1
JEE Advanced 2019 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
Let $$\Gamma$$ denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to I at a point P intersect the y-axis at YP. If PYP has length 1 for each point P on I, then which of the following options is/are correct?
A
$$xy' + \sqrt {1 - {x^2}} = 0$$
B
$$xy' - \sqrt {1 - {x^2}} = 0$$
C
$$y = {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) - \sqrt {1 - {x^2}}$$
D
$$y = - {\log _e}\left( {{{1 + \sqrt {1 - {x^2}} } \over x}} \right) + \sqrt {1 - {x^2}}$$
2
JEE Advanced 2017 Paper 2 Offline
MCQ (More than One Correct Answer)
+4
-2
If $$g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt$$, then
A
$$g'\left( { - {\pi \over 2}} \right) = 0$$
B
$$g'\left( { - {\pi \over 2}} \right) = - 2\pi$$
C
$$g'\left( {{\pi \over 2}} \right) = 2\pi$$
D
$$g'\left( {{\pi \over 2}} \right) = 0$$
3
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
A solution curve of the differential equation

$$\left( {{x^2} + xy + 4x + 2y + 4} \right){{dy} \over {dx}} - {y^2} = 0,$$ $$x>0,$$ passes through the

point $$(1,3)$$. Then the solution curve
A
intersects $$y=x+2$$ exactly at one point
B
intersects $$y=x+2$$ exactly at two points
C
intersects $$y = {\left( {x + 2} \right)^2}$$
D
does NOT intersect $$\,y = {\left( {x + 3} \right)^2}$$
4
JEE Advanced 2016 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2

Let $$f:(0,\infty ) \to R$$ be a differentiable function such that $$f'(x) = 2 - {{f(x)} \over x}$$ for all $$x \in (0,\infty )$$ and $$f(1) \ne 1$$. Then

A
$$\mathop {\lim }\limits_{x \to {0^ + }} f'\left( {{1 \over x}} \right) = 1$$
B
$$\mathop {\lim }\limits_{x \to {0^ + }} xf\left( {{1 \over x}} \right) = 2$$
C
$$\mathop {\lim }\limits_{x \to {0^ + }} {x^2}f'(x) = 0$$
D
$$\left| {f(x)} \right| \le 2$$ for all $$x \in (0,2)$$
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