GATE CSE 2005 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let $$P(x)$$ and $$Q(x)$$ be arbitrary predicates. Which of the following statement is always TRUE?

$$\left( {\forall x\left( {P\left( x \right) \vee Q\left( x \right)} \right)} \right) \Rightarrow \left( {\left( {\forall xP\left( x \right)} \right) \vee \left( {\forall xQ\left( x \right)} \right)} \right)$$

$$\left( {\forall x\left( {P\left( x \right) \Rightarrow Q\left( x \right)} \right)} \right) \Rightarrow \left( {\left( {\forall xP\left( x \right)} \right) \Rightarrow \left( {\forall xQ\left( x \right)} \right)} \right)$$

$$\left( {\left( {\forall x\left( {P\left( x \right)} \right) \Rightarrow \left( {\forall xQ\left( x \right)} \right)} \right) \Rightarrow \left( {\forall x\left( {P\left( x \right) \Rightarrow Q\left( x \right)} \right)} \right)} \right)$$

$$\left( {\left( {\forall x\left( {P\left( x \right)} \right)} \right)} \right) \Leftrightarrow \left( {\forall x\left( {Q\left( x \right)} \right)} \right) \Rightarrow \left( {\forall x\left( {P\left( x \right) \Leftrightarrow Q\left( x \right)} \right)} \right)$$

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Let $$P, Q$$ and $$R$$ be three atomic prepositional assertions. Let $$X$$ denotes $$\left( {P \vee Q} \right) \to R$$ and $$Y$$ denote $$\left( {P \to R} \right) \vee \left( {Q \to R} \right)$$.

Which one of the following is a tautology?

$$X \equiv Y$$

$$X \to Y$$

$$Y \to X$$

$$\neg Y \to X$$

GATE CSE 2005

MCQ (Single Correct Answer)

-0.3

What is the swap space in the disk used for?

Saving temporary html pages

Saving process data

Storing the super-block

Storing device drivers

GATE CSE 2005

MCQ (Single Correct Answer)

-0.6

Suppose n processes, P₁,......., P_n share m identical resource units, which can be reserved and released one at a time. The maximum resource requirement of process P_i is S_i, where S_i > 0. Which one of the following is a sufficient condition for ensuring that deadlock does not occur?

$$\forall i,{s_i} < m$$

$$\forall i,{s_i} < n$$

$$\sum\limits_{i = 1}^n {{s_i}} < \left( {m + n} \right)$$

$$\sum\limits_{i = 1}^n {{s_i}} < \left( {m \times n} \right)$$

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