1
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Read the given information carefully and answer the given questions.

If $$p = X\cos \theta - Y\sin \theta $$,

$$q = X\sin \theta + Y\cos \theta $$ and

$${p^2} + 4pq + {q^2} = A{X^2} + B{Y^2}$$, $$0 \le \theta \le {\pi \over 2}$$.
What is the value of B?
A
$$-$$ 1
B
0
C
1
D
2
2
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Read the given information carefully and answer the given questions.

It is given that $$\cos (\theta - \alpha ) = a$$, $$\cos (\theta - \beta ) = b$$.
What is $$\cos (\alpha - \beta )$$ equal to?
A
$$ab + \sqrt {1 - {a^2}} \sqrt {1 - {b^2}} $$
B
$$ab - \sqrt {1 - {a^2}} \sqrt {1 - {b^2}} $$
C
$$a\sqrt {1 - {b^2}} - b\sqrt {1 - {a^2}} $$
D
$$a\sqrt {1 - {b^2}} + b\sqrt {1 - {a^2}} $$
3
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
Read the given information carefully and answer the given questions.

It is given that $$\cos (\theta - \alpha ) = a$$, $$\cos (\theta - \beta ) = b$$.
What is $${\sin ^2}(\alpha - \beta ) + 2ab\cos (\alpha - \beta )$$ equal to?
A
a2 + b2
B
a2 $$-$$ b2
C
b2 $$-$$ a2
D
$$-$$ (a2 + b2)
4
NDA 2019 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If $$\sin \alpha + \cos \alpha = p$$, then what is $${\cos ^2}(2\alpha )$$ equal to?
A
p2
B
p2 $$-$$ 1
C
p2 (2 $$-$$ p2)
D
p2 + 1
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