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JEE Advanced 2014 Paper 1
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© examsnet.com
Question : 54
Total: 60
Let
a
,
b
,
c
be positive integers such that
b
a
is an integer.If
a
,
b
,
c
are in geometric progression and the arithmetic mean of
a
,
b
,
c
is
b
+
2
,then the value of
a
2
+
a
−
14
a
+
1
is _________
Your Answer:
Validate
Solution:
b
a
=
c
b
=
(
i
n
t
e
g
e
r
)
b
2
=
a
c
⇒
c
=
b
2
a
a
+
b
+
c
3
=
b
+
2
a
+
b
+
c
=
3
b
+
6
⇒
a
−
2
b
+
c
=
6
a
−
2
b
+
b
2
a
=
6
⇒
1
−
2
b
a
+
b
2
a
2
=
6
a
(
b
a
−
1
)
2
=
6
a
⇒
a
=
6
only
© examsnet.com
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