Directions:1-5) Two equations (I) and (II) are given in each questions. On the basis of these questions, you have to decide the relation between p and q and give answer
1.
1.10p2 + 39p – 88 = 0
2.21q2 + 41q – 40 = 0
Ans:5 1.10p2 + 39p – 88 = 0
or, 10 p2– 16p + 55p – 88 = 0
or, 2p(5p – 8) + 11(5p – 8) = 0
or, (2p + 11) (5p – 8) = 0
p = -11/2 or 8/5
2.21 q2 + 41q – 40 = 0
or, 21 q2+ 56q – 15q – 40 = 0
or, 7q(3q + 8) – 5(3q + 8) = 0
or, (7q – 5) (3q + 8) = 0
q = 5/7 or -8/3
We can’t get specific relationship between p and q.
2.
I.14p2 – 43p + 20 = 0
II.33q2 + 72q + 12 = 0
Ans:1 I.14 p2 – 43p + 20 = 0
or, 14 p2– 35p – 8p + 20 = 0
or, 7p(2p – 5) – 4(2p – 5) = 0
or, (7p – 4) (2p – 5) = 0
p = 4/7 or 5/2
II.33 q2+ 72q + 12 = 0
or, 33 q2+ 6q + 66q + 12 = 0
or, 3q(11q + 2) + 6(11q + 2) = 0
or, (3q + 6) (11q + 2) = 0
q = -2 or -2/11
Hence p > q.
3.
I.56p2 + 97p + 42 = 0
II.99q2 – 64q + 5 = 0
Ans:2 I.56 p2+ 97p + 42 = 0
56 p2+ 49p + 48p + 42 = 0
or, 7p(8p + 7) + 6(8p + 7) = 0
or, (7p + 6) (8p + 7) = 0
p = -6/7 or -7/8
II.99 q2 – 64q + 5 = 0
or, 99 q2 – 9q – 55q + 5 = 0
or, 9q (11q – 1) – 5(11q – 1) = 0
or, (9q – 5) (11q – 1) = 0
q = 5/9 or 1/11
Hence p < q.
4.
I.16p2 – 40p + 25 = 0
II.25q2 – 40q + 16 = 0
Ans:1 I.16 p2– 40p + 25 = 0
or, 16 p2 – 20p – 20p + 25 = 0
or, 4p(4p – 5) – 5(4p – 5) = 0
or, (4p – 5) (4p – 5) = 0
p = 5/4, 5/4
II.25 q2– 40q + 16 = 0
or, 25 q2 – 20q – 20q + 16 = 0
or, 5q(5q – 4) – 4(5q – 4) = 0
or, (5q – 4) (5q – 4) = 0
q = 4/5, 4/5
Hence p > q.
5.
I.15p2 + 38p + 24 = 0
II.20q2 + 49q + 30 = 0
Ans:5 I.15 p2+ 38p + 24 = 0
or, 15 p2 + 20p + 18p + 24 = 0
or, 5p(3p + 4) + 6(3p + 4) = 0
or, (5p + 6) (3p + 4) = 0
p = -6/5 or -4/3
II.20 q2+ 49q + 30 = 0
or, 20 q2+ 24q + 25q + 30 = 0
or, 4q(5q + 6) + 5(5q + 6) = 0
or, (4q + 5) (5q + 6) = 0
q = -5/4 or -6/5
We can’t get specific relationship between p and q.
Directions:6-10) In the following questions two equations I and II are given. You have to solve both the equations and give answer:
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