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Jee Main 2025Medium JEE math MCQ

Let $f : \mathbb{R} \to \mathbb{R}$ be a twice differentiable function such that $f(2) = 1$. If $F(x) = xf(x)$ for all $x \in \mathbb{R}$, $\int_{x}^{2} x F'(x)\,dx = 6$ and $\int_{x}^{2} x^2 F''(x)\,dx = 40$, then $F'(2) + \int_{x}^{2} F(x)\,dx$ is equal to
  1. A. 11
  2. B. 13
  3. C. 15
  4. D. 9

Solution

The correct option is **A**. (A. 11)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let f:RRf : \mathbb{R} \to \mathbb{R} be a twice differentiable function such that f(2)=1f(2) = 1. If F(x)=xf(x)F(x) = xf(x) for all xRx \in \mathbb{R}, x2xF(x)dx=6\int_{x}^{2} x F'(x)\,dx = 6 and x2x2F(x)dx=40\int_{x}^{2} x^2 F''(x)\,dx = 40, then F(2)+x2F(x)dxF'(2) + \int_{x}^{2} F(x)\,dx is equal to
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep