1
GATE CSE 2023
MCQ (More than One Correct Answer)
+1
-0

Let $$f$$ and $$g$$ be functions of natural numbers given by $$f(n)=n$$ and $$g(n)=n^2$$. Which of the following statements is/are TRUE?

A
$$f \in O(g)$$
B
$$f \in \Omega (g)$$
C
$$f \in o(g)$$
D
$$f \in \Theta (g)$$
2
GATE CSE 2022
MCQ (Single Correct Answer)
+1
-0.33

Which one of the following statements is TRUE for all positive functions f(n) ?

A
f(n2) = $$\theta$$(f(n)2), when f(n) is a polynomial
B
f(n2) = o(f(n)2)
C
f(n2) = O(f(n)2), when f(n) is an exponential function
D
f(n2) = $$\Omega$$(f(n)2)
3
GATE CSE 2021 Set 1
MCQ (Single Correct Answer)
+1
-0.33

Consider the following three functions.

f1 = 10n, f2 = nlogn, f3 = n√n

Which one of the following options arranges the functions in the increasing order of asymptotic growth rate?

A
f1 , f2, f3
B
f2, f1, f3
C
f3, f2, f1
D
f2, f3, f1
4
GATE CSE 2020
MCQ (Single Correct Answer)
+1
-0.33
For parameters a and b, both of which are $$\omega \left( 1 \right)$$,
T(n) = $$T\left( {{n^{1/a}}} \right) + 1$$, and T(b) = 1.
Then T(n) is
A
$$\Theta \left( {{{\log }_a}{{\log }_b}n} \right)$$
B
$$\Theta \left( {{{\log }_{ab}}n} \right)$$
C
$$\Theta \left( {{{\log }_b}{{\log }_a}n} \right)$$
D
$$\Theta \left( {{{\log }_2}{{\log }_2}n} \right)$$
GATE CSE Subjects
Software Engineering
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