Question 1 |
Let A and B be sets and let A^c and B^c denote the complements of the sets A and B. The set (A-B) \cup (B-A) \cup (A \cap B) is equal to
A \cup B | |
A^c \cup B^c | |
A \cap B | |
A^c \cap B^c |
Question 1 Explanation:
Question 2 |
Let X = \{2, 3, 6, 12, 24\}, Let \leq be the partial order defined by X \leq Y if x divides y. Number of edges in the Hasse diagram of (X, \leq) is
3 | |
4 | |
9 | |
None of the above |
Question 2 Explanation:
Question 3 |
Suppose X and Y are sets and |X| and |Y| are their respective cardinality. It is given that there are exactly 97 functions from X to Y. From this one can conclude that
|X| =1, |Y| =97 | |
|X| =97, |Y| =1 | |
|X| =97, |Y| =97 | |
None of the above |
Question 3 Explanation:
Question 4 |
Which of the following statements is FALSE?
The set of rational numbers is an abelian group under addition | |
The set of integers in an abelian group under addition | |
The set of rational numbers form an abelian group under multiplication | |
The set of real numbers excluding zero is an abelian group under multiplication |
Question 4 Explanation:
Question 5 |
Two dice are thrown simultaneously. The probability that at least one of them will have 6 facing up is
\frac{1}{36} | |
\frac{1}{3} | |
\frac{25}{36} | |
\frac{11}{36} |
Question 5 Explanation:
Question 6 |
The formula used to compute an approximation for the second derivative of a function f at a point x_0 is
\dfrac{f(x_0 +h) + f(x_0 - h)}{2} | |
\dfrac{f(x_0 +h) - f(x_0 - h)}{2h} | |
\dfrac{f(x_0 +h) + 2f(x_0) + f(x_0 - h)}{h^2} | |
\dfrac{f(x_0 +h) - 2f(x_0) + f(x_0 - h)}{h^2} |
Question 6 Explanation:
Question 7 |
Let AX = b be a system of linear equations where A is an m \times n matrix and b is a m \times 1 column vector and X is an n \times 1 column vector of unknowns. Which of the following is false?
The system has a solution if and only if, both A and the augmented matrix [Ab] have the same rank. | |
If m < n and b is the zero vector, then the system has infinitely many solutions. | |
If m=n and b is a non-zero vector, then the system has a unique solution. | |
The system will have only a trivial solution when m=n, b is the zero vector and rank (A) =n. |
Question 7 Explanation:
Question 8 |
Which two of the following four regular expressions are equivalent? (\varepsilon is the empty string).
(i). (00)^ * (\varepsilon +0)
(ii). (00)^*
(iii). 0^*
(iv). 0(00)^*
(i). (00)^ * (\varepsilon +0)
(ii). (00)^*
(iii). 0^*
(iv). 0(00)^*
(i) and (ii) | |
(ii) and (iii) | |
(i) and (iii) | |
(iii) and (iv) |
Question 8 Explanation:
Question 9 |
Which of the following statements is false?
The Halting Problem of Turing machines is undecidable | |
Determining whether a context-free grammar is ambiguous is undecidable | |
Given two arbitrary context-free grammars G_1 and G_2it is undecidable whether L(G_1) = L(G_2) | |
Given two regular grammars G_1 and G_2 it is undecidable whether L(G_1) = L(G_2) |
Question 9 Explanation:
Question 10 |
Let L \subseteq \Sigma^* where \Sigma = \left\{a,b \right\}. Which of the following is true?
L = \left\{x \mid x \text{ has an equal number of } a\text{'s and }b\text{'s}\right \} is regular | |
L = \left\{a^nb^n \mid n \geq 1\right \} is regular | |
L = \left\{x \mid x \text{ has more number of }a\text{'s than }b\text{'s}\right \} is regular | |
L = \left\{a^mb^n \mid m \geq 1, n \geq 1 \right \} is regular |
Question 10 Explanation:
There are 10 questions to complete.
