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Jee Main 2025 — Medium JEE math MCQ

Let \((2, 3)\) be the largest open interval in which the function \(f(x) = 2\log_e(x - 2) - x^2 + ax + 1\) is strictly increasing and \((b, c)\) be the largest open interval, in which the function \(g(x) = (x - 1)^3(x + 2 - a)^2\) is strictly decreasing. Then \(100(a + b - c)\) is equal to
  1. A. 420
  2. B. 360
  3. C. 160
  4. D. 280

Solution

The correct option is **B**. (B. 360)

MATH

medium • PYQ Reworded
Question
Read carefully, then pick the best option.
Let (2,3)(2, 3) be the largest open interval in which the function f(x)=2log⁡e(x−2)−x2+ax+1f(x) = 2\log_e(x - 2) - x^2 + ax + 1 is strictly increasing and (b,c)(b, c) be the largest open interval, in which the function g(x)=(x−1)3(x+2−a)2g(x) = (x - 1)^3(x + 2 - a)^2 is strictly decreasing. Then 100(a+b−c)100(a + b - c) is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep