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 class of organic compounds that mostly contain an ether group in which the oxygen atom is bonded to two alkyl or aryl groups are referred to as Ethers. For the same, C-O-C is the functional group.
Ethers are less polar as well as less reactive, and they do not react with active metals (Na, K), cold dilute acid, oxidizing and reducing agents or other chemicals.
The reason is that they do not have an active functional group.