Correct Answer - Option 4 : x ≤ y
Calculations:
From I,
6x2 + (1/2) = (7/2)x
⇒ 12x2 - 7x+ 1 = 0
⇒ 12x2 - 4x - 3x + 1 = 0
⇒ 4x(3x - 1) - 1(3x - 1) = 0
⇒ (4x - 1)(3x - 1) = 0
Taking,
⇒ 3x - 1 = 0 or 4x - 1 = 0
⇒ x = 1/3 or x = 1/4
From II,
12y2 + 2 = 10y
⇒ 12y2 - 10y + 2 = 0
⇒ 12y2 - 6y - 4y + 2 = 0
⇒ 6y(2y - 1) - 2(2y - 1) = 0
Taking,
⇒ 2y - 1 = 0 or 6y - 2 = 0
⇒ y = 1/2 or y = 1/3
Comparison between x and y (via Tabulation):
x
|
Y
|
Relation
|
1/3
|
1/2
|
x < y
|
1/3
|
1/3
|
x = y
|
1/4
|
1/2
|
x < y
|
1/4
|
1/3
|
x < y
|
∴ x ≤ y.