Multiple choice

Passage

Q56_Q60(212975)Canara_1543821686_hindi.html

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer accordingly. Mark your answer as I. x2 - 15x + 50 = -4 II. y2 - 21y + 96 = -12

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

  5. if x = y, or the relationship cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 - 15x + 54 = 0 -> (x-6)(x-9)=0 -> x=6, 9. II: y^2 - 21y + 108 = 0 -> (y-9)(y-12)=0 -> y=9, 12. Comparing sets: 6 < 9, 6 < 12, 9 = 9, 9 < 12. Thus x <= y.

AI explanation

Rearranging the first equation gives x squared minus 15x plus 54 equals zero, which factors into (x minus 6) and (x minus 9), meaning x equals 6 or 9. Rearranging the second equation gives y squared minus 21y plus 108 equals zero, which factors into (y minus 9) and (y minus 12), meaning y equals 9 or 12. Since x equals 9 is equal to y equals 9 but less than y equals 12, while x equals 6 is also less than y, x is less than or equal to y.

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