Examsnet
Unconfined exams practice
Home
Exams
Banking Entrance Exams
Defence Exams
Engineering Exams
Finance Entrance Exams
GATE Exams
Insurance Exams
International Exams
JEE Exams
LAW Entrance Exams
MBA Entrance Exams
MCA Entrance Exams
Medical Entrance Exams
Other Entrance Exams
Police Exams
Public Service Commission (PSC)
RRB Entrance Exams
SSC Exams
State Govt Exams
Subjectwise Practice
Teacher Exams
State Eligibility Tests
UPSC Entrance Exams
Aptitude
Algebra and Higher Mathematics
Arithmetic
Commercial Mathematics
Data Based Mathematics
Geometry and Mensuration
Number System and Numeracy
Problem Solving
English
Competitive English
Board Exams
Andhra
Bihar
CBSE
Gujarat
Haryana
ICSE
Jammu and Kashmir
Karnataka
Kerala
Madhya Pradesh
Maharashtra
Odisha
Tamil Nadu
Telangana
Uttar Pradesh
Certifications
Technical
Cloud Tech Certifications
Security Tech Certifications
Management
IT Infrastructure
More
About
Careers
Contact Us
Our Apps
Privacy
Test Index
KVPY SX SB Exam 20141 Question Paper
Show Para
Hide Para
Share question:
© examsnet.com
Question : 1
Total: 120
PART - I
MATHEMATICS
Let
C
0
be a circle of radius I. For n ≥ 1, let C
n
be a circle whose area equals the area of a square inscribed in C
n
−
1
.
Then
∞
∑
i
=
0
Area
(
C
i
)
equals
π
2
π
−
2
π
2
1
π
2
π
2
π
−
2
Validate
Solution:
∞
∑
i
=
0
Area
(
C
i
)
=
π
r
0
2
+
π
r
1
2
+
π
r
2
2
+
π
r
3
2
+
.
.
.
.
.
∞
Area of
C
n
=
π
r
n
2
=
(
√
2
r
n
−
1
)
2
r
n
2
=
2
π
r
2
n
−
1
so
r
1
2
=
2
π
r
0
2
,
r
2
2
=
2
π
r
1
2
=
2
π
(
2
π
r
0
2
)
r
3
2
=
2
π
(
r
2
2
)
=
2
π
(
2
π
2
π
r
0
2
)
So
∞
∑
i
=
0
Area
(
C
i
)
=
π
[
r
0
2
+
2
π
r
0
2
+
2
π
.2
π
r
0
2
+
.
.
.
∞
]
=
π
r
0
2
1
−
2
π
=
π
2
r
0
2
π
−
2
∀
r
0
=
1
=
π
2
π
−
2
© examsnet.com
Go to Question:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
Next Question
Examsnet