Correct Answer  Option 5 : No relation in x and y or x = y
Calculation:
From I,
6x2  19x + 15 = 0
⇒ 6x2  10x  9x + 15 = 0
⇒ 2x(3x  5)  3(3x  5) = 0
⇒ (2x  3)(3x  5) = 0
Taking,
⇒ 2x  3 = 0 or 3x  5 = 0
⇒ x = 3/2 or x = 5/3
From II,
2y2  11y + 5 = 0
⇒ 2y2  10y  y + 5 = 0
⇒ 2y(y  5)  1(y  5) = 0
⇒ (2y  1)(y  5) = 0
Taking,
⇒ 2y  1 = 0 or y  5 = 0
⇒ y = 1/2 or y = 5
Comparison between x and y (via Tabulation):
x

Y

Relation

3/2

1/2

x > y

3/2

5

x < y

5/3

1/2

x > y

5/3

5

x < y

∴ After comparing x and y both, No relation in x and y or x = y.