If the unit of the rate constant is \( \text{mol} \, (\text{dm}^{-3} \text{s}^{-1}) \), the order of the reaction would be ____________.
In the given graph, \( E_a \) for the reverse reaction will be
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]