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JEE Advanced 2020 Concept Recapitulation Test 4 Paper 1
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© examsnet.com
Question : 51
Total: 54
Let the line
y
=
100
x
−
199
be intersect the graph of a function
f
(
x
)
=
x
3
−
6
x
2
+
a
x
−
2
a
+
17
,
a
∈
R
at three distinct points whose abscissae are
x
1
,
x
2
and
x
3
(
x
1
<
x
2
<
x
3
)
such that
x
3
−
x
1
=
6
.
If
∫
x
1
x
1
(
f
(
x
)
−
98
x
+
198
)
d
x
=
λ
, then find the value of
λ
.
Your Answer:
Validate
Solution:
f
(
x
)
=
x
3
−
6
x
2
+
a
x
−
2
a
+
17
f
′
(
x
)
=
3
x
2
−
12
x
+
a
f
′
′
(
x
)
=
6
x
−
12
f
′
′
(
x
)
=
0
⇒
x
=
2
f
(
2
)
=
1
(
2
,
1
)
is the point of inflection on the graph
y
=
f
(
x
)
Straight line
y
=
100
x
−
199
is also passing through
(
2
,
1
)
x
1
+
x
3
=
4
and
x
3
−
x
1
=
6
∫
x
1
x
1
(
f
(
x
)
−
98
+
198
)
d
x
=
∫
x
1
x
1
(
f
(
x
)
−
100
x
+
199
+
2
x
−
1
)
d
x
∫
x
x
1
(
2
x
−
1
)
d
x
=
(
x
2
−
x
)
x
1
x
3
=
x
3
2
−
x
3
−
(
x
1
2
−
x
1
)
=
(
x
3
−
x
1
)
(
x
3
+
x
1
)
−
(
x
3
−
x
1
)
=
4
×
6
−
6
=
18
∴
λ
=
18
© examsnet.com
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