Question 1 |

\lim_{x\rightarrow \infty }\frac{x-sin x}{x+cos x} equals

1 | |

-1 | |

\infty | |

-\infty |

Question 1 Explanation:

Question 2 |

If P, Q, R are subsets of the universal set U, then (P\cap Q\cap R)\cup (P^{C} \cap Q \cap R)\cup Q^{C} \cup R^{C} is

Q^{C} \cup R^{C} | |

P \cup Q^{C} \cup R^{C} | |

p^{C}\cup Q^{C} \cup R^{C} | |

U |

Question 2 Explanation:

Question 3 |

The following system of equations

x_{1}+x_{2}+2x_{3}=1

x_{1}+2x_{2}+3x_{3}=2

x_{1}+4x_{2}+\alpha x_{3}=4

has a unique solution. The only possible value(s) for \alpha is/are

x_{1}+x_{2}+2x_{3}=1

x_{1}+2x_{2}+3x_{3}=2

x_{1}+4x_{2}+\alpha x_{3}=4

has a unique solution. The only possible value(s) for \alpha is/are

0 | |

either 0 or 1 | |

one of 0, 1 or -1 | |

any real number other than 5 |

Question 3 Explanation:

Question 4 |

In the IEEE floating point representation the hexadecimal value 0x00000000
corresponds to

The normalized value 2^{-127} | |

The normalized value 2^{-126} | |

The normalized value +0 | |

The special value +0 |

Question 4 Explanation:

Question 5 |

In the Karnaugh map shown below, x denotes a don't care term. What is the
minimal form of the function represented by the Karnaugh map?

\bar{b}\cdot \bar{d}+\bar{a}\cdot \bar{d} | |

\bar{a}\bar{b}+\bar{b}\cdot \bar{d}+\bar{a}b\cdot \bar{d} | |

\bar{b}\cdot \bar{d}+\bar{a}b\cdot \bar{d} | |

\bar{a}\bar{b}+\bar{b}\cdot \bar{d}+\bar{a}\cdot \bar{d} |

Question 5 Explanation:

Question 6 |

Let r denote number system radix. The only value(s) of r that satisfy the
equation \sqrt{121_{r}}=11_{r} is / are

decimal 10 | |

decimal 11 | |

decimal 10 and 11 | |

any value \gt 2 |

Question 6 Explanation:

Question 7 |

The most efficient algorithm for finding the number of connected components in
an undirected graph on n vertices and m edges has time complexity

\Theta (n) | |

\Theta (m) | |

\Theta (m+n) | |

\Theta (mn) |

Question 7 Explanation:

Question 8 |

Given f1, f3 and f in canonical sum of products form (in decimal) for the circuit

f_{1}=\sum m(4,5,6,7,8)

f_{3}=\sum m(1,6,15)

f=\sum m(1,6,8,15)

then f_{2} is

f_{1}=\sum m(4,5,6,7,8)

f_{3}=\sum m(1,6,15)

f=\sum m(1,6,8,15)

then f_{2} is

\summ(4,6) | |

\summ(4,8) | |

\summ(6,8) | |

\summ(4,6,8) |

Question 8 Explanation:

Question 9 |

Which of the following is true for the language{ a^{p}|p is a prime} ?

It is not accepted by a Turing Machine | |

It is regular but not context-free | |

It is context-free but not regular | |

It is neither regular nor context-free, but accepted by a Turing machine |

Question 9 Explanation:

Question 10 |

Which of the following are decidable?

I. Whether the intersection of two regular languages is infinite

II. Whether a given context-free language is regular

III. Whether two push-down automata accept the same language

IV. Whether a given grammar is context-free

I. Whether the intersection of two regular languages is infinite

II. Whether a given context-free language is regular

III. Whether two push-down automata accept the same language

IV. Whether a given grammar is context-free

I and II | |

I and IV | |

II and III | |

II and IV |

Question 10 Explanation:

There are 10 questions to complete.