In the given figure,what do $A$ and $B$ represent respectively?

The differential equation of the family of parabolas with vertex at $(0, -1)$ and having axis along the $Y$-axis is

Consider the following reactions at $1000\,^oC$:
$(I)$ $Zn_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow ZnO_{(s)}; \Delta G^o = -360\,kJ\,mol^{-1}$
$(II)$ $C_{(s)} + \frac{1}{2}O_{2(g)} \rightarrow CO_{(g)}; \Delta G^o = -460\,kJ\,mol^{-1}$
Choose the correct statement at $1000\,^oC$.

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about ..... $km$.

Let $A = \{x \in R, x \neq 0, -4 \leq x \leq 4\}$ and $f: A \rightarrow R$ be defined by $f(x) = \frac{|x|}{x}$ for $x \in A$. Then,the range of $f$ is

If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(B) = \frac{3}{2} P(A)$ and $P(C) = \frac{1}{2} P(B)$,then $P(A \cup C)$ equals to