1
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
The value of $${\sin ^2}5^\circ + {\sin ^2}10^\circ + {\sin ^2}15^\circ + {\sin ^2}20^\circ + .... + {\sin ^2}90^\circ $$ is
A
7
B
8
C
9
D
$${{19} \over 2}$$
2
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
On simplifying $${{{{\sin }^3}A + \sin 3A} \over {\sin A}} + {{{{\cos }^3}A - \cos 3A} \over {\cos A}}$$ we get
A
$$\sin 3A$$
B
$$\cos 3A$$
C
$$\sin A + \cos A$$
D
3
3
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\sin x + \sin y = a$$ and $$\cos x + \cos y = b$$, then $${\tan ^2}\left( {{{x + y} \over 2}} \right) + {\tan ^2}\left( {{{x - y} \over 2}} \right)$$ is equal to
A
$${{{a^4} + {b^4} + 4{b^2}} \over {{a^2}{b^2} + {b^4}}}$$
B
$${{{a^4} - {b^4} + 4{b^2}} \over {{a^2}{b^2} + {b^4}}}$$
C
$${{{a^4} - {b^4} + 4{a^2}} \over {{a^2}{b^2} + {a^4}}}$$
D
None of these
4
NDA 2015 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$p = \tan \left( { - {{11\pi } \over 6}} \right)$$, $$q = \tan \left( {{{21\pi } \over 4}} \right)$$ and $$r = \cot \left( {{{283\pi } \over 6}} \right)$$, then which of the following is/are correct?

1. The value of p $$\times$$ r is 2.

2. p, q and r are in GP.

Select the correct answer using the code given below.
A
Only 1
B
Only 2
C
Both 1 and 2
D
Neither 1 nor 2
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