1

### 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
$$-6,-32$$
2

### IIT-JEE 2000 Screening

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
$$a = 3,\,r = {1 \over 4}$$
3

### IIT-JEE 1999

Let $${a_1},{a_2},......{a_{10}}$$ be in $$A,\,P,$$ and $${h_1},{h_2},......{h_{10}}$$ be in H.P. If $${a_1} = {h_1} = 2$$ and $${a_{10}} = {h_{10}} = 3,$$ then $${a_4}{h_7}$$ is
A
2
B
3
C
5
D
6
4

### IIT-JEE 1999

The harmonic mean of the roots of the equation $$\left( {5 + \sqrt 2 } \right){x^2} - \left( {4 + \sqrt 5 } \right)x + 8 + 2\sqrt 5 = 0$$ is
A
2
B
4
C
6
D
8

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