1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider the equality $$\sum\limits_{i = 0}^n {{i^3}} = X$$ and the following choices for $$X$$
$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\Theta \left( {{n^4}} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\Theta \left( {{n^5}} \right) \cr & \,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,O\left( {{n^5}} \right) \cr & \,\,\,{\rm I}V.\,\,\,\,\,\,\Omega \left( {{n^3}} \right) \cr} $$
The equality above remains correct if $$š‘‹$$ is replaced by
A
Only $${\rm I}$$
B
Only $${\rm II}$$
C
$${\rm I}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm II}$$
D
$${\rm II}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm I}$$
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider the following array of elements.

$$\,\,\,\,\,\,\,\,$$$$āŒ©89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100āŒŖ$$

The minimum number of interchanges needed to convert it into a max-heap is
A
$$4$$
B
$$5$$
C
$$2$$
D
$$3$$
3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Assume that a mergesort algorithm in the worst case takes $$30$$ seconds for an input of size $$64.$$ Which of the following most closely approximates the maximum input size of a problem that can be solved in $$6$$ minutes?
A
$$256$$
B
$$512$$
C
$$1024$$
D
$$2048$$
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$f\left( n \right) = n$$ and $$g\left( n \right) = {n^{\left( {1 + \sin \,\,n} \right)}},$$ where $$n$$ is a positive integer. Which of the following statements is/are correct?

$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = O\left( {g\left( n \right)} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = \Omega \left( {g\left( n \right)} \right) \cr} $$

A
Only $${\rm I}$$
B
Only $${\rm I}$$$${\rm I}$$
C
both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$
D
Neither $${\rm I}$$ nor $${\rm I}$$$${\rm I}$$
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