The reaction of HClO3 with HCl gives a paramagnetic gas, which upon reaction with O3 produces
The reaction of chloric acid (\( \text{HClO}_3 \)) with hydrogen chloride (\( \text{HCl} \)) results in the formation of chlorine dioxide (\( \text{ClO}_2 \)), which is a paramagnetic gas. This is because chlorine dioxide has an unpaired electron in its structure, making it paramagnetic. The reaction can be written as: \[ \text{HClO}_3 + \text{HCl} \rightarrow \text{ClO}_2 + \text{H}_2\text{O} \]
When chlorine dioxide (\( \text{ClO}_2 \)) reacts with ozone (\( \text{O}_3 \)), it forms dichlorine hexaoxide (\( \text{Cl}_2\text{O}_6 \)). The reaction can be written as: \[ 2 \text{ClO}_2 + \text{O}_3 \rightarrow \text{Cl}_2\text{O}_6 \] This reaction shows that \( \text{ClO}_2 \) reacts with ozone to form the compound \( \text{Cl}_2\text{O}_6 \).
Based on the reactions described above, the correct compound formed after the reaction of the paramagnetic gas with \( \text{O}_3 \) is \( \text{Cl}_2\text{O}_6 \), which corresponds to option C.
The correct option is C: \( \text{Cl}_2\text{O}_6 \).
Given below are two statements. 
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements:
Statement I: Nitrogen forms oxides with +1 to +5 oxidation states due to the formation of $\mathrm{p} \pi-\mathrm{p} \pi$ bond with oxygen.
Statement II: Nitrogen does not form halides with +5 oxidation state due to the absence of d-orbital in it.
In the light of the above statements, choose the correct answer from the options given below:
Given below are the pairs of group 13 elements showing their relation in terms of atomic radius. $(\mathrm{B}<\mathrm{Al}),(\mathrm{Al}<\mathrm{Ga}),(\mathrm{Ga}<\mathrm{In})$ and $(\mathrm{In}<\mathrm{Tl})$ Identify the elements present in the incorrect pair and in that pair find out the element (X) that has higher ionic radius $\left(\mathrm{M}^{3+}\right)$ than the other one. The atomic number of the element (X) 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 ________.