We are given the following reaction in aqueous solution:
\[ \text{Pb(NO}_3\text{)}_2 + \text{NaCl} \rightarrow \text{PbCl}_2 (\text{precipitate}) + 2 \text{NaNO}_3 \]
When the precipitate, \( \text{PbCl}_2 \), is formed and then dissolves upon the addition of HCl, this dissolution is due to the formation of a soluble complex ion.
When \( \text{Pb(NO}_3\text{)}_2 \) and \( \text{NaCl} \) are mixed in water, a precipitation reaction occurs: \[ \text{Pb}^{2+} + 2 \text{Cl}^- \rightarrow \text{PbCl}_2 (s) \] Here, lead(II) chloride (\( \text{PbCl}_2 \)) forms as a white precipitate.
Upon adding excess HCl, the \( \text{PbCl}_2 \) precipitate dissolves, forming a soluble lead(II) chloride complex. This occurs because the chloride ions from HCl coordinate with lead ions to form a complex. The formation of the complex ion can be represented as: \[ \text{PbCl}_2 (s) + 2 \text{Cl}^- \rightleftharpoons [\text{PbCl}_4]^{2-} \] The \( [\text{PbCl}_4]^{2-} \) complex is soluble in water, which leads to the dissolution of the precipitate.
The dissolution of \( \text{PbCl}_2 \) is due to the formation of the soluble \( [\text{PbCl}_4]^{2-} \) complex ion. Therefore, the correct answer is:
The correct option is C: \( [\text{PbCl}_4]^{2-} \)
When lead ions (Pb2+) react with chloride ions (Cl−), a white precipitate of lead(II) chloride (PbCl2) forms.
This precipitate is soluble in concentrated hydrochloric acid due to formation of tetrachloroplumbate (II) ion
So the correct answer option is (C)
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 ________.