GATE CSE 2021 Set 1 | Complexity Analysis and Asymptotic Notations Question 11 | Algorithms

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GATE CSE 2021 Set 1

MCQ (Single Correct Answer)

-0.33

Consider the following three functions.

f₁ = 10ⁿ, f₂ = n^logn, f₃ = n^√n

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

f₁ , f₂, f₃

f₂, f₁, f₃

f₃, f₂, f₁

f₂, f₃, f₁

GATE CSE 2020

MCQ (Single Correct Answer)

-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

$$\Theta \left( {{{\log }_a}{{\log }_b}n} \right)$$

$$\Theta \left( {{{\log }_{ab}}n} \right)$$

$$\Theta \left( {{{\log }_b}{{\log }_a}n} \right)$$

$$\Theta \left( {{{\log }_2}{{\log }_2}n} \right)$$

GATE CSE 2017 Set 1

MCQ (Single Correct Answer)

-0.33

Consider the following functions from positive integers to real numbers :

$10, \sqrt{n}, n, \log _2 n, \frac{100}{n}$.

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is :

$\log _2 n, \frac{100}{n}, 10, \sqrt{n}, n$

$\frac{100}{n}, 10, \log _2 n, \sqrt{n}, n$

$10, \frac{100}{n}, \sqrt{n}, \log _2 n, n$

$\frac{100}{n}, \log _2 n, 10, \sqrt{n}, n$

GATE CSE 2015 Set 3

MCQ (Single Correct Answer)

-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 $$𝑋$$ is replaced by

Only $${\rm I}$$

Only $${\rm II}$$

$${\rm I}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm II}$$

$${\rm II}$$ or $${\rm III}$$ or $${\rm IV}$$ but not $${\rm I}$$

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