Which of the following figures represents the variation of particle momentum $p$ and the associated de-Broglie wavelength $\lambda$?

If the vectors $a \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+b \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+c \hat{k}$ $(a \neq 1, b \neq 1, c \neq 1, a \neq b \neq c)$ are coplanar,then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is:

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

If $S_{n} = 1^3 + 2^3 + \ldots + n^3$ and $T_{n} = 1 + 2 + \ldots + n$,then

Match the appropriate pairs from List-$I$ and List-$II$ :

List-$I$	List-$II$
$1$. Nitrogen molecules	$(A)$ Continuous spectrum
$2$. Incandescent solids	$(B)$ Absorption spectrum
$3$. Fraunhoffer lines	$(C)$ Band spectrum
$4$. Electric arc between iron rods	$(D)$ Emission spectrum

Leaching of $Ag_2S$ is carried out by heating it with a dilute solution of