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1

IIT-JEE 2005 Screening

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
$$\Delta = 0$$
2

IIT-JEE 2004 Screening

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
$$x > 10$$
3

IIT-JEE 2002 Screening

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
$${1 \over 2} - {1 \over {\sqrt 2 }}$$
4

IIT-JEE 2001 Screening

Let the positive numbers $$a,b,c,d$$ be in A.P. Then $$abc,$$ $$abd,$$ $$acd,$$ $$bcd,$$ are
A
NOT in A.P./GP./H.P.
B
inA.P.
C
in GP.
D
in H.P.

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