Multiple choice

Two equations (I) and (II) are given in each question. On the basis of these equations you have to decide the relation between ‘x’ and ‘y’ and give answer. $I. (6x^2 - 19x + 15 = 0)$ $II. (10y^2 - 29y + 21 = 0)$

  1. $\(x > y\)$
  2. $\(x \ge y\)$
  3. $\(x < y\)$
  4. $\(x \le y\)$

  5. x = y or relation can’t be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving equation I: 6x² - 19x + 15 = 0. Factors: (3x-5)(2x-3) = 0, so x = 5/3 or x = 3/2. Solving equation II: 10y² - 29y + 21 = 0. Using quadratic formula: y = (29 ± √(841-840))/20 = (29 ± 1)/20, so y = 30/20 = 3/2 or y = 28/20 = 7/5. Values: x ∈ {5/3, 3/2}, y ∈ {3/2, 7/5}. Common value is 3/2. When x = 5/3, y = 7/5: 5/3 > 7/5. When x = y = 3/2, they are equal. Therefore x ≥ y. Option B is correct.

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