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JEE Advanced 2020 Full Test 6 Paper 2
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© examsnet.com
Question : 46
Total: 54
Set
f
(
x
)
=
a
x
4
+
b
x
3
+
c
x
2
+
d
x
+
e
,
a
≠
0
, is a function such that
x
=
1
,
x
=
2
and
x
=
3
are normals to the curve
y
=
f
(
x
)
such that
f
(
2
)
is always greater than
f
(
0
)
,
then which of the following are true for
f
(
x
)
(i)
f
(
x
)
has 2 local maxima
(ii) There exist only one value of
k
such that Rolle's theorem is applicable to
f
(
x
)
on the interval
[
0
,
k
]
(iii)
f
(
x
)
=
0
has two imaginary roots.
Only (iii) and (i) are true
(ii) is true and (iii) is false
Only (i) & (ii) are true
All are true
Validate
Solution:
Since
x
=
1
,
2
,
3
are normals
⇒
f
′
(
x
)
=
4
a
x
3
+
3
b
x
2
+
2
c
x
+
d
⇒
b
=
−
8
a
,
c
=
22
a
,
d
=
−
24
a
Also
f
(
2
)
>
f
(
0
)
∴
x
=
1
&
3
are point of local maxima
Also
f
(
k
)
=
f
(
0
)
⇒
a
k
4
+
b
k
3
+
c
k
2
+
d
k
=
0
⇒
a
k
(
k
−
4
)
(
k
2
−
4
k
+
6
)
=
0
⇒
k
=
4
© examsnet.com
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