1
NDA 2018 Paper 2
MCQ (Single Correct Answer)
+2.5
-0.83
If $$A = {\sin ^2}\theta + {\cos ^4}\theta $$, then for all real $$\theta$$, which one of the following is correct?
A
$$1 \le A \le 2$$
B
$${3 \over 4} \le A \le 1$$
C
$${{13} \over {16}} \le A \le 1$$
D
$${3 \over 4} \le A \le {{13} \over {16}}$$
2
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
What is $${{\sin 5x - \sin 3x} \over {\cos 5x + \cos 3x}}$$ equal to?
A
sin x
B
cos x
C
tan x
D
cot x
3
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
If x, x $$-$$ y and x + y are the angles of a triangle (not an equilateral triangle) such that tan (x $$-$$ y), tan x and tan (x + y) are in GP, then what is x equal to?
A
$${\pi \over 4}$$
B
$${\pi \over 3}$$
C
$${\pi \over 6}$$
D
$${\pi \over 2}$$
4
NDA 2018 Paper 1
MCQ (Single Correct Answer)
+2.5
-0.83
ABC is a triangle inscribed in a circle with centre O. Let $$\alpha$$ = $$\angle$$BAC, where 45$$^\circ$$ < $$\alpha$$ < 90$$^\circ$$. Let $$\beta$$ = $$\angle$$BOC. Which one of the following is correct?
A
$$\cos \beta = {{1 - {{\tan }^2}\alpha } \over {1 + {{\tan }^2}\alpha }}$$
B
$$\cos \beta = {{1 + {{\tan }^2}\alpha } \over {1 - {{\tan }^2}\alpha }}$$
C
$$\cos \beta = {{2\tan \alpha } \over {1 + {{\tan }^2}\alpha }}$$
D
$$\sin \beta = 2{\sin ^2}\alpha $$
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