1
IIT-JEE 2007
+4
-1
Let $${A_1}$$, $${G_1}$$, $${H_1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \ge 2,\,Let\,{A_{n - 1}}\,\,and\,\,{H_{n - 1}}$$ have arithmetic, geometric and harminic means as $${A_n},{G_n}\,,{H_n}$$ repectively.

Which one of the following statements is correct ?

A
$${G_1} > {G_2}\, > {G_3} > ...$$
B
$${G_1} < {G_2}\, < {G_3} < ...$$
C
$${G_1} = {G_2}\, = {G_3} = ...$$
D
$${G_1} < {G_2}\, < {G_3} < ...$$ and $${G_1} > {G_2}\, > {G_3} > ...$$
2
IIT-JEE 2005 Screening
+2
-0.5
In the quadratic equation $$\,\,a{x^2} + bx + c = 0,$$ $$\Delta$$ $$= {b^2} - 4ac$$ and $$\alpha + \beta ,\,{\alpha ^2} + {\beta ^2},\,{\alpha ^3} + {\beta ^3},$$ are in G.P. where $$\alpha ,\beta$$ are the root of $$\,\,a{x^2} + bx + c = 0,$$ then
A
$$\Delta \ne 0$$
B
$$b\Delta = 0$$
C
$$c\Delta = 0$$
D
$$\Delta = 0$$
3
IIT-JEE 2004 Screening
+2
-0.5
An infinite G.P. has first term '$$x$$' and sum '$$5$$', then $$x$$ belongs to
A
$$x < - 10$$
B
$$- 10 < x < 0$$
C
$$0 < x < 10$$
D
$$x > 10$$
4
IIT-JEE 2002 Screening
+2
-0.5
Suppose $$a, b, c$$ are in A.P. and $${a^2},{b^2},{c^2}$$ are in G.P. If $$a < b < c$$ and $$a + b + c = {3 \over 2},$$ then the value of $$a$$ is
A
$${1 \over {2\sqrt 2 }}$$
B
$${1 \over {2\sqrt 3 }}$$
C
$${1 \over 2} - {1 \over {\sqrt 3 }}$$
D
$${1 \over 2} - {1 \over {\sqrt 2 }}$$
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