1
GATE CSE 2015 Set 3
+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 $${\rm I}$$$${\rm I}$$
2
GATE CSE 2013
+2
-0.6
The number of elements that can be stored in $$\Theta (\log n)$$ time using heap sort is
A
$$\Theta (1)$$
B
$$\Theta (\sqrt {\log n} )$$
C
$$\Theta ({{\log \,n} \over {\log \,\log \,n}})$$
D
$$\Theta (\log n)$$
3
GATE CSE 2011
+2
-0.6
Which of the given options provides the increasing order of asymptotic Complexity of functions f1, f2, f3 and f4?
f1 = 2n f2 = n3/2
f3(n) = $$n\,\log _2^n$$
f4 (n) = n log2n
A
f3, f2, f4, f1
B
f3, f2, f1, f4
C
f2, f3, f1, f4
D
f2, f3, f4, f1
4
GATE CSE 2008
+2
-0.6
Consider the following functions: F(n) = 2n
G(n) = n!
H(n) = nlogn
Which of the following statements about the asymptotic behaviour of f(n), g(n), and h(n) is true?
A
f(n) = O (g(n)); g(n) = O(h(n))
B
f(n) = $$\Omega$$ (g(n)); g(n) = O(h(n))
C
g(n) = O (f(n)); h(n) = O(f(n))
D
h(n) = O (f(n)); g(n) = $$\Omega$$ (f(n))
GATE CSE Subjects
EXAM MAP
Medical
NEET