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

Match List-$I$ with List-$II$ :

List-$I$ (Defects)	List-$II$ (Shown by)
$a$. Frenkel defect	$i$. Non-ionic solids and density of the solid decreases
$b$. Schottky defect	$ii$. Non-ionic solids and density of the solid increases
$c$. Vacancy defect	$iii$. Ionic solids and density of the solid decreases
$d$. Interstitial defect	$iv$. Ionic solids and density of the solid remains constant

Choose the correct answer from the options given below :

If $\vec{a}, \vec{b}, \vec{c}$ are mutually perpendicular vectors having magnitudes $1, 2, 3$ respectively,then $[\vec{a}+\vec{b}+\vec{c} \quad \vec{b}-\vec{a} \quad \vec{c}]=$

If $P(A \cup B)=0.8$ and $P(A \cap B)=0.3$,then $P(\bar{A})+P(\bar{B})$ is equal to:

If $1, \log_9(3^{1-x} + 2), \log_3(4 \cdot 3^x - 1)$ are in $A.P.$,then $x$ equals