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Match the statements in Column $I$ with the properties Column $II$ and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
| $(A)$ Two intersecting circles | $(p)$ have a common tangent |
| $(B)$ Two mutually external circles | $(q)$ have a common normal |
| $(C)$ two circles, one strictly inside the other | $(r)$ do not have a common tangent |
| $(D)$ two branches of a hyperbola | $(s)$ do not have a common normal |
$A \rightarrow q, s ; B \rightarrow p, s ; C \rightarrow q, p ; D \rightarrow q, p$
$A \rightarrow s, r ; B \rightarrow p, s ; C \rightarrow r, r ; D \rightarrow p, s$
$A \rightarrow s, r ; B \rightarrow s, r ; C \rightarrow s, r ; D \rightarrow r, s$
$A \rightarrow p, q ; B \rightarrow p, q ; C \rightarrow q, r ; D \rightarrow q, r$
Solution
$(A)$ When two circles are intersecting they have a common normal and common tangent.
$(B)$ Two mutually external circles have a common normal and common tangent.
$(C)$ When one circle lies inside of other then, they have a common normal but no common tangent.
$(D)$ Two branches of a hyperbola have a common normal but no common tangent.
