Statement I:
D-glucose pentaacetate reacts with 2,4-dinitrophenylhydrazine.
D-glucose pentaacetate is a derivative of glucose in which all the hydroxyl (–OH) groups are esterified. As a result, there is no free carbonyl group (aldehyde or ketone) available for reaction.
2,4-Dinitrophenylhydrazine (DNPH) specifically reacts with aldehydes and ketones through a nucleophilic addition to the carbonyl group, forming 2,4-dinitrophenylhydrazones.
Since D-glucose pentaacetate lacks a free carbonyl group, it **does not** react with 2,4-dinitrophenylhydrazine.
Therefore, Statement I is false.
Statement II:
Starch, on heating with concentrated sulfuric acid at 100°C and under 2–3 atmosphere pressure, produces glucose.
Starch is a polysaccharide composed of multiple glucose units linked by glycosidic bonds.
Under acidic conditions and upon heating under pressure, starch undergoes **acid-catalyzed hydrolysis**, breaking the glycosidic linkages and ultimately yielding glucose molecules.
Therefore, Statement II is true.
Conclusion:
Statement I is false, and Statement II is true.
Final Answer:
The final answer is $ \text{Statement I is false but Statement II is true} $.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: