jee-advanced 2016 Q43

jee-advanced · India · paper1 First order differential equations (integrating factor)

Let $f:(0,\infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f'(x) = 2 - \frac{f(x)}{x}$ for all $x \in (0,\infty)$ and $f(1) \neq 1$. Then
(A) $\lim_{x \rightarrow 0+} f'\left(\frac{1}{x}\right) = 1$
(B) $\lim_{x \rightarrow 0+} xf\left(\frac{1}{x}\right) = 2$
(C) $\lim_{x \rightarrow 0+} x^2 f'(x) = 0$
(D) $|f(x)| \leq 2$ for all $x \in (0,2)$

Let $f:(0,\infty) \rightarrow \mathbb{R}$ be a differentiable function such that $f'(x) = 2 - \frac{f(x)}{x}$ for all $x \in (0,\infty)$ and $f(1) \neq 1$. Then\\
(A) $\lim_{x \rightarrow 0+} f'\left(\frac{1}{x}\right) = 1$\\
(B) $\lim_{x \rightarrow 0+} xf\left(\frac{1}{x}\right) = 2$\\
(C) $\lim_{x \rightarrow 0+} x^2 f'(x) = 0$\\
(D) $|f(x)| \leq 2$ for all $x \in (0,2)$

Paper Questions

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