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Byju's Answer
Standard XII
Mathematics
Principal Solution of Trigonometric Equation
Observe the f...
Question
Observe the following lists
List - I
List - II
A) minimum value of
|
x
−
5
|
is
1) -1
B) minimum value of
|
x
−
3
|
+
|
x
−
7
|
is
2) 0
C) maximum value of
|
sin
5
x
|
3)
√
2
D) maximum value of
|
sin
+
cos
x
|
4) 1
5) 4
A
A - 2, B - 5, C - 3, D - 2.
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B
A - 2, B - 5, C - 4, D - 3.
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C
A - 2, B - 3, C - 1, D - 4.
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D
A - 2, B - 3, C - 5, D - 1.
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Solution
The correct option is
D
A - 2, B - 5, C - 4, D - 3.
A
)
∣
x
−
5
∣
≥
0
So the minimum value of
|
x
−
5
|
is
0
B
)
∣
x
−
3
∣
+
∣
x
−
7
∣
The minimum value will be at
x
=
7
+
3
2
=
5
So the minimum value of
∣
x
−
3
∣
+
∣
x
−
7
∣
is
|
5
−
3
|
+
|
5
−
7
|
=
2
+
2
=
4
C
)
sin
5
x
∈
[
−
1
,
1
]
⟹
|
sin
5
x
|
∈
[
0
,
1
]
So the maximum value is
1
D
)
sin
x
+
cos
x
∈
[
−
√
2
,
√
2
]
⟹
∣
sin
x
+
cos
x
∣
∈
[
0
,
√
2
]
So the maximum value is
√
2
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0
Similar questions
Q.
Arrange A, B, C, D in ascending order
A) Maximum value of sin5x
B)
Minimum value of
x
+
1
x
(
x
>
0
)
C) Minimum value of
4
×
2
(
x
2
−
3
)
3
+
27
D) Minimum value of
5
sin
2
x
+
3
cos
2
x
Q.
Observe the following lists
List - I
List - II
A) minimum value of
a
2
sin
2
x
+
b
2
cos
e
c
2
x
1)
2
√
a
b
B) minimum value of acotx + b tanx
2)
(
a
+
b
)
2
C) minimum value of
a
2
sec
2
x
+
b
2
cos
e
c
2
x
3)
−
√
a
2
+
b
2
D) minimum value of
a
cos
x
+
b
sin
x
4) ab
5) 2ab
Q.
Observe the following lists
List-I
List-II
(A) Maximum value of
x
y
subject to
x
+
y
=
7
is
1)
72
(B) If
l
2
+
m
2
=
1
, then the maximum value of
l
+
m
is
2)
1
(C) If
x
+
y
=
12
, then the minimum Value of
x
2
+
y
2
is
3)
√
2
(D) Minimum value
x
2
−
8
x
+
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is
4)
49
4
5)
0
Q.
2a + 3b + c + d ----(1)
6b + 3c + 9d + 4a--(2)
5a + 7b - 2c - d-----(3)
What is the value of (1) + (2) - (3)?
Q.
Let
f
(
x
)
=
sin
−
1
x
+
2
tan
−
1
x
+
x
5
−
5
x
4
+
5
x
3
+
1
. Then
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