Given below are two statements :
Statement I : Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes.
Statement II : Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes.
In the light of the above statements, choose the Correct answer from the options given below
Statement I: Wet cotton clothes made of cellulose-based carbohydrate take comparatively longer time to get dried than wet nylon polymer-based clothes. Cotton is primarily cellulose, which has numerous hydroxyl (-OH) groups.
These hydroxyl groups can form strong hydrogen bonds with water molecules, holding the water within the fabric structure. Nylon, a synthetic polyamide, also has polar amide (-CONH-) groups that can form hydrogen bonds with water, but to a lesser extent than cellulose due to differences in the polymer structure and the availability of hydrogen bonding sites.
Because cotton retains more water due to stronger hydrogen bonding, it takes longer to dry.
Therefore, Statement I is true. Statement II: Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes.
As explained above, cellulose (cotton) has a higher density of hydroxyl groups compared to the amide groups in nylon, leading to more extensive hydrogen bonding with water molecules in cotton.
Nylon has polar amide groups that can hydrogen bond with water, but the overall intermolecular hydrogen bonding with water is less than in cotton. Therefore, Statement II is false.
In conclusion, Statement I is true, but Statement II is false. This corresponds to option (2).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: