1
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the circuit in the diagram. The $$ \oplus $$ operator represents $$EX$$-$$OR.$$ The $$D$$ flip-flops are initialized to zeros (cleared). GATE CSE 2006 Digital Logic - Sequential Circuits Question 10 English

The following data: $$100110000$$ is supplied to the ''data'' terminal in nine clock cycles. After that the values of $${q_2}{q_1}{q_0}$$ are

A
$$000$$
B
$$001$$
C
$$010$$
D
$$101$$
2
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Which one of the first order predicate calculus statements given below correctly expresses the following English statement?

Tigers and lion attack if they are hungry of threatened.

A
$$\forall x[(tiger(x) \wedge lion(x)) \to $$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
B
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ (hungry(x) \wedge threatened(x)) \to attacks(x)\} ]$$
C
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ attacks(x) \to (hungry(x)) \vee threatened(x))\} ]$$
D
$$\forall x[(tiger(x) \vee lion(x)) \to $$$$\{ (hungry(x) \vee threatened(x)) \to attacks(x)\} ]$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the following propositional statements:


$${\rm P}1:\,\,\left( {\left( {A \wedge B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \wedge \left( {B \to C} \right)} \right)$$
$${\rm P}2:\,\,\left( {\left( {A \vee B} \right) \to C} \right) \equiv \left( {\left( {A \to C} \right) \vee \left( {B \to C} \right)} \right)$$ Which one of the following is true?

A
$$P1$$ is tautology, but not $$P2$$
B
$$P2$$ is tautology, but not $$P1$$
C
$$P1$$ and $$P2$$ are both tautologies
D
Both $$P1$$ and $$P2$$ are not tautologies
4
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
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
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