What is the molar solubility of $Ag_2CO_3$ $(K_{sp} = 4 \times 10^{-13})$ in $0.1 \ M \ Na_2CO_3$ solution?

If the position vectors of $A, B, C, D$ are $\hat{i}+2\hat{j}+2\hat{k}, 2\hat{i}-\hat{j}, \hat{i}+\hat{j}+3\hat{k}$ and $4\hat{j}+5\hat{k}$ respectively,then the quadrilateral $ABCD$ is a

In the given circuit, the current flowing through it is: (in $ A$)

Let $Q$ be the set of all rational numbers in $[0,1]$ and $f:[0,1] \rightarrow [0,1]$ be defined by $f(x) = \begin{cases} x & \text{for } x \in Q \\ 1-x & \text{for } x \notin Q \end{cases}$. Then,the set $S = \{x \in [0,1] : (f \circ f)(x) = x\}$ is equal to

The percentage composition of an organic compound $A$ is: carbon $85.71 \%$ and hydrogen $14.29 \%$. Its vapour density is $14$. Consider the following reaction sequence:
$A$ $\xrightarrow{Cl_2 / H_2O} B$ $\xrightarrow[(ii) H_3O^+]{(i) KCN / EtOH} C$
Identify $\underline{C}$.

Which of the following represents the correct order of the acidity in the given compounds?