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1

IIT-JEE 1986

MCQ (Single Correct Answer)
The expression $$2\left[ {{{\sin }^6}\left( {{\pi \over 2} + \alpha } \right) + {{\sin }^6}\left( {5\pi - \alpha } \right)} \right]$$ is equal to
A
0
B
1
C
3
D
$$\sin \,4\,\alpha + \cos \,6\,\alpha \,\,\,\,$$
2

IIT-JEE 1984

MCQ (Single Correct Answer)
$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ is equal to
A
$${1 \over 2}$$
B
$$\cos {\pi \over 8}$$
C
$${1 \over 8}$$
D
$${{1 + \sqrt 2 } \over {2\sqrt 2 }}$$
3

IIT-JEE 1981

MCQ (Single Correct Answer)
The general solution of the trigonometric equation sin x+cos x=1 is given by:
A
$$2n\pi ;\,n = 0,\, \pm 1,\, \pm 2....$$
B
$$x = 2n\pi + \pi /2;\,n = 0,\, \pm 1,\, \pm 2....$$
C
$$x = n\pi + {\left( { - 1} \right)^n}\,\,\,\,\,\,\,{\pi \over 4} - {\pi \over 4}$$ ; $$n = 0,\, \pm 1,\, \pm 2..$$
D
none of these
4

IIT-JEE 1980

MCQ (Single Correct Answer)
The equation $$\,2{\cos ^2}{x \over 2}{\sin ^2}x = {x^2} + {x^{ - 2}};\,0 < x \le {\pi \over 2}$$ has
A
no real solution
B
one real solution
C
more than one solution
D
none of these

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