1
IIT-JEE 1990
+2
-0.5
The equation $$\left( {\cos p - 1} \right){x^2} + \left( {\cos p} \right)x + \sin p = 0\,$$ In the variable x, has real roots. Then p can take any value in the interval
A
$$\left( {0,2\pi } \right)\,$$
B
$$\left( { - \pi ,0} \right)\,\,\,$$
C
$$\left[ { - {\pi \over 2},{\pi \over 2}} \right]\,$$
D
$$\left( {0,\pi } \right)$$
2
IIT-JEE 1989
+2
-0.5
The general solutions of $$\,\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$$ is
A
$$n\pi + {\pi \over 8}$$
B
$${{n\pi } \over 2} + {\pi \over 8}$$
C
$${\left( { - 1} \right)^n}{{n\pi } \over 2} + {\pi \over 8}\,\,$$
D
$$2n\pi + {\cos ^{ - 1}}{3 \over 2}$$
3
IIT-JEE 1988
+2
-0.5
The value of the expression $$\sqrt 3 \,\cos \,ec\,{20^0} - \sec \,{20^0}$$ is equal to
A
2
B
$$2\sin {20^0}/\sin {40^0}$$
C
4
D
$$4\sin {20^0}/\sin {40^0}$$
4
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
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