1
IIT-JEE 1986
+2
-0.5
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
+3
-0.75
$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ 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
+2
-0.5
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
+2
-0.5
Given $$A = {\sin ^2}\theta + {\cos ^4}\theta$$ then for all real values of $$\theta$$
A
$$1 \le A \le 2$$
B
$${3 \over 4} \le A \le 1$$
C
$${13\over 16} \le A \le 1$$
D
$${3 \over 4} \le A \le {{13} \over {16}}$$
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