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EAMCET Engineering 2005 Solved Paper
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© examsnet.com
Question : 144
Total: 160
Observe the following statements
I.
f
(
x
)
=
a
x
41
+
b
x
−
40
⇒
f
′
′
(
x
)
f
(
x
)
=
1640
x
−
2
II.
d
d
x
tan
−
1
(
2
x
1
−
x
2
)
=
1
1
+
x
2
Which of the following is correct?
I is true, but II is false
Both I and II are true
Neither I nor II is true
I is false, but II is true
Validate
Solution:
I.
f
(
x
)
=
a
x
41
+
b
x
−
40
f
′
(
x
)
=
41
a
x
40
−
40
b
x
−
41
f
′
′
(
x
)
=
1640
a
x
39
+
1640
b
x
−
42
Now,
f
′
′
(
x
)
f
(
x
)
=
1640
(
a
x
39
+
b
x
−
42
)
a
x
41
+
b
x
−
40
=
1640
x
−
2
II.
d
d
x
tan
−
1
(
2
x
1
−
x
2
)
=
d
d
x
tan
−
1
(
tan
2
x
)
=
d
d
x
2
x
=
2
∴
Statement I is true, but II is false.
© examsnet.com
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