Directions (Q.1–5): In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer

(1) if p > q

(2) if p > q

(3) if p < q

(4) if p < q

(5) if p = q or no relation can be established between p and q.

1. I. 2.3p – 20.01 = 0

II. 2.9q – p = 0

2. I. p = √1764

II. q^2 = 1764

3. I. p2 – 26p + 168 = 0

II. q2 – 25q + 156 = 0

4. I. p2 – 13p + 42 = 0

II. q2 + q – 42 = 0

5. I. 6p – 5q = –47

II. 5p + 3q = 11

(1) if p > q

(2) if p > q

(3) if p < q

(4) if p < q

(5) if p = q or no relation can be established between p and q.

1. I. 2.3p – 20.01 = 0

II. 2.9q – p = 0

2. I. p = √1764

3. I. p2 – 26p + 168 = 0

II. q2 – 25q + 156 = 0

4. I. p2 – 13p + 42 = 0

II. q2 + q – 42 = 0

5. I. 6p – 5q = –47

II. 5p + 3q = 11

Answers

1. 1; I. 2.3p – 20.01 = 0

? p =

20.01/2.3 = 8.7

II. 2.9q – p = 0

or, p = 2.9q

? q =8.7/2.9 = 3

ie p > q

2. 2; I. p = √1764

? p = 42

II. q^2 = 1764

? q = +42

ie p > q

3. 5; I. p2 – 26p + 168 = 0

? ?p2 – 12p – 14p + 168 = 0

? ?p(p – 12) – 14(p – 12) = 0

? ?(p – 12) (p – 14) =0

? p = 12, 14

II. q2 – 25q + 156 = 0

? ?q2 – 13q – 12q + 156 = 0

? ?q(q – 13) – 12(q – 13) = 0

? ?(q – 12) (q – 13) = 0

? q = 12, 13

Hence, no relation can be established between p and q.

4. 2; I. p2 – 13q + 42 = 0

? ?p2 – 6p – 7p + 42 = 0

? ?p(p – 6) – 7(p – 6) = 0

? ?(p – 6) (p – 7) = 0

? p = 6, 7

II. q2 + q – 42 = 0

? ?q2 + 7q – 6p – 42 = 0

? ?q(q + 7) – 6(q + 7) = 0

? ?(q – 6) (q + 7) = 0

? q = 6, –7 ie p > q

5. 3; eqn(I) × 3 18p –15q = –141

eqn(II) × 5 25p *15q * 55/43p = –86

? p = –86/ 43 = –2

5p + 3q = 11

? ?3q = 11 – 5p

? ?3q = 11 + 10

? ?3q = 21

? q = 7 ie p