1
JEE Advanced 2022 Paper 2 Online
Numerical
+3
-1 If $y(x)$ is the solution of the differential equation

$$x d y-\left(y^{2}-4 y\right) d x=0 \text { for } x > 0, y(1)=2,$$

and the slope of the curve $y=y(x)$ is never zero, then the value of $10 y(\sqrt{2})$ is
2
JEE Advanced 2018 Paper 2 Offline
Numerical
+3
-0
Let f : R $$\to$$ R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential equation $${{dy} \over {dx}} = (2 + 5y)(5y - 2)$$, then the value of $$\mathop {\lim }\limits_{n \to - \infty } f(x)$$ is ...........
3
IIT-JEE 2011 Paper 1 Offline
Numerical
+3
-1

Let $$f:[1,\infty ) \to [2,\infty )$$ be a differentiable function such that $$f(1) = 2$$. If $$6\int\limits_1^x {f(t)dt = 3xf(x) - {x^3} - 5}$$ for all $$x \ge 1$$, then the value of f(2) is ___________.

4
IIT-JEE 2011 Paper 2 Offline
Numerical
+4
-0
Let $$y'\left( x \right) + y\left( x \right)g'\left( x \right) = g\left( x \right),g'\left( x \right),y\left( 0 \right) = 0,x \in R,$$ where $$f'(x)$$ denotes $${{df\left( x \right)} \over {dx}}$$ and $$g(x)$$ is a given non-constant differentiable function on $$R$$ with $$g(0)=g(2)=0.$$ Then the value of $$y(2)$$ is
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