Question 1 |

In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?

\left(\dfrac{3}{23}\right) | |

\left(\dfrac{6}{23}\right) | |

\left(\dfrac{3}{10}\right) | |

\left(\dfrac{3}{5}\right) |

Question 1 Explanation:

Question 2 |

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Programming Language and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.
How many students have not taken any of the three courses?

15 | |

20 | |

25 | |

30 |

Question 2 Explanation:

Question 3 |

Let a(x, y), b(x, y,) and c(x, y) be three statements with variables x and y chosen from some universe. Consider the following statement:

\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]

Which one of the following is its equivalent?

\qquad(\exists x)(\forall y)[(a(x, y) \wedge b(x, y)) \wedge \neg c(x, y)]

Which one of the following is its equivalent?

(\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)] | |

(\exists x)(\forall y)[(a(x, y) \vee b(x, y)) \wedge\neg c(x, y)] | |

\neg (\forall x)(\exists y)[(a(x, y) \wedge b(x, y)) \to c(x, y)] | |

\neg (\forall x)(\exists y)[(a(x, y) \vee b(x, y)) \to c(x, y)] |

Question 3 Explanation:

Question 4 |

Let R_{1} be a relation from A =\left \{ 1,3,5,7 \right \} to B = \left \{ 2,4,6,8 \right \}. R_{2} be another relation from B to C = {1, 2, 3, 4} as defined below:

i. An element x in A is related to an element y in B (under R_{1}) if x + y is divisible by 3.

ii. An element x in B is related to an element y in C (under R_{2}) if x + y is even but not divisible by 3.

Which is the composite relation R_{1}R_{2} from A to C?

i. An element x in A is related to an element y in B (under R_{1}) if x + y is divisible by 3.

ii. An element x in B is related to an element y in C (under R_{2}) if x + y is even but not divisible by 3.

Which is the composite relation R_{1}R_{2} from A to C?

R_{1}R_{2} = {(1, 2), (1, 4), (3, 3), (5, 4), (7, 3)} | |

R_{1}R_{2} = {(1, 2), (1, 3), (3, 2), (5, 2), (7, 3)} | |

R_{1}R_{2} = {(1, 2), (3, 2), (3, 4), (5, 4), (7, 2)} | |

R_{1}R_{2} = {(3, 2), (3, 4), (5, 1), (5, 3), (7, 1)} |

Question 4 Explanation:

Question 5 |

What is the maximum number of edges in an acyclic undirected graph with n vertices?

n-1 | |

n | |

n+1 | |

2n-1 |

Question 5 Explanation:

Question 6 |

What values of x, y and z satisfy the following system of linear equations?

\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}

\begin{bmatrix} 1 &2 &3 \\ 1& 3 &4 \\ 2& 2 &3 \end{bmatrix} \begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 6\\8 \\ 12 \end{bmatrix}

x = 6, y = 3, z = 2 | |

x = 12, y = 3, z = - 4 | |

x = 6, y = 6, z = - 4 | |

x = 12, y = - 3, z = 0 |

Question 6 Explanation:

Question 7 |

Which one of the following regular expressions is NOT equivalent to the regular expression (a + b + c)^*?

(a^* + b^* + c^*)^* | |

(a^*b^*c^*)^* | |

((ab)^* + c^*)^* | |

(a^*b^* + c^*)^* |

Question 7 Explanation:

Question 8 |

What is the minimum number of NAND gates required to implement a 2-input EXCLUSIVE-OR function without using any other logic gate?

2 | |

4 | |

5 | |

6 |

Question 8 Explanation:

Question 9 |

Which one of the following statements is FALSE?

There exist context-free languages such that all the context-free grammars generating them are ambiguous | |

An unambiguous context-free grammar always has a unique parse tree for each string of the language generated by it | |

Both deterministic and non-deterministic pushdown automata always accept the same set of languages | |

A finite set of string from some alphabet is always a regular language |

Question 9 Explanation:

Question 10 |

What is the minimum size of ROM required to store the complete truth table of an 8-bit \times 8-bit multiplier?

32 K \times 16 bits | |

64 K \times 16 bits | |

16 K \times 32 bits | |

64 K \times 32 bits |

Question 10 Explanation:

There are 10 questions to complete.