1
IIT-JEE 1987
+2
-0.5
The number of all possible triplets $$\left( {{a_1},\,{a_2},\,{a_3}} \right)$$ such that $${a_1} + {a_2}\,\,\cos \left( {2x} \right) + {a_3}{\sin ^2}\left( x \right) = 0\,$$ for all $$x$$ is
A
zero
B
one
C
three
D
infinite
2
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
$$\sin \,4\,\alpha + \cos \,6\,\alpha \,\,\,\,$$
3
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
$${{1 + \sqrt 2 } \over {2\sqrt 2 }}$$
4
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
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