Match the following:

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 ________.
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:
A chemical element with the symbol Cl and the atomic number 17 is ‘Chlorine’. It is the second-lightest of the halogens that appears between fluorine and bromine in the periodic table and its properties are median between them. At room temperature, it is a yellow-green gas. Also, it has two stable isotopes, 35Cl and 37Cl. These are the only two natural isotopes occurring in quantity, with 35Cl making up 76% of natural chlorine and 37Cl making up the remaining 24%.