Consider the circles $| z - 1 | = 3$ and $| z - z_{0} | = 4$ ,    $z_{0} \in C$
Match the items of List I with items of List II and choose the correct option.
COLUMN - I
COLUMN – II
1 If two circles cut orthogonally, then the maximum value of   $| z_{0} |$ ,    is P 4
2 If two circles touch internally, then the maximum value of   $| z_{0} |$ , is Q 8
3 If two circles touch externally, then the minimum value of $| z_{0} |$ , is R 6
4 If two circles cut orthogonally, then the minimum value of   $| z_{0} |$ , is S 2

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1 - R, 2 - R , 3 - S, 4 - P

1 - S, 2 - S, 3 - P, 4 - Q

1 - R, 2 - S, 3 - R , 4 - P

1 - S, 2 - Q, 3 - R, 4 - P

answer is D.

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Detailed Solution

A)    $\begin{array}{l} | z_{0} - 1 | = 5 \\ \Rightarrow | z_{0} - 1 | \geq | | z_{0} | - 1 | \Rightarrow 5 \geq | | z_{0} | - 1 | \\ \Rightarrow | | z_{0} | - 1 | \leq 5 \Rightarrow | z_{0} | \leq 6 \end{array}$
B)    $| z_{0} - 1 | = 1 \Rightarrow | z_{0} | \leq 2$
C)    $| z_{0} - 1 | = 7 \Rightarrow | z_{0} | \geq 6$
D) $| z_{0} - 1 | = 5 \Rightarrow | z_{0} | \geq 4$

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COLUMN - I		COLUMN – II
1	If two circles cut orthogonally, then the maximum value of $\| z_{0} \|$ , is	P	4
2	If two circles touch internally, then the maximum value of $\| z_{0} \|$ , is	Q	8
3	If two circles touch externally, then the minimum value of $\| z_{0} \|$ , is	R	6
4	If two circles cut orthogonally, then the minimum value of $\| z_{0} \|$ , is	S	2