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.