GATE CSE 2007 | GATE CSE Year Wise Previous Years Questions

GATE CSE 2007

MCQ (Single Correct Answer)

-0.6

Consider the set of (column) vectors defined by $$X = \,\{ \,x\, \in \,{R^3}\,\left| {{x_1}\, + \,{x_2}\, + \,{x_3} = 0} \right.$$, where $${x^T} = \,{[{x_1}\, + \,{x_2}\, + \,{x_3}]^T}\} .$$ Which of the following is TRUE?

$$\left\{ {{{\left[ {1,\, - 1,\,0} \right]}^T},\,{{\left[ {1,\,\,0 ,- 1,\,} \right]}^T}} \right\}$$ is a basis for the subspace X.

$$\left\{ {{{\left[ {1,\, - 1,\,0} \right]}^T},\,{{\left[ {1,\,\,0,\, - 1,\,} \right]}^T}} \right\}$$ is a linearly independent set, but it does not span X and therefore is not a basis of X.

X is not a subspace of $${R^3}$$.

None of the above.

GATE CSE 2007

MCQ (Single Correct Answer)

-0.3

The maximum number of binary trees that can be formed with three unlabeled nodes is:

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)

-0.3

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

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