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NIMCET 2021 Question Paper with solutions
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© examsnet.com
Question : 8
Total: 120
If
|
k
|
=
5
,
0
°
≤
θ
≤
360
°
, then total number of different solutions of
3
cos
θ
+
4
sin
θ
=
k
is
0
1
2
infinite
Validate
Solution:
Given equation
3
cos
θ
+
4
sin
θ
=
k
Also
(
k
)
=
5
⇒
k
=
±
5
3
cos
θ
+
4
sin
θ
=
±
5
3
5
cos
θ
+
4
5
sin
θ
=
±
1
.
.
.
.
.
.
(1)
Let
3
5
=
r
sin
α
and
4
5
=
r
cos
α
Where
r
=
1
and
=
α
=
tan
−
1
(
3
4
)
By eq. (1)
Sin
α
cos
θ
+
cos
α
sin
θ
=
±
1
Sin
(
θ
+
α
)
=
±
1
Since
0
°
<
θ
<
360
°
Hence two solution exists.
© examsnet.com
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