1

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

### IIT-JEE 2001 Screening

If the sum of the first $$2n$$ terms of the A.P.$$2,5,8,......,$$ is equal to the sum of the first $$n$$ terms of the A.P.$$57,59,61,.....,$$ then $$n$$ equals
A
10
B
12
C
11
D
13
3

### 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.
4

### IIT-JEE 2001 Screening

Let $$\alpha$$, $$\beta$$ be the roots of $${x^2} - x + p = 0$$ and $$\gamma ,\delta$$ be the roots of $${x^2} - 4x + q = 0.$$ If $$\alpha ,\beta ,\gamma ,\delta$$ are in G.P., then the integral values of $$p$$ and $$q$$ respectively, are
A
$$-2,-32$$
B
$$-2,3$$
C
$$-6,3$$
D
$$-6,-32$$

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