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CBSE Questions for Class 11 Engineering Maths Trigonometric Functions Quiz 16 - MCQExams.com
CBSE
Class 11 Engineering Maths
Trigonometric Functions
Quiz 16
If
s
i
n
α
+
s
i
n
β
=
1
2
s
i
n
α
+
s
i
n
β
=
1
2
and
c
o
s
α
+
c
o
s
β
=
√
3
2
c
o
s
α
+
c
o
s
β
=
√
3
2
then
3
β
+
α
=
3
β
+
α
=
Report Question
0%
0
o
0
o
0%
60
o
60
o
0%
120
o
120
o
0%
90
o
90
o
The value of
csc
π
13
−
√
3
sec
π
18
csc
π
13
−
√
3
sec
π
18
is a
Report Question
0%
Surd
0%
Rational which is not integral
0%
Negative integer
0%
Natural number
The number of solution of the equation
x
3
+
2
x
2
+
5
x
+
2
cos
x
=
0
i
n
[
0
,
2
π
]
x
3
+
2
x
2
+
5
x
+
2
cos
x
=
0
i
n
[
0
,
2
π
]
is
Report Question
0%
0
0
0%
1
1
0%
2
2
0%
3
3
tan
2
θ
tan
2
θ
−
1
+
csc
2
θ
sec
2
θ
−
csc
2
θ
=
1
sin
2
θ
−
cos
2
θ
tan
2
θ
tan
2
θ
−
1
+
csc
2
θ
sec
2
θ
−
csc
2
θ
=
1
sin
2
θ
−
cos
2
θ
.
Report Question
0%
True
0%
False
s
e
c
2
(
T
a
n
−
1
2
)
+
C
o
s
e
c
2
(
C
o
t
−
1
3
)
=
s
e
c
2
(
T
a
n
−
1
2
)
+
C
o
s
e
c
2
(
C
o
t
−
1
3
)
=
Report Question
0%
5
0%
10
0%
15
0%
20
1
cosec
θ
+
cot
θ
−
1
sin
θ
=
1
sin
θ
−
1
cosec
θ
−
cot
θ
1
cosec
θ
+
cot
θ
−
1
sin
θ
=
1
sin
θ
−
1
cosec
θ
−
cot
θ
Report Question
0%
True
0%
False
If y = acosx + bsinx then find the maximum value of y
Report Question
0%
√
a
2
+
b
2
√
a
2
+
b
2
0%
a
2
+
b
2
a
2
+
b
2
0%
a
+
b
2
a
+
b
2
0%
√
a
2
+
b
2
2
√
a
2
+
b
2
2
The value of
9
∑
r
=
0
sin
2
π
r
18
i
s
e
q
u
a
l
t
o
9
∑
r
=
0
sin
2
π
r
18
i
s
e
q
u
a
l
t
o
Report Question
0%
9
2
9
2
0%
7
2
7
2
0%
5
0%
None of these
If
csc
θ
=
x
2
−
y
2
x
2
+
y
2
csc
θ
=
x
2
−
y
2
x
2
+
y
2
where
x
x
and
y
y
are two unequal non-zero real numbers, then the number of real values of
θ
is
Report Question
0%
0
0%
1
0%
2
0%
i
n
f
i
n
i
t
e
n
−
1
∑
r
=
1
cos
2
(
r
π
n
)
=
?
Report Question
0%
n
2
0%
n
−
2
2
0%
n
−
1
2
0%
n
−
2
4
Explanation
As we know that
cos
2
A
=
2
cos
2
A
−
1
cos
2
A
=
1
+
cos
2
A
2
say ,
A
=
π
π
n
⇒
n
−
1
∑
r
=
1
1
+
cos
2
(
r
π
n
)
=
1
2
[
n
−
1
∑
r
=
1
cos
2
π
π
n
+
n
−
1
∑
n
=
1
1
]
⇒
1
2
[
cos
2
π
n
+
cos
4
π
n
+
…
+
cos
2
(
n
−
1
)
n
π
+
(
n
−
1
)
]
As we know that
cos
α
+
cos
(
α
+
β
)
+
cos
(
α
+
2
β
)
+
⋯
+
cos
(
α
+
(
n
−
1
)
β
)
=
sin
(
n
β
2
)
sin
β
2
⋅
cos
(
2
α
+
(
n
−
1
)
β
2
)
=
1
2
[
sin
(
(
n
−
1
)
π
n
)
sin
(
π
n
)
⋅
cos
(
4
π
n
+
(
n
−
2
)
2
π
n
2
)
+
n
−
1
]
=
1
2
[
−
sin
(
n
−
1
n
π
)
sin
π
n
+
n
−
1
]
=
1
2
[
−
{
sin
sin
(
π
−
(
n
−
1
)
n
)
π
sin
π
n
}
}
+
n
−
1
]
=
1
2
[
−
s
i
n
π
n
s
i
n
π
n
+
n
−
1
]
=
1
2
(
−
1
+
n
−
1
)
=
n
−
2
2
Hence,
(
B
)
is the correct option.
If
s
i
n
x
+
s
i
n
2
x
=
1
,
then value of
c
o
s
2
x
+
c
o
s
4
x
is
Report Question
0%
1
0%
2
0%
1.5
0%
none of these
If
cos
θ
p
=
sin
θ
q
, then
p
sec
2
θ
+
q
c
o
s
e
c
2
θ
is equal to
Report Question
0%
p
0%
q
0%
qp
0%
none of these
The value of
10
∑
r
=
1
cos
3
r
π
3
=
?
Report Question
0%
−
1
8
0%
−
7
8
0%
−
9
8
0%
None of the above
If
x
+
y
=
2
π
3
a
n
d
c
o
s
x
+
c
o
s
y
=
√
3
2
,
t
h
e
n
x
,
y
i
s
e
q
u
a
l
t
o
Report Question
0%
π
3
,
π
6
0%
π
2
,
π
6
0%
π
4
,
π
3
0%
no solution
√
1
+
c
o
s
x
1
−
c
o
s
x
Report Question
0%
1
+
c
o
s
x
1
−
c
o
s
x
0%
c
o
s
e
c
x
+
c
o
t
x
0%
c
o
s
e
c
x
−
c
o
t
x
0%
c
o
s
e
c
x
If
f
(
x
)
=
cos
2
x
+
sin
4
x
sin
2
x
+
cos
4
x
for
x
∈
R
then
f
(
2002
)
=
Report Question
0%
1
0%
2
0%
3
0%
4
If
T
n
=
(
sin
n
θ
+
cos
n
θ
)
,
t
h
e
n
f
o
r
p
e
r
m
i
s
s
i
b
l
e
v
a
l
u
e
s
o
f
θ
,
T
5
−
T
3
T
7
−
T
5
is always equal to
Report Question
0%
T
1
T
3
0%
T
2
T
4
0%
T
5
T
7
0%
T
3
T
7
The smallest value of 0 satisfying the equation
√
3
(
c
o
t
0
+
t
a
n
0
)
=
4
is
Report Question
0%
2
x
/
3
0%
π
/
3
0%
π
/
6
0%
π
/
12
The number of real values of x such that
(
2
−
x
+
2
x
−
2
cos
x
)
(
3
x
+
π
+
3
−
x
−
π
+
2
cos
x
)
(
5
π
−
x
−
2
cos
x
+
5
x
−
π
)
=
0
,
i
s
Report Question
0%
1
0%
2
0%
3
0%
infinite
The number of solutions of the equation sin
(
π
x
2
√
3
)
=
x
2
−
2
√
3
x
+
4
is
Report Question
0%
0
0%
2
0%
1
0%
none of these
Find the fix point through which the line
(
2
c
o
s
Θ
+
3
s
i
n
Θ
)
x
+
(
3
c
o
s
Θ
−
5
s
i
n
Θ
)
y
−
(
5
c
o
s
Θ
−
2
s
i
n
Θ
)
=
0
passes for all values of
Θ
-
Report Question
0%
(0,0)
0%
(1,1)
0%
(2,1)
0%
None of these
The principal solutions of
s
e
c
x
=
2
√
3
are _________
Report Question
0%
π
3
,
|
|
π
6
0%
π
6
,
11
π
6
0%
π
4
,
|
|
π
4
0%
π
6
,
|
|
π
4
tan
θ
1
−
cot
θ
+
cot
θ
1
−
tan
θ
is equal to
Report Question
0%
1
+
tan
θ
+
cot
θ
0%
1
−
tan
θ
−
cot
θ
0%
1
+
tan
θ
−
cot
θ
0%
none of these
c
o
s
4
Θ
−
s
i
n
4
Θ
is equal
Report Question
0%
1
−
t
a
n
2
Θ
1
+
t
a
n
2
Θ
0%
2
c
o
s
2
Θ
−
1
0%
1
−
2
s
i
n
2
Θ
0%
s
i
n
2
Θ
−
c
o
s
2
Θ
32
s
i
n
6
15
0
−
48
s
i
n
4
15
0
+
18
s
i
n
2
15
0
=
Report Question
0%
1
0%
2
0%
3
0%
-1
Choose the correct answer.
(
1
+
tan
2
θ
)
sin
2
θ
=
Report Question
0%
tan
2
θ
0%
cot
2
θ
0%
sin
2
θ
0%
cos
2
θ
The number of solutions of the equation
sin
(
9
x
)
+
sin
(
3
x
)
=
0
in the closed interval
[
0
,
2
π
]
is
Report Question
0%
7
0%
13
0%
19
0%
25
Explanation
sin
9
x
+
sin
3
x
=
0
,
x
∈
[
0
,
2
π
]
⇒
3
sin
3
x
−
4
sin
3
3
x
+
sin
3
x
=
0
⇒
4
sin
3
x
−
4
sin
3
3
x
=
0
⇒
4
sin
3
x
(
1
−
sin
2
3
x
)
=
0
⇒
sin
3
x
=
0
,
(
1
−
sin
2
3
x
)
=
0
⇒
sin
3
x
=
0
,
sin
2
3
x
=
1
⇒
3
x
=
n
π
,
n
∈
I
or
3
x
=
k
π
+
π
2
,
k
∈
I
⇒
x
=
n
π
3
,
x
=
k
π
3
+
π
6
,
k
∈
I
For
n
=
0
,
1
,
2
,
3
,
4
,
5
,
6
we have
x
=
0
,
π
3
,
2
π
3
,
π
,
4
π
3
,
5
π
3
,
2
π
For
k
=
0
,
1
,
2
,
3
,
4
,
5
we have
x
=
π
6
,
π
3
+
π
6
,
2
π
3
+
π
6
,
π
+
π
6
,
4
π
3
+
π
6
,
5
π
3
+
π
6
or
x
=
π
6
,
2
π
6
+
π
6
,
4
π
6
+
π
6
,
6
π
+
π
6
,
8
π
6
+
π
6
,
10
π
6
+
π
6
or
x
=
π
6
,
3
π
6
,
5
π
6
,
7
π
6
,
9
π
6
,
11
π
6
or
x
=
π
6
,
π
2
,
5
π
6
,
7
π
6
,
3
π
2
,
11
π
6
Thus, the solutions are
{
0
,
π
3
,
2
π
3
,
π
,
4
π
3
,
5
π
3
,
2
π
,
π
6
,
π
2
,
5
π
6
,
7
π
6
,
3
π
2
,
11
π
6
}
or
{
0
,
π
2
,
π
6
,
π
3
,
2
π
3
,
3
π
2
,
π
,
4
π
3
,
5
π
3
,
5
π
6
,
7
π
6
,
11
π
6
,
2
π
}
=
13
solutions
If
s
e
c
A
=
a
+
(
1
4
a
)
, then sec A + tan A is equal to
Report Question
0%
2
a
o
r
1
2
a
0%
a
o
r
1
a
0%
2
a
o
r
1
a
0%
a
o
r
1
2
a
If
s
i
n
−
1
x
+
s
i
n
−
1
y
+
s
i
n
−
1
z
=
3
π
/
2
then the value of
x
100
+
y
100
+
z
100
−
3
x
101
+
y
101
+
z
101
is
Report Question
0%
0
0%
1
0%
2
0%
3
Indicate the relation which is true
Report Question
0%
t
a
n
|
t
a
n
−
1
x
|
=
|
x
|
0%
c
o
t
|
c
o
t
−
1
x
|
=
x
0%
t
a
n
−
1
|
t
a
n
x
|
=
|
x
|
0%
s
i
n
|
s
i
n
−
1
|
=
|
x
|
0:0:1
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19
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22
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28
29
30
0
Answered
1
Not Answered
29
Not Visited
Correct : 0
Incorrect : 0
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