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Byju's Answer
Standard XII
Mathematics
Square Root of a Complex Number
Let the small...
Question
Let the smallest possible value of
f
(
x
)
=
√
10
x
−
67
be
m
. Then the value of
m
is
A
0
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B
2
3
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C
1
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D
2
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Solution
The correct option is
B
0
The domain of the above function will be
10
x
−
67
≥
0
. or
x
≥
67
10
.
Hence
x
ϵ
[
6.7
,
∞
)
.
Hence, the minimum value of
f
(
x
)
is at
x
=
6.7
which is
0
.
Suggest Corrections
0
Similar questions
Q.
Let
f
(
x
)
=
cos
π
x
+
10
x
+
3
x
2
+
x
3
,
−
2
≤
x
≤
3.
The absolute minimum value of
f
(
x
)
is
Q.
Let
W
1
and
W
2
denote the circles
x
2
+
y
2
+
10
x
−
24
y
−
87
=
0
and
x
2
+
y
2
−
10
x
−
24
y
+
153
=
0
respectively. Let
m
be the smallest positive value of
a
for which the line
y
=
a
x
contains the centre of a circle that is externally tangent to
W
2
and internally tangent to
W
1
.
If
m
2
=
p
q
,
where
p
and
q
are co-prime, then the value of
(
p
+
q
)
is
Q.
Let
f
′
(
x
)
=
192
x
3
(
2
+
s
i
n
4
(
n
π
)
)
for all
x
∈
R
with
f
(
1
/
2
)
=
0
. If
m
≤
∫
1
1
/
2
f
(
x
)
d
x
≤
M
, then the possible values of
m
and
M
are
Q.
Let
f
′
(
x
)
=
192
x
3
2
+
s
i
n
4
π
x
for all
x
∈
R
with
f
(
1
2
)
=
0
. If
m
≤
∫
1
1
2
f
(
x
)
d
x
≤
M
, then the possible values of m and M are ?
Q.
Let
M
and
m
respectively be the maximum and minimum values of the function
f
(
x
)
=
tan
−
1
(
sin
x
+
cos
x
)
in
[
0
,
π
2
]
.
Then the value of
tan
(
M
−
m
)
is equal to
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