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UPSC NDA II 2015 Mathematics Solved Paper
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© examsnet.com
Question : 4
Total: 120
Consider the following statements in respect of the determinant
|
cos
2
α
2
sin
2
α
2
sin
2
β
2
cos
2
β
2
|
where α,β are complementary angles
1. The value of the determinant is
1
√
2
c
o
s
(
α
−
β
2
)
2. The maximum value of the determinant is
1
√
2
Which of the above statements is/are correct
[NDA II 2015]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
α
+
β
=
90
°
|
cos
2
α
2
sin
2
α
2
sin
2
β
2
cos
2
β
2
|
=
cos
2
α
2
cos
2
β
2
−
sin
2
α
2
sin
2
β
2
=
(
cos
α
2
cos
β
2
+
sin
α
2
sin
β
2
)
(
cos
α
2
cos
β
2
−
sin
α
2
sin
β
2
)
=
cos
(
α
−
β
)
2
+
cos
(
α
+
β
)
2
=
cos
(
α
−
β
)
2
+
cos
(
90
∘
)
2
=
cos
(
α
−
β
)
2
+
1
√
2
Maximum value of
cos
(
α
−
β
2
)
is 1. So maximum value of determinant is
(
1
+
1
√
2
)
So neither 1 nor 2 is correct.
© examsnet.com
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