Directions: 1-5)In the following questions, two equations I and II are given. You have to solve both the equations.

Give Answer

1.

  1. p2 – 18p + 72= 0
  2. 5q2 – 18q + 9 = 0

Ans:
p2 – 18p + 72= 0
(p-12)(p-6) = 0
Gives p = 6, 12
5q2 – 18q + 9 = 0
5q2 – 15q – 3q + 9 = 0

5q (q-3) – 3(q-3) =0

(5q-3) (q-3) =0
Gives q = 3/5, 3
Put on number line
3/5   3    6  12

P > q

2.

  1. p2 = 4
  2. 2.3q2 – 4q – 4 = 0

Ans:
p2 = 4
Gives p = 2 , -2
3q2 – 4q – 4 = 0
3q2 – 6q + 2q – 4 = 0
Gives q = -2/3, 2
Put on number line
-2      -2/3        2
So no relation

3.

  • 6p2 – 5p – 6 = 0
  • 2q2 – 13q + 20 = 0

Ans:
6p2 – 5p – 6 = 0
6p2 – 9p + 4p – 6 = 0
Gives p = -2/3, 3/2
2q2 – 13q + 20 = 0
2q2 – 8q – 5q +20 = 0
Gives q = 4, 5/2
Put on number line
-2/3   3/2    5/2    4

P < q

4.

  1. 2p2 – 5p = 0
  2. 3q2 – 7q – 6 = 0

Ans:
2p2 – 5p = 0
p(2p-5) = 0
Gives p = 0, 5/2
3q2 – 7q – 6 = 0
3q2 – 9q + 2q – 6 = 0
Gives q = -2/3, 3
Put on number line
-2/3    0   5/2         3

There is no relation.

5.

1. 2p2 + 5p + 2= 0
2.2q2 + 19q + 45 = 0

Ans:
2p2 + 5p + 2= 0
2p2 + 4p + p + 2= 0
Gives p = -1/2, -2
2q2 + 19q + 45 = 0
2q2 + 10q + 9q + 45 = 0
Gives q= -10/2, -9/2
Put on number line
-10/2     -9/2    -2     -1/2

P > q

Directions:6-10) In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option.

6.

i) 3x2-23x+44=0
ii) y2-23y+132=0

Ans:
i) 3x2-23x+44=0

3x2-12x-11x+44=0

(x-4)(3x-11)=0

x= 4 or 11/3

ii) y2-23y+132=0

(y-12)(y-11)=0

y= 12 or 11

Thus x<y

7.

i) x2-6√3x-480=0
ii) y2-11√2y-420=0

Ans:
i) x2-6√3x-480=0

x2-6x-160=0

(x-16)(x+10)=0

x= 16 or -10

ii) y2-11√2y-420=0

y2– 11y- 210=0

(y-21)(y+10)=0

y=21 or -10

Hence The relationship cannot be determined.

8.

i) 7x-5y-74=0
ii) 3x+2y-301=0

Ans:
7x-5y-74=0 ………… (1)

3x+2y-301=0 …………….. (2)

After solving (1) and (2), we have

x= 57 and y= 65

x < y

9.

i) x(4/3)/289=25/x(2/3)
ii) y(4/5)/4913=125/y(11/5)

Ans:
i) x(4/3)/289=25/x(2/3)

x(4/3)*x(2/3)=7225

x2= 7225

x=85 and -85

ii) y(4/5)/4913=125/y(11/5)

y(15/5)=125*4913

y= 85

Thus x ≤ y

10.

i) 2x2+8x-42=0
ii) 6y2-101y+33=0

Ans:
i) 2x2+8x-42=0

x2+4x-21=0

(x-3)(x+7)=0

x=3 or -7

ii) 6y2-101y+33=0

6y2-2y-99y+33=0

(3y-1)(2y-33)=0

y=1/3 or 33/2

Hence the relationship cannot be determined.

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