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1

### JEE Advanced 2014 Paper 2 Offline

The function $$y=f(x)$$ is the solution of the differential equation
$${{dy} \over {dx}} + {{xy} \over {{x^2} - 1}} = {{{x^4} + 2x} \over {\sqrt {1 - {x^2}} }}\,$$ in $$(-1,1)$$ satisfying $$f(0)=0$$.
Then $$\int\limits_{ - {{\sqrt 3 } \over 2}}^{{{\sqrt 3 } \over 2}} {f\left( x \right)} \,d\left( x \right)$$ is
A
$${\pi \over 3} - {{\sqrt 3 } \over 2}$$
B
$${\pi \over 3} - {{\sqrt 3 } \over 4}$$
C
$${\pi \over 6} - {{\sqrt 3 } \over 4}$$
D
$${\pi \over 6} - {{\sqrt 3 } \over 2}$$
2

### JEE Advanced 2013 Paper 1 Offline

A curve passes through the point $$\left( {1,{\pi \over 6}} \right)$$. Let the slope of
the curve at each point $$(x,y)$$ be $${y \over x} + \sec \left( {{y \over x}} \right),x > 0.$$
Then the equation of the curve is
A
$$sin\left( {{y \over x}} \right) = \log x + {1 \over 2}$$
B
$$cos\,ec\left( {{y \over x}} \right) = \log x + 2$$
C
$$\,s\,ec\left( {{{2y} \over x}} \right) = \log x + 2\,$$
D
$$\,cos\left( {{{2y} \over x}} \right) = \log x + {1 \over 2}$$
3

### IIT-JEE 2008

Let a solution $$y=y(x)$$ of the differential equation $$x\sqrt {{x^2} - 1} \,\,dy - y\sqrt {{y^2} - 1} \,dx = 0$$ satify $$y\left( 2 \right) = {2 \over {\sqrt 3 }}.$$

STATEMENT-1 : $$y\left( x \right) = \sec \left( {{{\sec }^{ - 1}}x - {\pi \over 6}} \right)$$ and
STATEMENT-2 : $$y\left( x \right)$$ given by $${1 \over y} = {{2\sqrt 3 } \over x} - \sqrt {1 - {1 \over {{x^2}}}}$$

A
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is a correct explanation for STATEMENT-1
B
STATEMENT-1 is True, STATEMENT-2 is True;STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C
STATEMENT-1 is True, STATEMENT-2 is False
D
STATEMENT-1 is False , STATEMENT-2 is True
4

### IIT-JEE 2005 Screening

The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with
A
variable radii and a fixed centre at $$(0,1)$$
B
variable radii and a fixed centre at $$(0,-1)$$
C
fixed radius $$1$$ and variable centres along the $$x$$-axis.
D
fixed radius $$1$$ and variable centrs along the $$y$$-axis.

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