1
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
If all the edge weights of an undirected graph are positive, then any subject of edges that connects all the vertices and has minimum total weight is a
A
Hamiltonian cycle
B
grid
C
hypercube
D
tree
2
GATE CSE 2006
MCQ (Single Correct Answer)
+1
-0.3
Consider a weighted complete graph $$G$$ on the vertex set $$\left\{ {{v_1},\,\,\,{v_2},....,\,\,\,{v_n}} \right\}$$ such that the weight of the edge $$\left( {{v_i},\,\,\,\,{v_j}} \right)$$ is $$2\left| {i - j} \right|$$. The weight of a minimum spanning tree of $$G$$ is
A
$$n - 1$$
B
$$2n - 2$$
C
$$\left( {\matrix{ n \cr 2 \cr } } \right)$$
D
$${n^2}$$
3
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
Consider the polynomial $$P\left( x \right) = {a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3},$$ where $${a_i} \ne 0,\forall i$$. The minimum number of multiplications needed to evaluate $$p$$ on an input $$x$$ is
A
$$3$$
B
$$4$$
C
$$6$$
D
$$5$$
4
GATE CSE 2006
MCQ (Single Correct Answer)
+2
-0.6
For each elements in a set of size $$2n$$, an unbiased coin in tossed. The $$2n$$ coin tosses are independent. An element is chhoosen if the corresponding coin toss were head.The probability that exactly $$n$$ elements are chosen is
A
$${{\left( {\matrix{ {2n} \cr n \cr } } \right)} \over {{4^n}}}$$
B
$${{\left( {\matrix{ {2n} \cr n \cr } } \right)} \over {{2^n}}}$$
C
$${1 \over {\left( {\matrix{ {2n} \cr n \cr } } \right)}}$$
D
$${1 \over 2}$$
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