The figure shows a network diagram for a construction project. The activities $\mathrm{A}, \mathrm{B}, \mathrm{C}$, D, E, and F are represented by arrows and their durations are in the figure.

The total float available for the activity E in day(s) is equal to _________ (round off to the nearest integer).

For the matrix $[\mathrm{A}]$ given below, the transpose is $\qquad$ .

$$ [A]=\left[\begin{array}{lll} 2 & 3 & 4 \\ 1 & 4 & 5 \\ 4 & 3 & 2 \end{array}\right] $$

Integration of $\ln (x)$ with $x$ i.e.

$$ \int \ln (x) d x= $$__________

Consider a velocity vector, $\vec{V}$ in ( $\mathrm{x}, \mathrm{y}, \mathrm{z}$ ) coordinates given below. Pick one or more CORRECT statement(s) from the choices given below:

$$ \vec{V}=u \vec{x}+v \vec{y} $$