Given below are two statements:
Statement (I): The first ionization energy of Pb is greater than that of Sn.
Statement (II): The first ionization energy of Ge is greater than that of Si.
In light of the above statements, choose the correct answer from the options given below:
The product (A) formed in the following reaction sequence is:

\[ \begin{array}{|c|c|} \hline \textbf{LIST-I (Redox Reaction)} & \textbf{LIST-II (Type of Redox Reaction)} \\ \hline A. \, CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) & I. \, \text{Disproportionation reaction} \\ B. \, 2NaH(s) \rightarrow 2Na(s) + H_2(g) & II. \, \text{Combination reaction} \\ C. \, V_2O_5(s) + 5Ca(s) \rightarrow 2V(s) + 5CaO(s) & III. \, \text{Decomposition reaction} \\ D. \, 2H_2O(aq) \rightarrow 2H_2(g) + O_2(g) & IV. \, \text{Displacement reaction} \\ \hline \end{array} \]
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Redox reactions are chemical reactions where oxidation and reduction take place simultaneously. In this type of reaction, there is a gain of electrons for one chemical species while the other loses electrons or simply involves transfer of electrons. The species that loses electrons is oxidized while the one that gains electrons is reduced.
Redox reactions can be differentiated into 4 categories namely combination reactions, decomposition reactions, displacement reactions, and disproportionation reactions. Each is explained separately below:
In this, the molecules combine to form new compounds. For example, when magnesium reacts to nitrogen.
Opposite to the combination reaction, here there is a breakdown of compounds to simpler substances. For example, electrolysis of water.
In this, the more reactive metal will displace the less reactive one in a chemical reaction. The reactivity of an element is represented in a series called the reactivity series (arranged in decreasing order of reactivity) which makes it easier to determine the chemical reaction and its products.
This is a peculiar type of reaction where an element showing a particular oxidation state will be oxidized and reduced simultaneously. Another thing to note is that these reactions will always have an element that can exhibit three oxidation states.