# In the given questions, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer. I. 6x2 - 19x

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In the given questions, two equations numbered l and II are given. You have to solve both the equations and mark the appropriate answer.

I. 6x2 - 19x + 15 = 0

II. 2y2 - 11y + 5 = 0

1. x > y
2. x < y
3. x ≥ y
4. x ≤ y
5. No relation in x and y or x = y

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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.