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KEAM 2019 Math Paper
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© examsnet.com
Question : 14
Total: 121
The third term in the expansion of
(
1
x
+
x
log
10
x
)
5
,
x
>
1
is 1000, then
x
equals.
1
10
100
√
10
1
√
10
Validate
Solution:
Given,
T
3
=
1000
⇒
5
C
2
(
1
x
)
5
−
2
(
x
log
10
x
)
2
=
1000
⇒
x
2
log
10
(
x
−
3
)
=
100
⇒
2
log
10
x
−
3
=
log
x
10
2
⇒
2
y
−
3
=
2
y
′
(
where
y
=
log
10
x
)
⇒
y
=
−
1
2
,
2
When
y
=
2
,
x
=
100
and when
y
=
−
1
2
,
x
=
10
−
1
∕
2
As,
x
>
1
, So,
x
=
100
© examsnet.com
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