GATE CSE 2007 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

Consider a weighted undirected graph with positive edge weights and let $$uv$$ be an edge in the graph. It is known that the shortest path from the source vertex $$s$$ to $$u$$ has weight 53 and the shortest path from $$s$$ to $$v$$ has weighted 65. Which one of the following statements is always true?

weight$$(u, v)$$ $$ < 12$$

weight$$(u, v)$$ $$ \le 12$$

weight$$(u, v)$$ $$ > 12$$

weight$$(u, v)$$ $$ \ge 12$$

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $$h$$ is:

$${2^h} - 1$$

$${2^{h - 1}} - 1$$

$${2^{h + 1}} - 1$$

$${2^{h + 1}}$$

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)

-0.3

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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