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KVPY 2019 SA Exam Previous Papers
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© examsnet.com
Question : 14
Total: 80
Let l > 0 be a real number, C denote a circle with circumference l, and T denote a triangle with perimeter l. Then
given any positive real number α, we can choose C and T as above such that the ratio
Area
(
C
)
Area
(
T
)
is greater than α
given any positive real number α, we can choose C and T as above such that the ratio
Area
(
C
)
Area
(
T
)
is less than α
given any C and T as above, the ratio
Area
(
C
)
Area
(
T
)
is independent of C and T
there exist real numbers a and b such that for any circle C and triangle T as above, we must have a <
Area
(
C
)
Area
(
T
)
< b
Validate
Solution:
Area
(
C
)
=
π
(
l
2
π
)
2
=
l
2
4
π
Area
(
T
)
≤
√
3
4
(
l
3
)
2
=
l
2
12
√
3
⇒
(
A
)
Hence
Area
(
c
)
Area
(
τ
)
≥
3
√
3
π
© examsnet.com
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