1
IIT-JEE 2000 Screening
+2
-0.5
Let $$f\left( \theta \right) = \sin \theta \left( {\sin \theta + \sin 3\theta } \right)$$. Then $$f\left( \theta \right)$$ is
A
$$\ge 0\,\,$$ only when $$\theta \ge 0$$
B
$$\le 0$$ for all real $$\theta$$
C
$$\ge 0$$ for all real $$\theta$$
D
$$\le 0$$ only when $$\theta \le 0$$
2
IIT-JEE 2000 Screening
+2
-0.5
If $${z_1},\,{z_2}$$ and $${z_3}$$ are complex numbers such that $$\left| {{z_1}} \right| = \left| {{z_2}} \right| = \left| {{z_3}} \right| = \left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right| = 1,$$ then $$\left| {{z_1} + {z_2} + {z_3}} \right|$$ is
A
equal to 1
B
less than 1
C
greater than 3
D
equal to 3
3
IIT-JEE 2000 Screening
+2
-0.5
If $$\arg \left( z \right) < 0,$$ then $$\arg \left( { - z} \right) - \arg \left( z \right) =$$
A
$$\pi$$
B
$$- \pi$$
C
$$- {\pi \over 2}$$
D
$${\pi \over 2}$$
4
IIT-JEE 2000 Screening
+2
-0.5
If b > a, then the equation (x - a) (x - b) - 1 = 0 has
A
both roots in (a, b)
B
both roots in (- $$\infty$$, a)
C
both roots in (b, + $$\infty$$)
D
one root in (- $$\infty$$, a) and the other in (b, + $$\infty$$)
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