, k + 21 = 22 198

, 2k + 1 = 26 199

and 2k + 31 = 34 200

. ONLY ONE of these four options is the correct answer. • For each question, choose the option corresponding to the correct answer. • Answer to each question will be evaluated according to the following marking scheme: Full Mark +3 If ONLY the correct option is chosen; Zero Marks 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks -1 In all other cases. Paragraph Let M = {(x, y) RxR:x 2 + y 2 r 2 }, where r > 0. Consider the geometric progression , n = 1, 2, 3,..... Let S 0 = 0 and for n 1, let S n denote the sum of the first n terms of this progression. For n > 1, let C n denote the circle with center (S n _ i, 0) and radius a n , and D n denote the circle with center (S n-1 , S n-1 ) and radius a n . (i) Consider M with r = . Let k be the number of all those circles C n that are inside M. Let 1 be the maximum possible number of circles among these k circles such that no two circles intersect. Then 3k + 21 = 40 (ii) Consider M with . The number of all those circles D n that are inside M is 201