Consider the following functions from positive integers to real number:

$10,\sqrt{n},n,lo{g}_{2}n,\frac{100}{n}$

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

Q. Consider the following three function:
$f_1$ = ${10}^n$, $f_2$ = $n^{logn}$, $f_3$ = $n^{\sqrt{n}}$
Which one of the following options arrange the functions in the increasing order of asymptotic growth rate?

Q. Arrange the following functions in increasing asymptotic order:

$\left(A\right)n^{1/3}$
$\left(B\right)e^n$
$\left(C\right)n^{7/4}$
$\left(D\right)nlo{g}^{9}n$
$\left(E\right){1.000000}^n$

Q. Consider the following statements :
1. $n({\sin }^{2}67\frac{1^o}{2}-{\sin }^{2}22\frac{1^o}{2})>1$ for all positive integers $n\ge 2$.
2. If x is any positive real number, then $nx>1$ for all positive integers $n\ge 2$.
Which of the above statements is/are correct ?

Q. Let N be the set of natural numbers. Consider the following sets:
P. Set of Rational numbers (positive and negative)
Q. Set of functions from {0, 1} to N
R. Set of functions from N to {0, 1}
S. Set of finite subsets of N
Which of the sets above is countable?

Q. Arrange the functions in the increasing order of rates of growth
$f_1:c.n^{\sqrt{n}},f_2:2^{\sqrt{n}logn},f_3:2^n(c>100)$