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JEE Advanced Model Paper 1 with solutions for online practice
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© examsnet.com
Question : 53
Total: 60
If a,b, A be given in a ΔABC and
C
1
,
C
2
be two possible values of third sidesuch that
C
1
2
+
C
1
C
2
+
C
2
2
=
a
2
then ∠A is
30°
60°
90°
120°
Validate
Solution:
cos A =
b
2
+
c
2
−
a
2
2
b
c
c
2
- 2bc cosA +
b
2
−
a
2
= 0
Let
C
1
,
C
2
be 2 roots
C
1
+
C
2
= 2bcosA
C
1
C
2
=
b
2
−
a
2
Given
C
1
2
+
C
1
C
2
+
C
2
2
=
a
2
(
C
1
+
C
2
)
2
-
C
1
C
2
=
a
2
4
b
2
c
o
s
2
A
-
(
b
2
−
a
2
)
=
a
2
c
o
s
2
A
=
1
4
, cosA = ±
1
2
A = 60° and 120°
© examsnet.com
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