# GATE IT 2006

 Question 1
In a certain town, the probability that it will rain in the afternoon is known to be 0.6. Moreover, meteorological data indicates that if the temperature at noon is less than or equal to $25^{\circ}C$, the probability that it will rain in the afternoon is 0.4. The temperature at noon is equally likely to be above $25^{\circ}C$, or at/below $25^{\circ}C$. What is the probability that it will rain in the afternoon on a day when the temperature at noon is above $25^{\circ}C$?
 A 0.4 B 0.6 C 0.8 D 0.9
Discrete Mathematics   Probability Theory
Question 1 Explanation:
 Question 2
For the set N of natural numbers and a binary operation $f : N \times N \to N$, an element $z \in N$ is called an identity for f, if f (a, z) = a = f(z, a), for all $a \in N$. Which of the following binary operations have an identity?
i. $f (x, y) = x + y - 3$
ii. $f (x, y) = \max(x, y)$
iii. $f (x, y) = x^y$
 A I and II only B II and III only C I and III only D None of these
Discrete Mathematics   Set Theory
Question 2 Explanation:

 Question 3
In the automaton below, s is the start state and t is the only final state. Consider the strings $u = abbaba, v = bab, \text{ and } w = aabb$. Which of the following statements is true?
 A The automaton accepts u and v but not w B The automaton accepts each of u, v, and w C The automaton rejects each of u, v, and w D The automaton accepts u but rejects v and w
Theory of Computation   Finite Automata
Question 3 Explanation:
 Question 4
In the context-free grammar below, S is the start symbol, a and b are terminals, and$\epsilon$ denotes the empty string
$S \rightarrow aSa \mid bSb \mid a \mid b \mid \epsilon$
Which of the following strings is NOT generated by the grammar?
 A aaaa B baba C abba D babaaabab
Theory of Computation   Context Free Grammar
Question 4 Explanation:
 Question 5
Which regular expression best describes the language accepted by the non-deterministic automaton below? A $(a + b)^* \ a(a + b)b$ B $(abb)^*$ C $(a + b)^* \ a(a + b)^* \ b(a + b)^*$ D $(a + b)^*$
Theory of Computation   Regular Expression
Question 5 Explanation:

There are 5 questions to complete.