Ethylene is a plant hormone responsible for regulating fruit ripening and stress responses.
1. Fruit Ripening: Ethylene accelerates ripening in climacteric fruits like bananas, mangoes, and tomatoes.
2. Leaf Abscission: Causes leaf and flower drop by weakening cell walls at the base of petioles.
3. Stem Thickening: Promotes lateral expansion, resulting in shorter, thicker stems.
4. Root Growth: Enhances root initiation and adventitious root formation.
5. Applications of Ethylene in Agriculture:
(i) Used in artificial fruit ripening in commercial agriculture.
(ii) Promotes flowering in pineapples.
(iii) Induces synchronized fruit maturation in crops.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]