Correct Answer  Option 5 : x = y or relation between x and y can not be established.
Calculation:
From I,
6x2 – 5x + 1 = 0
⇒ 6x2 – 2x – 3x + 1 = 0
⇒ 2x(3x – 1) – 1(3x – 1) = 0
⇒ (3x – 1)(2x – 1) = 0
Taking,
⇒ (3x – 1) = 0 or (2x – 1) = 0
⇒ x = (1/3) or (1/2)
From II,
y2 + y – 2 = 0
⇒ y^{2} + 2y – y – 2 = 0
⇒ y(y + 2) – 1(y + 2) = 0
⇒ (y + 2)(y – 1) = 0
Taking,
⇒ (y + 2) = 0 or (y – 1) = 0
⇒ y = 2 or 1
Comparison between x and y (via Tabulation):
Value of x

Value of y

Relation

1/3

2

x > y

1/3

1

x < y

1/2

2

x > y

1/2

1

x < y

∴ x = y or relation between x and y can not be established.