, 8, 9, 12, 10, 15, 25

III. 2, 7, 10, 8, 14, 16, 20

IV. 4, 6, 7, 9 18, 20, 25

I and IV only | |

II and III only | |

II and IV only | |

II only |

Question 7 Explanation:

Question 8 |

Which one of the following is TRUE at any valid state in shift-reduce parsing?

Viable prefixes appear only at the bottom of the stack and not inside | |

Viable prefixes appear only at the top of the stack and not inside | |

The stack contains only a set of viable prefixes | |

The stack never contains viable prefixes |

Question 8 Explanation:

Question 9 |

Which one of the following is NOT equivalent to p\leftrightarrow q?

(\neg p\vee q)\wedge (p\vee \neg q) | |

(\neg p\vee q)\wedge (q \rightarrow p) | |

(\neg p \wedge q)\vee (p \wedge \neg q) | |

(\neg p \wedge \neg q)\vee (p \wedge q) |

Question 9 Explanation:

Question 10 |

For a set A, the power set of A is denoted by 2^{A}. If A={5,{6},{7}}, which of the following options are TRUE?

I. \phi \in 2^{A}

II. \phi \subseteq 2^{A}

III. {5,{6}} \in 2^{A}

IV. {5,{6}}\subseteq 2^{A}

I. \phi \in 2^{A}

II. \phi \subseteq 2^{A}

III. {5,{6}} \in 2^{A}

IV. {5,{6}}\subseteq 2^{A}

I and III only | |

II and III only | |

I, II and III only | |

I, II and IV only |

Question 10 Explanation:

There are 10 questions to complete.