Name the method of asexual reproduction in lichens.

$\sum_{k=1}^5 \frac{1^3+2^3+\ldots+k^3}{1+3+5+\ldots+(2k-1)}$ is equal to (in $.5$)

The solution of the differential equation $(3xy + y^2)dx + (x^2 + xy)dy = 0$ is

Kangaroo rat is found in .........

If $a^{1/x} = b^{1/y} = c^{1/z}$ and $b^2 = ac$,then $x + z = $

Observe the following statements:
$I. f(x) = a x^{41} + b x^{-40} \Rightarrow \frac{f^{\prime \prime}(x)}{f(x)} = 1640 x^{-2}$
$II. \frac{d}{d x} \tan ^{-1}\left(\frac{2 x}{1-x^2}\right) = \frac{1}{1+x^2}$
Which of the following is correct?