Given below are two statements:
Statement I: Mohr's salt is composed of only three types of ions—ferrous, ammonium, and sulphate.
Statement II: If the molar conductance at infinite dilution of ferrous, ammonium, and sulphate ions are $ x_1 $, $ x_2 $, and $ x_3 $ $ \text{S cm}^2 \, \text{mol}^{-1} $, respectively, then the molar conductance for Mohr's salt solution at infinite dilution would be given by $ x_1 + x_2 + 2x_3 $.
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
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 ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.
Conductance is an expression of the ease with which electric current flows through materials like metals and nonmetals. In equations, an uppercase letter G symbolizes conductance. The standard unit of conductance is siemens (S), formerly known as mho.
Conductance in electricity is considered the opposite of resistance (R). Resistance is essentially the amount of friction a component presents to the flow of current.