The magnifying power of a telescope with tube length $60 \ cm$ is $5$. Then the focal length of its eyepiece is: (in $cm$)

If $a$ and $b$ are two non-zero perpendicular vectors, then a vector $y$ satisfying the equations $a \cdot y = c$ (where $c$ is a scalar) and $a \times y = b$ is

If the functions $f$ and $g$ are defined by $f(x) = 3x - 4$ and $g(x) = 2 + 3x$ for $x \in R$, then $g^{-1}(f^{-1}(5))$ is equal to

Choose the correct option from the following:
$I$. Dehydration and dormancy of mature seed are crucial for seed storage.
$II$. Seed of $Lupinus \; arcticus$ is the oldest one which germinated after $2,000 \; years$.
$III$. Orchid seed is one of the largest seeds in the plant kingdom.
$IV$. Seeds of parasitic plants $Orobanche$ and $Striga$ are tiny seeds.

Which one of the following is the first step in taxonomy?

An open-ended $U$-tube of uniform cross-sectional area contains water (density $1.0 \, g/cm^3$) standing initially $20 \, cm$ from the bottom in each arm. An immiscible liquid of density $4.0 \, g/cm^3$ is added to one arm until a layer $5 \, cm$ high forms,as shown in the figure. What is the ratio $h_2/h_1$ of the heights of the liquid in the two arms?