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JEE Advanced 2020 Full Test 5 Paper 1

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Answer questions 47,48 and 49 by appropriately matching the information given in the three columns of the following table.
   Column -1    Column -2    Column -3
 (I)  If S={Z:|Z+Z|+2|Z−Z|=4 and |Z| is minimum } then ‌
25
8
A is (where A is area of polygon formed of all points in S taking as vertices)		  (i)  If the Point (sec‌α,cosecα) moves in the plane of circle x2+y2=3 and the minimum distance of this point from circle is a−√b(a,b∈N) then a+b  (P)  2
 (II)  Let S={z|zz−(3−4i)Z−(3+4i)Z+21=0|} If M and m be maximum value and minimum value of ‌
Z−Z
i(Z+Z)
 then ‌
1
M
+‌
1
m
 is		  (ii)  Two circles x2+y2+2n1x+2y+‌
1
2
=0 and x2+y2+n2x+n2y+n1=‌
1
2
 intersect each other orthogonally where n1,n2 are integers then the number of possible ordered pairs (n1,n2) is		  (Q)  3
 (III)  Let x is the minimum value of |Z|2+|Z−3|2+|Z−6i|2 then ‌
x
10
 is		  (iii)  If an=√1+(1+‌
1
n
)2+√1+(1−‌
1
n
)2 then the value of (
20
∑
n=1
‌
1
an
)−3i		  (R)   4
 (IV)  Consider a triangle formed by the points A(‌
2
√3
ei(π2)),B(‌
2
√3
e−4‌
Ï€
6
)),C(‌
2
√3
e−(‌
5Ï€
6
)) Let P(Z) is any point on it's incircle, then AP2+BP2+CP2 is		  (iv)  The ea n9x3+9x2y−45x2=4y3+4xy2−20y2 represents 3 straight lines two of which pass through origin then ‌
1
10
 (Area of triangle formed by these lines)		  (S)   5
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Question : 49
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