## Algebra For SBI PO : Set – 19

D.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

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

1. I. 2x2+x – 1 = 0

II. 6y2 – 13y + 5 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(d) I. 2x2 + 2x – x – 1 = 0

or, 2x(x + 1) – 1(x + 1) = 0

or, (x + 1) (2x – 1) = 0

x=-1,1/2

II. 6y2 – 3y – 10y + 5 = 0

or, 3y(2y – 1) – 5(2y – 1) = 0

or, (3y – 5)(2y – 1) = 0

y=-3,11/3

2. I. 21x2 – 122x + 165 = 0

II. 3y2 – 2y – 33 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(e) I. 21x2 – 45x – 77x + 165 = 0

or, 3x(7x – 15) – 11 (7x – 15) = 0

or, (3x – 11) (7x – 15) = 0

x=11/3,15/7

II. 3y2 + 9y – 11y – 33 = 0

or, (y + 3) – 11(y + 3) = 0

or, (3y – 11) (y + 3) = 0

y=-3,11/3

Hence, no relation can be established between x and y.

3. I. 5x2 – 29x + 36 = 0

II. 10y2 – 3y – 27 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(c) I. 5x2 – 20x – 9x + 36 = 0

or, 5x(x – 4) – 9(x – 4) = 0

or, (x – 4) (5x – 9) = 0

x=4,9/5

II. 10y2 + 15y – 18y – 27 = 0

or, 5y(2y + 3) – 9(2y + 3) = 0

or, (2y + 3) (5y – 9) = 0

y=9/5,-3/2

4. I. 7x + 4y = 3

II. 5x + 3y = 3

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(b) eqn (I) × 3 – eqn (II) × 4

21x + 12y = 9

20x + 12y = 12

Solving 2 equations we get

x = – 3

and y = 6

x < y

5. I. 7x2 – 54x + 99 = 0

II. 4y2– 16y + 15 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(a) I. 7x2 – 21x – 33x + 99 = 0

or, 7x(x – 3) – 33(x – 3) = 0

or, (x – 3) (7x – 33) = 0

x=3,33/7

II. 4y2 – 6y – 10y + 15 = 0

or, 2y(2y – 3) – 5(2y – 3) = 0

or, (2y – 3)(2y – 5) = 0

y=3/2,5/2

D.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

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

6. I. 5x2 – 87x + 378 = 0

II. 3y2 – 49y + 200 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(a) I. 5x2 – 45x – 42x + 378 = 0

or, 5x(x – 9) – 42(x – 9) = 0

or, (5x – 42) (x – 9) = 0

x=9,42/5

II. 3y2 – 24y – 25y + 200 = 0

or, 3y(y – 8) – 25(y – 8) = 0

or, (y – 8) (3y – 25) = 0

y=8,25/3

7. I. 10x2 – x – 24 = 0

II. y2 – 2y = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(e) I. 10x2 – 16x + 15x – 24 = 0

or, 2x(5x – 8) + 3(5x – 8) = 0

or, (2x + 3) (5x – 8) = 0

x=-3/2,8/5

II. y2 – 2y = 0

or, y(y – 2) = 0

y = 0, 2

i.e. no relationship exists between x and y.

8. I. x2 – 5x + 6 = 0

II. 2y2 – 15y + 27 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(d) I. x2 – 2x – 3x + 6 = 0

or, x(x – 2) – 3(x – 2) = 0

or, (x – 2) (x – 3) = 0

x = 2, 3

II. 2y2 – 6y – 9y + 27 = 0

or, 2y(y – 3) – 9(y – 3) = 0

or, (y – 3) (2y – 9) = 0

y=3,9/2

9. I. 3x + 2y = 301

II. 7x – 5y = 74

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(b) I. eqn (I) × 5 + eqn (II) × 2

15x + 10y = 1505

14x – 10y = 148

29x = 1653

x=1653/29=57

and y = 65 x < y

10. I. 14x2 – 37x + 24 = 0

II. 28y2 – 53y + 24 = 0

(a) if x > y

(b) if x < y

(c)if x ≥ y

(d) if x ≤ y

(e) if x = y, or no relation can be established between x and y.

(c) I. 14x2 – 37x + 24 = 0

or, 14x2 – 21x – 16x + 24 = 0

or, 7x(2x – 3) – 8(2x – 3) = 0

or, (2x – 3) (7x – 8) = 0

x=3/2,8/7

II. 28y2 – 53y + 24 = 0

or, 28y2 – 21y – 32y + 24 = 0

or, 7y(4y – 3) – 8(4y – 3) = 0

or, (7y – 8) (4y – 3) = 0

y=8/7,3/4