1
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
In how many ways can $$b$$ blue balls and $$r$$ red balls be distributed in $$n$$ distinct boxes?
A
$${{\left( {n + b - 1} \right)!\left( {n + r - 1} \right)!} \over {\left( {n - 1} \right)!b!\left( {n - 1} \right)!r!}}$$
B
$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {\left( {n - 1} \right)!\left( {n - 1} \right)!\left( {b + r} \right)!}}$$
C
$${{n!} \over {b!r!}}$$
D
$${{\left( {n + \left( {b + r} \right) - 1} \right)!} \over {n!\left( {b + r - 1} \right)!}}$$
2
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
When $$n = {2^{2k}}$$ for some $$k \ge 0$$, the recurrence relation $$$T\left( n \right) = \sqrt 2 T\left( {n/2} \right) + \sqrt n ,\,\,T\left( 1 \right) = 1$$$
evaluates to
A
$$\sqrt n \left( {\log \,n + 1} \right)$$
B
$$\sqrt n \,\log \,n$$
C
$$\sqrt n \,\log \,\sqrt n $$
D
$$n\,\log \sqrt n $$
3
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
Which of the following statements is true for every planar graph on $$n$$ vertices?
A
The graph is connected
B
The graph is Eulerian
C
The graph has a vertex-cover of size at most $$3n/4$$
D
The graph has an independent set of size at least $$n/3$$
4
GATE CSE 2008
MCQ (Single Correct Answer)
+2
-0.6
$$G$$ is a simple undirected graph. Some vertices of $$G$$ are of odd degree. Add a node $$v$$ to $$G$$ and make it adjacent to each odd degree vertex of $$G$$. The resultant graph is sure to be
A
Regular
B
Complete
C
Hamiltonian
D
Euler
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