Multiple choice

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values.(3^{x + 5}. 9^{2x – 4} = 9^{5x – 14})and, (2y^{2} – 15y – 28 = 3y^{2} – 23y – 13)Quantity I: Value of ‘x’ Quantity II: Value of ‘y’

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equation 1: 3^(x+5) × 9^(2x-4) = 9^(5x-14). Converting 9 to 3²: 3^(x+5) × 3^(4x-8) = 3^(10x-28). So 5x-3 = 10x-28, 5x = 25, x = 5. Equation 2: 2y² - 15y - 28 = 3y² - 23y - 13. Rearranging: y² - 8y + 15 = 0, (y-3)(y-5) = 0, so y = 3 or y = 5. Quantity I = 5, Quantity II = 3 or 5. Since x ≥ y (5 ≥ 3 and 5 ≥ 5), option C is correct.

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