Ion having highest hydration enthalpy among the given alkaline earth metal ions is:
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 ________.
Group one of alkali metals is s-block elements with just one electron in their s-orbital. They are are alkali metals. They are named so because of the alkaline nature of the hydroxides and oxides.
Alkali metals are characterized by one s-electron in the valence shell of their atoms.
Alkali metals have a corresponding [Noble gas] ns1 electronic configuration. They occupy the first column of the periodic table. Alkali elements are:
They have occupied successive periods from first to seven. Francium is a radioactive element with very low half-life.
This makes them the most electropositive elements and due to the same reason, they are not found in the pure state.