Particular Solution of a Differential Equation

Q.

The locus of mid point of that chord of parabola which subtends right angle on the vertex will be

1. 

2. 

3. 

4. 

Q. A continuously differentiable function $\varphi \left(x\right)$ in $(0,\pi )$ satisfying $y^{\prime }=1+y^2,y\left(0\right)=0=y\left(\pi \right)$ is

1. $x(x-\pi )$
2. tan x
3. $(x-\pi )(1-e^x)$
4. Not possible

Q.

If the angle between the two lines represented by $2x^2+5xy+3y^2+6x+7y+4=0$ is ${\tan }^{-1}m$, then m =

1. 1

2. 1/5

3. 7/5

4. 7

Q. $\underset{n\to \infty }{lim}\frac{x^n+y^n}{x^n-y^n}$, where $x>y>0$ is equal to

1. -1
2. 0
3. 1
4. none of these

Q. Solution of the differential equation $2ysinx\frac{dy}{dx}=2sinxcosx-y^{2}cosx$ satisfying $y\left(\frac{\pi }{2}\right)=1)$is given by

1. $y^2=sinx$
2. $y=si{n}^{2}x$
3. $y^2=cosx+1$
4. $y^2=sinx=4co{s}^{2}x$