Correct Answer  Option 2 : x < y
Given:
I. 6x2 + 19x  25 = 0
II. y2  10y + 24 = 0
Calculation:
From I,
6x2 + 19x  25 = 0
⇒ 6x2 + 25x  6x  25 = 0
⇒ x(6x + 25)  1(6x + 25) = 0
⇒ (6x + 25)(x  1) = 0
Taking,
⇒ (6x + 25) = 0 or (x  1) = 0
⇒ x = (25/6) or 1
From II,
y2  10y + 24 = 0
⇒ y2  6y  4y + 24 = 0
⇒ y(y  6)  4(y  6) = 0
⇒ (y  6)(y  4) = 0
Taking,
⇒ (y  6) = 0 or (y  4) = 0
⇒ y = 6 or 4
Comparison between x and y (via Tabulation):
Value of x

Value of y

Relation

25/6

6

x < y

25/6

4

x < y

1

6

x < y

1

4

x < y

∴ x < y.