1
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Which one of these first-order logic formulae is valid?
A
$$\forall x\left( {P\left( x \right) \Rightarrow Q\left( x \right)} \right) \Rightarrow \left( {\left( {\forall xP\left( x \right)} \right) \Rightarrow \left( {\forall xQ\left( x \right)} \right)} \right)$$
B
$$\exists x\left( {P\left( x \right) \vee Q\left( x \right)} \right) \Rightarrow \left( {\left( {\exists xP\left( x \right)} \right) \Rightarrow \left( {\exists xQ\left( x \right)} \right)} \right)$$
C
$$\exists x\left( {P\left( x \right) \wedge Q\left( x \right)} \right) \Leftrightarrow \left( {\left( {\exists xP\left( x \right)} \right) \wedge \left( {\exists xQ\left( x \right)} \right)} \right)$$
D
$$\forall x\exists yP\left( {x,y} \right) \Rightarrow \exists y\forall xP\left( {x,y} \right)$$
2
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
Suppose we uniformly and randomly select a permutation from the 20! permutations of 1, 2, 3,..., 20. What is the promutations that 2 appears at an earlier position than any other even number in the selected permutation?
A
$${{1 \over 2}}$$
B
$${{1 \over 10}}$$
C
$${{9! \over 20!}}$$
D
None of the above.
3
GATE CSE 2007
MCQ (Single Correct Answer)
+1
-0.3
Suppose there are two coins. The first coin gives heads with probability 5/8 when tossed, while the second coin gives heads with probability 1/4. On e of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads?
A
7/8
B
$${\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}$$
C
7/16
D
5/32
4
GATE CSE 2007
MCQ (Single Correct Answer)
+2
-0.6
A virtual memory system uses First In First Out (FIFO) page replacement policy and allocates a fixed number of frames to a process. Consider the following statements:
$$P:$$ Increasing the number of page frames allocated to a process sometimes increases the page fault rate.
$$Q:$$ Some programs do not exhibit locality of reference.

Which one of the following is TRUE?

A
Both P and Q are true, and Q is the reason for P
B
Both P and Q are true, but Q is not the reason for P.
C
P is false, but Q is true
D
Both P and Q are false.
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