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UPSC 2015 CDS II Math Paper
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© examsnet.com
Question : 25
Total: 100
If the roots of the quadratic equation
x
2
−
4
x
−
l
o
g
10
N
=
0
are all real then the minimum value of N is
[2015 CDS-II]
1
100
1
1000
1
10000
10000
Validate
Solution:
The roots of the equation
x
2
−
4
x
−
log
10
N
=
0
are real if
D
≥
0
⇒
16
+
4
log
10
N
≥
0
(
D
=
b
2
−
4
a
c
)
⇒
4
log
10
N
≥
−
16
⇒
log
10
N
≥
−
4
⇒
N
≥
10
−
4
=
1
1000
Thus, the minimum value of N is
1
10000
© examsnet.com
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