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JEE Advanced 2014 Paper 2
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© examsnet.com
Question : 57
Total: 60
Match the following
List I
List II
(P)
The number of polynomial f(x) with non-negative integer coefficients of degree ≤2, satisfying f(0)=0 and
1
∫
0
f
(
x
)
d
x
=
1
,is
(1)
8
(Q)
The number of points in the interval
[
−
√
13
,
√
13
]
at which
f
(
x
)
=
s
i
n
(
x
2
)
+
c
o
s
(
x
2
)
attains its maximum value is
(2)
2
(R)
2
∫
−
2
3
x
2
(
1
+
e
x
)
d
x
equals
(3)
4
(S)
(
1
2
∫
−
1
2
c
o
s
2
x
.
l
o
g
(
1
+
x
1
−
x
)
d
x
)
(
1
2
∫
0
c
o
s
2
x
.
l
o
g
(
1
+
x
1
−
x
)
d
x
)
(4)
0
P
3
Q
2
R
4
S
1
P
2
Q
3
R
4
S
1
P
3
Q
2
R
1
S
4
P
2
Q
3
R
1
S
4
Validate
Solution:
(P)
f
(
x
)
=
a
x
2
+
b
x
,
1
∫
0
f
(
x
)
d
x
=
1
⇒
2
a
+
3
b
=
6
⇒
(
a
,
b
)
≡
(
0
,
2
)
and
(
3
,
0
)
(
Q
)
f
(
x
)
=
√
2
c
o
s
(
x
2
−
π
4
)
For maximum value
,
x
2
−
π
4
=
2
n
π
⇒
x
2
=
2
n
π
+
π
4
⇒
x
=
±
√
π
4
,
±
√
9
π
4
as
x
∊
[
−
√
3
,
√
13
]
.
(R)
2
∫
0
(
3
x
2
1
+
e
x
+
3
x
2
1
+
e
−
x
)
d
x
2
=
0
3
x
2
d
x
=
8
(S)
1
2
∫
−
1
2
c
o
s
2
x
I
n
(
1
+
x
1
−
x
)
d
x
=
0
as it is an odd function
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