1
IIT-JEE 2001 Screening
+2
-0.5
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
$$-6,-32$$
2
IIT-JEE 2001 Screening
+2
-0.5
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.
3
IIT-JEE 2001 Screening
+2
-0.5
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
4
IIT-JEE 2000 Screening
+2
-0.5
Consider an infinite geometric series with first term a and common ratio $$r$$. If its sum is 4 and the second term is 3/4, then
A
$$a = {4 \over 7},r = {3 \over 7}\,\,\,\,$$
B
$$a = 2,\,r = {3 \over 8}$$
C
$$a = {3 \over 2},r = {1 \over 2}$$
D
$$a = 3,\,r = {1 \over 4}$$
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