JEE Advanced Mathematics question

MathematicsComplex NumbersJEE Advanced

In each question, match every entry of Column I with the correct entry of Column II. (An entry of Column II may be used more than once.) Column I: (i) If and then the minimum value of is (ii) If is a nonzero finite number then the integer is (iii) If for then the minimum value of is (iv) If is a complex number satisfying then the greatest value of is Column II: (a) (b) (c) (d)

Answer: (2)

Solution

**(i)** lies on the circle with centre and radius , which passes through the origin, so . lies on . Then , with equality for and . The minimum is → **(c)**. - **(ii)** As , \cos$

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Question ID VK-110295