GATE CSE 2007 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2007

MCQ (Single Correct Answer)

-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?

$${{1 \over 2}}$$

$${{1 \over 10}}$$

$${{9! \over 20!}}$$

None of the above.

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Which one of these first-order logic formulae is valid?

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

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

$$\exists x\left( {P\left( x \right) \wedge Q\left( x \right)} \right) \Leftrightarrow \left( {\left( {\exists xP\left( x \right)} \right) \wedge \left( {\exists xQ\left( x \right)} \right)} \right)$$

$$\forall x\exists yP\left( {x,y} \right) \Rightarrow \exists y\forall xP\left( {x,y} \right)$$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

How many different non-isomorphic Abelian groups of order 4 are there?

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

Let $$S$$ be a set6 of $$n$$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $$S$$ are

$$n$$ and $$n$$

$${n^2}\,$$ and $$n$$

$${n^2}\,$$ and $$0$$

$$n$$ and $$1$$

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