Directions (Q. 1-5): Two equations (I) and (II) are given in each question. On the basis of these equations you have to decide the relation between ‘x’ and ‘y’ and give answer.

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

1) I. 6x2 – 19x + 15 = 0 II. 10y2 – 29y + 21 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

3)

I. 6x2– 9x – 10x + 15 = 0

or, 3x(2x – 3) – 5(2x – 3) = 0

or, (3x – 5) (2x – 3) = 0

x = 5/3,3/2

II. 10y2– 15y – 14y + 21 = 0

or, 5y(2y – 3) – 7(2y – 3) = 0

or, (5y – 7) (2y – 3) = 0

y=  7/3 , 5/2

x ≥y

2) I. 12x2 + 11x – 56 = 0 II. 4y2 – 15y + 14 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

4)

I. 12X2 + 32x – 21x – 56 = 0

or, 4x(3x + 8) – 7(3x + 8) = 0

or, (4x – 7) (3x + 8) = 0

x= 7/8,4/3

II. 4y2 – 8y – 7y + 14 = 0

or, 4y(y – 2) – 7(y – 2) = 0

or, (4y – 7) (y – 2) = 0

y = 2 , 7/4

x ≤ y

3) I. 3x2 + 13x + 12 = 0 II. y2 + 9y + 20 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

1)

I. 3X2 + 9x + 4x + 12 = 0

or, 3x(x + 3) + 4(x + 3) = 0

or, (3x + 4) (x + 3) = 0

x= – 4/ 3 , 3

II. y2 + 5y + 4y + 20 = 0

or, y(y + 5) + 4(y + 5) = 0

or, (y + 4) (y + 5) = 0

y = – 4, – 5

x > y

4) I. 8x2 – 15x + 7 = 0 II. 2y2 – 7y + 6 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

2)

I. 8X2 – 8x – 7x + 7 = 0

or, 8x(x – 1) -7(x – 1) = 0

or, (8x – 7) (x – 1) = 0

x = 7/8 ,1

II. 2y2– 4y – 3y + 6 = 0

or, 2y(y – 2) -3(y – 2) = 0

or, (y – 2) (2y – 3) = 0

y = 2, 3/2

x < y

5) I. 7x – 3y = 13 II. 5x + 4y = 40

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

2)

Eqn (I) × 4 + Eqn (II) × 3

28x – 12y = 52

15x + 12y = 120

43x = 172

x = 4 and y = 5

x < y

Directions (Q. 6-10): Two equations (I) and (II) are given in each question. On the basis of these equations you have to decide the relation between ‘x’ and ‘y’ and give answer.

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

6) I. 2X2 – 11x + 15 = 0 II. 21y2 – 23y + 6 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

1)

I. 2X2 – 6x – 5x + 15 = 0

or,2x(x – 3) – 5(x – 3) = 0

or, (2x – 5) (x – 3) = 0

x 3,5/2

II .21y2 – 14y – 9y + 6 = 0

or,7y(3y – 2) – 3 (3y – 2) = 0

or,(7y – 3)(3y – 2) = 0

y 3/7, 2/3    x>y

7) I. 5X2 – 16x + 11= 0 II. 5y2– 3y – 2 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

3)

I. 5×2 – 5x – 11x + 11 = 0

or,5x(x – 1) – 11(x – 1) = 0

or,(x – 1) (5x – 11) = 0

x = 1,11/5  x > y

II. 5y2 – 5y + 2y – 2 = 0

or, 5y (y – 1) + 2(y – 1) = 0

or, (5y + 2)(y – 1) = 0

y = 1, -2/5

x > y

8) I. X2 + 11x + 28 = 0 II. 2y2 + 13y + 20 = o

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

4)

I. X2 + 4x + 7x + 28 = 0

or, x(x + 4) +7(x + 7) = 0

or, (x + 4) (x + 7) = 0

x = – 4, – 7

II. 2y2 + 8y + 5y + 20 = 0

or, 2y(y + 4) + 5(y + 4) = 0

or, (y + 4) (2y + 5) = 0

y = -4, -5/2

x < y

9) I. 6X2 + 29x + 35 = 0 II. 3y2+ 19y + 30 = 0

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

1)

I. 6X2 + 15x + 14x + 35 = 0

or, 3x(2x + 5) + 7(2x + 5) = 0

or,(3x + 7) (2x + 5) = 0

x = -7/5 , -3/2

3y2 + 9y + 10y + 30 = 0

or, 3y(y + 3) +10(y + 3) = 0

or,(3y + 10) (y + 3) = 0

y = -3, 10/3

x > y

10) I. 2x + 5y = 6 II. 5x + 11y = 9

(1) if x > y

(2) if x < y

(3) if x ≥y

(4) if x ≤ y

(5) if x = y or no relation can be established between ‘x’ and ‘y’.

2)

eqn (I) × 5 – eqn (II) × 2

10x + 25y = 30

10x ± 22y = 18

3y = 12

y = 4 and x = -7

y > x