Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the matrix given in the ORS. [2007]

Question

Match the statements in Column I with the properties in Column II and indicate your answer by darkening the appropriate bubbles in the $4 \times 4$ matrix given in the ORS. [2007]

	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

Smart Achievers · Accepted Answer

(2)

$(A) - p, q$

It is clear from the figure that two intersecting circles have a common tangent and a common normal joining the centres.

$(B) - p, q$

$(C) - q, r$

Two circles, when one is strictly inside the other, have a common normal $C_{1} C_{2}$ but no common tangent.

$(D) - q, r$

Two branches of hyperbola have no common tangent but have a common normal joining $S_{1} S_{2} .$

Solution

1 $(A) \to (q, r); (B) \to (p, q); (C) \to (q, r); (D) \to (p, q)$

2 $(A) \to (p, q); (B) \to (p, q); (C) \to (q, r); (D) \to (q, r)$

3 $(A) \to (q, r); (B) \to (q, r); (C) \to (p, q); (D) \to (p, q)$

4 $(A) \to (p, q); (B) \to (p, q); (C) \to (q, r); (D) \to (q, r)$

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Solution

1 (A)→(q,r); (B)→(p,q); (C)→(q,r); (D)→(p,q)

2 (A)→(p,q); (B)→(p,q); (C)→(q,r); (D)→(q,r)

3 (A)→(q,r); (B)→(q,r); (C)→(p,q); (D)→(p,q)

4 (A)→(p,q); (B)→(p,q); (C)→(q,r); (D)→(q,r)

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1 $(A) \to (q, r); (B) \to (p, q); (C) \to (q, r); (D) \to (p, q)$

2 $(A) \to (p, q); (B) \to (p, q); (C) \to (q, r); (D) \to (q, r)$

3 $(A) \to (q, r); (B) \to (q, r); (C) \to (p, q); (D) \to (p, q)$

4 $(A) \to (p, q); (B) \to (p, q); (C) \to (q, r); (D) \to (q, r)$