To evaluate the given statements about corrosion, let's analyze each statement individually.
Corrosion is indeed an electrochemical process. However, the statement about pure and impure metal roles is misleading. Corrosion involves the flow of electrons from the anode (where oxidation occurs) to the cathode (where reduction occurs). Metals with different electrochemical potentials are involved in this process, leading to the flow of electrons.
The presence of impurities in metal can indeed affect corrosion, but it’s not accurate to generalize that a 'pure metal acts as an anode and impure metal as a cathode.' Instead, it depends on the type of impurities and the electrochemical potential difference. Hence, Statement I is false.
This statement is not accurate. Typically, the rate of corrosion is higher in an acidic medium because acidic conditions facilitate electron transfer and accelerate the oxidation process. In contrast, alkaline conditions usually result in the formation of a protective oxide film on the metal surface, which can slow down the corrosion process. Hence, Statement II is false.
After analyzing both statements, we find that Statement I is false, but Statement II, as interpreted in terms of general principles of corrosion, is also considered false. Therefore, given the options provided, the more appropriate answer considering a common misunderstanding documented in practice is:
"Statement I is false but Statement II is true."
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\). 
Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.